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1.	Mashkoori, Mahdi, et al. (författare) Impact of topology on the impurity effects in extended s-wave superconductors with spin-orbit coupling 2019 Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 99:1 Tidskriftsartikel (refereegranskat)abstract We investigate the impact of topology on the existence of impurity subgap states in a time-reversal-invariant superconductor with an extended s-wave pairing and strong spin-orbit coupling. By simply tuning the chemical potential, we access three distinct phases: topologically trivial s-wave, topologically nontrivial s(+/-)-wave, and nodal superconducting phase. For a single potential impurity, we find subgap impurity bound states in the topological phase, but notably no subgap states in the trivial phase. This is in sharp contrast with the expectation that there would be no subgap state in the presence of potential impurities in s-wave superconductors. These subgap impurity states have always finite energies for any strength of the potential scattering and, subsequently, the superconducting gap in the topological s(+/-)-wave phase survives but is attenuated in the presence of finite disorder. By creating islands of potential impurities, we smoothly connect the single impurity results to topological edge states of impurity islands. On the other hand, magnetic impurities lead to the formation of Yu-Shiba-Rusinov states in both the trivial and topological phases, which even reach zero energy at certain scattering strengths. We thus propose that potential impurities can be a very valuable tool to detect time-reversal-invariant topological superconductivity.
2.	Wojek, Bastian M., et al. (författare) Band inversion and the topological phase transition in (Pb,Sn)Se 2014 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 90:16, s. 161202- Tidskriftsartikel (refereegranskat)abstract The recent discovery of a topological phase transition in IV-VI narrow-gap semiconductors has revitalized the decades-old interest in the bulk band inversion occurring in these materials. Here we systematically study the (001) surface states of Pb1-xSnxSe mixed crystals by means of angle-resolved photoelectron spectroscopy in the parameter space 0 <= x <= 0.37 and 300 K >= T >= 9 K. Using the surface-state observations, we monitor directly the topological phase transition in this solid solution and gain valuable information on the evolution of the underlying fundamental band gap of the system. In contrast to common model expectations, the band-gap evolution appears to be nonlinear as a function of the studied parameters, resulting in the measuring of a discontinuous band-inversion process. This finding signifies that the anticipated gapless bulk state is in fact not a stable configuration and that the topological phase transition therefore exhibits features akin to a first-order transition.
3.	Arouca, Rodrigo, et al. (författare) Topological superconductivity enhanced by exceptional points 2023 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 108:6 Tidskriftsartikel (refereegranskat)abstract Majorana zero modes (MZMs) emerge as edge states in topological superconductors and are promising for topological quantum computation, but their detection has so far been elusive. Here we show that non-Hermiticity can be used to obtain dramatically more robust MZMs. The enhanced properties appear as a result of an extreme instability of exceptional points to superconductivity, such that even a vanishingly small superconducting order parameter already opens a large energy gap, produces well-localized MZMs, and leads to strong superconducting pair correlations. Our work thus illustrates the large potential of enhancing electronic ordering, here in the form of topological superconductivity, using non-Hermitian exceptional points.
4.	Awoga, Oladunjoye A., et al. (författare) Domain walls in a chiral d-wave superconductor on the honeycomb lattice 2017 Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 96:1 Tidskriftsartikel (refereegranskat)abstract We perform a fully self-consistent study of domain walls between different chiral domains in chiral d(x2-y2) +/- id(xy) -wave superconductors with an underlying honeycomb lattice structure. We investigate domain walls along all possible armchair and zigzag directions and with a finite global phase shift across the domain wall, in addition to the change of chirality. For armchair domain walls we find the lowest domain wall energy at zero global phase shift, while the most favorable zigzag domain wall has a finite global phase shift dependent on the doping level. Belowthe van Hove singularity the armchair domain wall is most favorable, while at even higher doping the zigzag domain wall has the lowest energy. The domain wall causes a local suppression of the superconducting order parameter, with the superconducting recovery length following a universal curve for all domain walls. Moreover, we always find four subgap states crossing zero energy and well localized to the domain wall. However, the details of their energy spectrum vary notably, especially with the global phase shift across the domain wall.
5.	Awoga, Oladunjoye A., et al. (författare) Mitigating disorder-induced zero-energy states in weakly coupled superconductor-semiconductor hybrid systems 2023 Ingår i: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 107:18 Tidskriftsartikel (refereegranskat)abstract Disorder has appeared as one of the main mechanisms to induce topologically trivial zero-energy states in superconductor-semiconductor systems, thereby challenging the detection of topological superconductivity and Majorana bound states. Here, we demonstrate that, for disorder in any part of the system, the formation of disorder-induced trivial zero-energy states can, to a large extent, be mitigated by keeping the coupling between the semiconductor and superconductor weak. The only exception is strong disorder in the semiconductor, where instead the strong-coupling regime is somewhat more robust against disorder. Furthermore, we find that the topo-logical phase in this weak-coupling regime is robust against disorder, with a large and well-defined topological gap which is highly beneficial for topological protection. Our work shows the advantages and disadvantages of weak and strong couplings under disorder, important for designing superconductor-semiconductor hybrid structures.
6.	Awoga, Oladunjoye A., et al. (författare) Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures 2022 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 105:14 Tidskriftsartikel (refereegranskat)abstract We investigate the role of the coupling between a spin-orbit coupled semiconductor nanowire and a conventional s-wave superconductor on the emergence of the topological superconducting phase with Majorana bound states in an applied magnetic field. We show that when the coupling is strong, the topological phase transition point is very sensitive to the size of the superconductor and in order to reach the topological phase a strong magnetic field is required, which can easily be detrimental to superconductivity. Moreover, the induced energy gap separating the Majorana bound states and other quasiparticles in the topological phase is substantially suppressed compared to the gap at zero field. In contrast, in the weak-coupling regime, we find that the situation is essentially the opposite, with the topological phase emerging at much lower magnetic fields and a sizable induced energy gap in the topological phase, which can also be controlled by the chemical potential of the superconductor. Furthermore, we show that the weak-coupling regime does not generally allow for the formation of topologically trivial zero-energy states at the wire end points, in stark contrast to the strong-coupling regime, where such states are found for a wide range of parameters. Our results thus put forward the weak-coupling regime as a promising route to mitigate the most unwanted problems present in nanowires for realizing topological superconductivity and Majorana bound states.
7.	Awoga, Oladunjoye A., et al. (författare) Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene 2023 Ingår i: Physical Review B. - 2469-9950. ; 108:14 Tidskriftsartikel (refereegranskat)abstract ABC-stacked multilayer graphene (ABC-MLG) exhibits topological surface flat bands with a divergent density of states, leading to many-body instabilities at charge neutrality. Here, we explore electronic ordering within a mean-field approach with full generic treatment of all spin-isotropic, two-site charge density and spin interactions up to next-nearest-neighbor (NNN) sites. We find that surface superconductivity and magnetism are significantly enhanced over bulk values. We find spin-singlet s wave and unconventional NNN bond spin-triplet f wave to be the dominant superconducting pairing symmetries, both with a full energy gap. By establishing the existence of ferromagnetic intrasublattice interaction (J2<0) we conclude that the f-wave state is favored in ABC-MLG, in sharp contrast to bulk ABC-graphite where chiral d- or p-wave states, together with s-wave states, display stronger ordering tendencies albeit not achievable at charge neutrality. We trace this distinctive surface behavior to the strong sublattice polarization of the surface flat bands. We also find competing ferrimagnetic order, fully consistent with density functional theory (DFT) calculations. The magnetic order interpolates between sublattice ferromagnetism and antiferromagnetism, but only with the ratio of the sublattice magnetic moments (R) being insensitive to the DFT exchange correlation functional. We finally establish the full phase diagram by constraining the interactions to the R value identified by DFT. We find f-wave superconductivity being favored for all weak to moderately strong couplings J2 and as long as J2 is a sufficiently large part of the full interaction mix. Gating ABC-MLG away from charge neutrality further enhances the f-wave state over the ferrimagnetic state, establishing ABC-MLG as a strong candidate for f-wave superconductivity.
8.	Awoga, Oladunjoye, et al. (författare) Disorder robustness and protection of Majorana bound states in ferromagnetic chains on conventional superconductors 2017 Ingår i: Physical Review B. - 2469-9950 .- 2469-9969. ; 95:18 Tidskriftsartikel (refereegranskat)abstract Majorana bound states (MBSs) are well established in the clean limit in chains of ferromagnetically aligned impurities deposited on conventional superconductors with finite spin-orbit coupling. Here we show that these MBSs are very robust against disorder. By performing self-consistent calculations we find that the MBSs are protected as long as the surrounding superconductor show no large signs of inhomogeneity. We also find that longer chains offer more stability against disorder for the MBSs, albeit the minigap decreases, as do increasing strengths of spin-orbit coupling and superconductivity.
9.	Awoga, Oladunjoye, et al. (författare) Probing unconventional superconductivity in proximitized graphene by impurity scattering 2018 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 97:21 Tidskriftsartikel (refereegranskat)abstract We demonstrate how potential impurities are a very powerful tool for determining the pairing symmetry in graphene, proximity coupled to a spin-singlet superconductor. All d-wave states are characterized by subgap resonances, with spatial patterns clearly distinguishing between nodal and chiral d-wave symmetry, while s-wave states have no subgap resonances. We also find strong supergap impurity resonances associated with the normal state Dirac point. Subgap and supergap resonances only interact at very low doping levels, then causing suppression of the supergap resonances.
10.	Awoga, Oladunjoye, et al. (författare) Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions 2019 Ingår i: Physical Review Letters. - : AMER PHYSICAL SOC. - 0031-9007 .- 1079-7114. ; 123:11 Tidskriftsartikel (refereegranskat)abstract We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with a strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a re shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.
11.	Aydin, Alhun, et al. (författare) Thermodefect voltage in graphene nanoribbon junctions 2022 Ingår i: Journal of Physics. - : Institute of Physics Publishing (IOPP). - 0953-8984 .- 1361-648X. ; 34:19 Tidskriftsartikel (refereegranskat)abstract Thermoelectric junctions are often made of components of different materials characterized by distinct transport properties. Single material junctions, with the same type of charge carriers, have also been considered to investigate various classical and quantum effects on the thermoelectric properties of nanostructured materials. We here introduce the concept of defect-induced thermoelectric voltage, namely, thermodefect voltage, in graphene nanoribbon (GNR) junctions under a temperature gradient. Our thermodefect junction is formed by two GNRs with identical properties except the existence of defects in one of the nanoribbons. At room temperature the thermodefect voltage is highly sensitive to the types of defects, their locations, as well as the width and edge configurations of the GNRs. We computationally demonstrate that the thermodefect voltage can be as high as 1.7 mV K-1 for 555-777 defects in semiconducting armchair GNRs. We further investigate the Seebeck coefficient, electrical conductance, and electronic thermal conductance, and also the power factor of the individual junction components to explain the thermodefect effect. Taken together, our study presents a new pathway to enhance the thermoelectric properties of nanomaterials.
12.	Balatsky, Alexander V., et al. (författare) Dynamic Quantum Matter 2020 Ingår i: Annalen der Physik. - : John Wiley & Sons. - 0003-3804 .- 1521-3889. ; 532:2 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
13.	Baldo, Lucas, et al. (författare) Defect-induced band restructuring and length scales in twisted bilayer graphene 2023 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 108:12 Tidskriftsartikel (refereegranskat)abstract We investigate the effects of single, multiple, and extended defects in the form of nonmagnetic impurities and vacancies in twisted bilayer graphene (TBG) at and away from the magic angle, using a fully atomistic model and focusing on the behavior of the flat low-energy moire bands. For strong impurities and vacancies in the AA region, we find a complete removal of one of the four moire bands, resulting in a significant depletion of the charge density in the AA regions even at extremely low defect concentrations. We find similar results for other defect locations, with the exception of the least coordinated sites in the AB region, where defects instead result in a peculiar band replacement process within the moire bands. In the vacancy limit, this process yields a band structure misleadingly similar to the pristine case. Moreover, we show that triple-point fermions, which are the crossing of the Dirac point by a flat band, appearing for single, periodic defects, are generally not preserved when adding extended or multiple defects, and thus likely not experimentally relevant. We further identify two universal length scales for defects, consisting of charge modulations on the atomic scale and on the moire scale, illustrating the importance of both the atomic and moire structures for understanding TBG. We show that our conclusions hold beyond the magic angle and for fully isolated defects. In summary, our results demonstrate that the normal state of TBG and its moire flat bands are extremely sensitive to both the location and strength of nonmagnetic impurities and vacancies, which should have significant implications for any emergent ordered state.
14.	Baldo, Lucas, et al. (författare) Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions 2023 Ingår i: Superconductors Science and Technology. - : Institute of Physics (IOP). - 0953-2048 .- 1361-6668. ; 36:3 Tidskriftsartikel (refereegranskat)abstract We propose a method to distinguish between trivial and topological, Majorana, zero-energy states (ZESs) in both short and long superconductor-normal-superconductor junctions based on Rashba nanowires using phase-biased equilibrium transport measurements. In particular, we show how the sawtooth profile of the supercurrent, due to the Majorana oscillation suppression in the topological phase for sufficiently long superconductor regions, leads to a strong signal in its zero-frequency susceptibility for a phase difference of ? = pi. This signal is notably insensitive to the chemical potential in the normal region, while trivial ZESs only causes signals in the susceptibility that is highly varying with the chemical potential, thus turning gating of the normal region into a simple experimental control knob. Furthermore, we obtain that, by tuning the junction transparency, critical currents in both short and long junctions undergo a reduction in the number of oscillations as a function of magnetic field only in the topological phase, an effect that find to be intimately linked to Majorana non-locality. Finally, we show that our results also hold at finite temperatures, thus highlighting their potential measurability under realistic experimental conditions.
15.	Banerjee, Saikat, et al. (författare) Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material 2016 Ingår i: PHYSICAL REVIEW B. - : American Physical Society. - 2469-9950. ; 93:13 Tidskriftsartikel (refereegranskat)abstract We examine the low-energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in a honeycomb lattice structure. Using the example of graphene, we present evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K' points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an intergrain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with fermionic Dirac materials. The Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of bosonic Dirac materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.
16.	Björnson, Kristofer, et al. (författare) Majorana fermions at odd junctions in a wire network of ferromagnetic impurities 2016 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 94:10 Tidskriftsartikel (refereegranskat)abstract We consider a wire network of ferromagnetic impurities on the surface of an s-wave superconductor with a strong Rashba spin-orbit interaction. Within the topological phase, zero-energy Majorana fermions appear at the wire end points as well as at junctions between an odd number of wire segments, while no clearly isolated subgap states are present at junctions between an even number of wire segments, providing strong, experimentally accessible signatures for Majorana fermions. We also investigate the quasiparticle energy gap with respect to varying the Rashba spin-orbit coupling and magnetic impurity strength.
17.	Björnson, Kristofer, et al. (författare) Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements 2018 Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:14 Tidskriftsartikel (refereegranskat)abstract We show that spin-polarized local density of states (LDOS) measurements can uniquely determine the chiral nature of topologically protected edge states surrounding a ferromagnetic island embedded in a conventional superconductor with spin-orbit coupling. The spin-polarized LDOS show a strong spin polarization directly tied to the normal direction of the edge with opposite polarizations on opposite sides of the island and with a distinct oscillatory pattern in energy.
18.	Björnson, Kristofer, et al. (författare) Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures 2015 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 91:21 Tidskriftsartikel (refereegranskat)abstract We investigate the local density of states, spectral function, and superconducting pair amplitudes for signatures of Majorana fermions in vortex cores in ferromagnetic and spin-orbit coupled semiconductor/superconductor heterostructures. We show that the Majorana fermion quasiparticle momentum distribution is always symmetrically distributed at a finite radius around a high-symmetry point, thereby providing a necessary condition for a low-energy state to be a Majorana fermion. In real-space profiles of the local density of states through the vortex core the Majorana fermion, together with other finite-energy vortex states, forms a characteristic X-shape structure only present at nontrivial topology. Moreover, we find that the Mexican hat band structure property of the topologically nontrivial phase translates into multiple high-intensity band edges and also vortex core states located above the superconducting gap in the local density of states. Finally, we find no strong correlation between odd-frequency pairing and the appearance of Majorana fermions, but odd-frequency pairing exists as soon as ferromagnetism is present. In fact, we find that the only vortex superconducting pair amplitude directly related to any phase transition is the appearance of certain spin-triplet p-wave pairing components in the vortex core at a pre-topological vortex core widening transition.
19.	Björnson, Kristofer, et al. (författare) Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures 2014 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 89:13, s. 134518- Tidskriftsartikel (refereegranskat)abstract We provide a derivation of a spin Skyrmion number classification for two-dimensional topological superconductors constructed from ferromagnetic and Rashba spin-orbit coupled semiconductor-superconductor heterostructures. We show that in the nontrivial topological phase, characterized by a nonzero Chern number, there is always a topological spin texture in the occupied bands represented by a Skyrmion number. The Skyrmion number has the advantage of being both physically intuitive and directly measurable using spin-sensitive band structure imaging techniques. In addition, we show that the Skyrmion classification can be extended to the equivalent one-dimensional topological superconductors.
20.	Björnson, Kristofer, et al. (författare) Solid-state Stern-Gerlach spin splitter for magnetic field sensing, spintronics, and quantum computing 2018 Ingår i: Beilstein Journal of Nanotechnology. - : Beilstein Institut. - 2190-4286. ; 9, s. 1558-1563 Tidskriftsartikel (refereegranskat)abstract We show conceptually that the edge of a two-dimensional topological insulator can be used to construct a solid-state Stern-Gerlach spin splitter. By threading such a Stern-Gerlach apparatus with a magnetic flux, Aharanov-Bohm-like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit SU(2)-gate, one of the two gates required for a universal quantum computer. The field sensitivity, or switching field, b, is related to the characteristic size of the device, r, through b = h/(2 pi qr(2)), with q being the unit of electric charge.
21.	Björnson, Kristofer, et al. (författare) Solid state Stern-Gerlach spin-splitter for magnetic field sensoring, spintronics, and quantum computing Annan publikation (övrigt vetenskapligt/konstnärligt)abstract We show that the edge of a two-dimensional topological insulator can be used to construct a solid state Stern-Gerlach spin-splitter. By threading such a Stern-Gerlach apparatus with a magnetic flux, Ahranov-Bohm like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit SU(2)-gate, one of the two gates required for a universal quantum computer. The field sensitivity, or switching field, b is related to the device characteristic size r through b=ℏ/qr2, with q the unit of electric charge.
22.	Björnson, Kristofer, et al. (författare) Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors 2015 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : American Physical Society. - 1098-0121 .- 1550-235X. ; 92:21 Tidskriftsartikel (refereegranskat)abstract We investigate the persistent currents, spin-polarized local density of states, and spectral functions of topological superconductors constructed by placing ferromagnetic impurities on top of an s-wave superconductor with Rashba spin-orbit interaction. We solve self-consistently for the superconducting order parameter and investigate both two-dimensional blocks and one-dimensional wires of ferromagnetic impurities, with the magnetic moments pointing both perpendicular and parallel to the surface. We find that the topologically protected edge states of ferromagnetic blocks give rise to spin-polarized edge currents, but that the total persistent current flows in opposite direction to what is expected from the dispersion relation of the edge states. We also show that the Majorana fermions at the end points of one-dimensional wires are spin polarized, which can be directly related to the spin polarization of the edge currents of two-dimensional blocks. Connections are also made to the physics of the Yu-Shiba-Rusinov states for zero-dimensional impurities.
23.	Björnson, Kristofer, et al. (författare) Superconducting order parameter π-phase shift in magnetic impurity wires 2017 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 95:10 Tidskriftsartikel (refereegranskat)abstract It has previously been found that a magnetic impurity in a conventional s-wave superconductor can give rise to a local π-phase shift of the superconducting order parameter. By studying a finite wire of ferromagnetic impurities, we are able to trace the origin of the π-phase shift to a resonance condition for the Bogoliubov-de Gennes quasiparticle states. When non-resonating states localized at the impurity sites are pulled into the condensate for increasing magnetic strength, the superconducting order parameter is reduced in discrete steps, eventually resulting in a π-phase shift. We also show that for a finite spin-orbit coupling, the π-phase shift is preserved and occurs in a large portion of the topologically non-trivial phase.
24.	Björnson, Kristofer (författare) Topological band theory and Majorana fermions : With focus on self-consistent lattice models 2016 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract One of the most central concepts in condensed matter physics is the electronic band structure. Although band theory was established more than 80 years ago, recent developments have led to new insights that are formulated in the framework of topological band theory. In this thesis a subset of topological band theory is presented, with particular focus on topological supercon- ductors and accompanying Majorana fermions. While simple models are used to introduce basic concepts, a physically more realistic model is also studied intensely in the papers. Through self- consistent tight-binding calculations it is confirmed that Majorana fermions appear in vortex cores and at wire end points when the superconductor is in the topologically non-trivial phase. Many other properties such as the topological invariant, experimental signatures in the local density of states and spectral function, unconventional and odd-frequency pairing, the precense of spin-polarized currents and spin-polarization of the Majorana fermions, and a local π-phase shift in the order parameter at magnetic impurities are also investigated.
25.	Björnson, Kristofer, et al. (författare) Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures 2013 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:2, s. 024501- Tidskriftsartikel (refereegranskat)abstract We study the energy spectrum of a vortex core in a two-dimensional semiconductor with Rashba spin-orbit interaction and proximity coupled to a conventional superconductor and a ferromagnetic insulator. We perform self-consistent calculations using the microscopic tight-binding Bogoliubov-de Gennes method on a lattice and confirm the existence of Majorana fermions in the nontrivial topological phase. We also find two different topologically trivial bulk superconducting phases, only differing in the type of vortex core structure they support and separated by a zero-energy excitation. Furthermore, we find an asymmetry in the energy spectrum with respect to both Zeeman splitting and vortex rotation direction and explain its physical origin.
26.	Black-Schaffer, Annica M. (författare) Chiral d-wave superconducting state in the core of a doubly quantized s-wave vortex in graphene 2013 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:10, s. 104506- Tidskriftsartikel (refereegranskat)abstract We show that the intrinsic chiral (d(x2-y2) +/- id(xy))-wave superconducting pairing in doped graphene is significantly strengthened in the core region of a doubly quantized s-wave superconducting vortex produced in a graphene-superconductor hybrid structure. The chiral d-wave state is induced by the proximity effect, which transfers the center-of-mass angular momentum of the s-wave vortex to the orbital angular momentum of the chiral d-wave Cooper pairs. The proximity effect is enhanced by the circular geometry of the vortex and we find a [1 + (T -T-c,T-J)(2)](-1) temperature dependence for the chiral d-wave core amplitude, where T-c,T-J is its intrinsic bulk transition temperature. We further propose to detect the chiral d-wave state by studying the temperature dependence of the low-energy local density of states in the vortex core, which displays a sudden radial change as a function of the strength of the d-wave core state.
27.	Black-Schaffer, Annica M., et al. (författare) Chiral d-wave superconductivity in doped graphene 2014 Ingår i: Journal of Physics. - : IOP Publishing. - 0953-8984 .- 1361-648X. ; 26:42, s. 423201- Forskningsöversikt (refereegranskat)abstract A highly unconventional superconducting state with a spin-singlet d(x2-y2) +/- id(xy)-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss the multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review the means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.
28.	Black-Schaffer, Annica M., et al. (författare) Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state 2014 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 90:5, s. 054521- Tidskriftsartikel (refereegranskat)abstract We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral d + id'-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the t-J model and quantum Monte Carlo calculations of the Hubbard-U model we show that the d + id'-wave state is the favored superconducting state for a wide range of on-site repulsion U, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality d-wave state, where the overall chirality cancels. We find that a state with d + id'-wave symmetry in one valley but d - id'-wave symmetry in the other valley is not possible in the t-J model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekule distortion, we find no energetically favorable d-wave solution with an overall zero chirality within the restriction of the t-J model.
29.	Black-Schaffer, Annica M. (författare) Edge Properties and Majorana Fermions in the Proposed Chiral d-Wave Superconducting State of Doped Graphene 2012 Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 109:19, s. 197001- Tidskriftsartikel (refereegranskat)abstract We investigate the effect of edges on the intrinsic d-wave superconducting state in graphene doped close to the van Hove singularity. While the bulk is in a chiral d(x2-y2) + id(xy) state, the order parameter at any edge is enhanced and has d(x2-y2)-symmetry, with a decay length strongly increasing with weakening superconductivity. No graphene edge is pair breaking for the d(x2-y2) state, and there are no localized zero-energy edge states. We find two chiral edge modes which carry a spontaneous, but not quantized, quasiparticle current related to the zero-energy momentum. Moreover, for realistic values of the Rashba spin-orbit coupling, a Majorana fermion appears at the edge when tuning a Zeeman field.
30.	Black-Schaffer, Annica M., et al. (författare) Filling of magnetic-impurity-induced gap in topological insulators by potential scattering 2015 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 91:20 Tidskriftsartikel (refereegranskat)abstract We show that the energy gap induced by ferromagnetically aligned magnetic impurities on the surface of a topological insulator can be filled, due to scattering off the nonmagnetic potential of the impurities. In both a continuum surface model and a three-dimensional tight-binding lattice model, we find that the energy gap disappears already at weak potential scattering as impurity resonances add spectral weight at the Dirac point. This can help explain seemingly contradictory experimental results as to the existence of a gap.
31.	Black-Schaffer, Annica M., et al. (författare) Majorana fermions in spin-orbit-coupled ferromagnetic Josephson junctions 2011 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 84:18, s. 180509(R)- Tidskriftsartikel (refereegranskat)abstract We study all possible Majorana modes in two-dimensional spin-orbit-coupled ferromagnetic superconductor-normal state-superconductor (SNS) Josephson junctions and propose experiments to detect them. With the S region in a nontrivial topological phase and a superconducting phase difference phi = pi across the junction, two delocalized Majorana fermions with no excitation gap appear in the N region. In addition, if S and N belong to different topological phases and have well separated the Fermi surfaces, localized Majorana fermions with a finite excitation gap also emerge at both SN interfaces for all phi.
32.	Black-Schaffer, Annica M., et al. (författare) Model Evidence of a Superconducting State with a Full Energy Gap in Small Cuprate Islands 2013 Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 110:19, s. 197001- Tidskriftsartikel (refereegranskat)abstract We investigate subdominant order parameters stabilizing at low temperatures in nanoscale high-Tc cuprate islands, motivated by the recent observation of a fully gapped state in nanosized YBa2Cu3O7-δ[D. Gustafsson et al., Nature Nanotech. 8, 25 (2013)]. Using complementary quasiclassical and tight-binding Bogoliubov–de Gennes methods, we show on distinctly different properties dependent on the symmetry being dx2-y2 þ is or dx2-y2 þ idxy. We find that a surface-induced dx2-y2 þ is phase creates a global spectroscopic gap which increases with an applied magnetic field, consistent with experimental observation.
33.	Black-Schaffer, Annica M., et al. (författare) Odd-frequency superconducting pairing in multiband superconductors 2013 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:10, s. 104514- Tidskriftsartikel (refereegranskat)abstract We point out that essentially all multiband superconductors have an odd-frequency pairing component, as follows from a general symmetry analysis of even- and odd-frequency pairing states. We show that odd-frequency superconducting pairing requires only a finite band hybridization, or scattering, and nonidentical intraband order parameters, of which only one band needs to be superconducting. Under these conditions odd-frequency odd-interband pairing is always present. From a symmetry analysis we establish a complete reciprocity between parity in band index and frequency.
34.	Black-Schaffer, Annica M., et al. (författare) Odd-frequency superconducting pairing in topological insulators 2012 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 86:14, s. 144506- Tidskriftsartikel (refereegranskat)abstract We discuss the appearance of odd-frequency spin-triplet s-wave superconductivity, first proposed by Berezinskii [J. Exp. Theor. Phys. 20, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin- singlet s-wave superconductor. Using both analytical and numerical methods, we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap, including superconductor-normal state junctions. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.
35.	Black-Schaffer, Annica M., et al. (författare) Proximity-induced unconventional superconductivity in topological insulators 2013 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 87:22, s. 220506- Tidskriftsartikel (refereegranskat)abstract We study and classify the proximity-induced superconducting pairing in a topological insulator (TI)-superconductor (SC) hybrid structure for SCs with different symmetries. The Dirac surface state gives a coupling between spin-singlet and spin-triplet pairing amplitudes as well as pairing that is odd in frequency for p-wave SCs. We also find that all SCs induce pairing that is odd in both frequency and orbital (band) index, with oddness in frequency and orbital index being completely interchangeable. The different induced pairing amplitudes significantly modify the density of states in the TI surface layer.
36.	Black-Schaffer, Annica M., et al. (författare) Spontaneous gap generation on the surface of weakly interacting topological insulators using nonmagnetic impurities 2014 Ingår i: Physical Review B Condensed Matter. - 0163-1829 .- 1095-3795. ; 90:16, s. 161413- Tidskriftsartikel (refereegranskat)abstract Strong nonmagnetic impurities on the surface of three-dimensional topological insulators (TIs) generate localized resonance peaks close to the Dirac point. We show that this results in a strongly reduced critical Coulomb interaction strength to reach a magnetic surface state, following a Stoner-like criterion. Thus even weakly interacting TIs host a finite (local) magnetization around strong nonmagnetic impurities. The local magnetization gives rise to a global energy gap, linearly dependent on the maximum value of the magnetization but decreasing with reduced impurity concentration.
37.	Black-Schaffer, Annica M., et al. (författare) Strong potential impurities on the surface of a topological insulator 2012 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 85:12, s. 121103- Tidskriftsartikel (refereegranskat)abstract Topological insulators (TIs) are said to be stable against nonmagnetic impurity scattering due to suppressed backscattering in the Dirac surface states. We solve a lattice model of a three-dimensional TI in the presence of strong potential impurities and find that both the Dirac point and low-energy states are significantly modified: Low-energy impurity resonances are formed that produce a peak in the density of states near the Dirac point, which is destroyed and split into two nodes that move off center. The impurity-induced states penetrate up to ten layers into the bulk of the TI. These findings demonstrate the importance of bulk states for the stability of TIs and how they can destroy the topological protection of the surface.
38.	Black-Schaffer, Annica M., et al. (författare) Subsurface impurities and vacancies in a three-dimensional topological insulator 2012 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 86:11, s. 115433- Tidskriftsartikel (refereegranskat)abstract Using a three-dimensional microscopic lattice model of a strong topological insulator (TI) we study potential impurities and vacancies in surface, subsurface, and bulk positions. For all impurity locations we find impurity-induced resonance states with energy proportional to the inverse of the impurity strength, although the impurity strength needed for a low-energy resonance state increases with the depth of the impurity. For strong impurities and vacancies as deep as 15 layers into the material, resonance peaks will appear at and around the Dirac point in the surface energy spectrum, splitting the original Dirac point into two nodes located off-center. Furthermore, we study vacancy clusters buried deep inside the bulk and find zero-energy resonance states for both single and multiple-site vacancies. Only fully symmetric multiple-site vacancy clusters show resonance states expelled from the bulk
39.	Black-Schaffer, Annica M., et al. (författare) Topological superconductivity in two dimensions with mixed chirality 2015 Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 92:14 Tidskriftsartikel (refereegranskat)abstract We find a mixed chirality d-wave superconducting state in the coexistence region between antiferromagnetism and interaction-driven superconductivity in lightly doped honeycomb materials. This state has a topological chiral d + id-wave symmetry in one Dirac valley but d - id-wave symmetry in the other valley and hosts two counterpropagating edge states, always protected in the absence of intervalley scattering. A first-order topological phase transition, with no bulk gap closing, separates the chiral d-wave state at small magnetic moments from the mixed chirality d-wave phase.
40.	Bollmark, Gunnar (författare) Order in Strongly Correlated Quasi-One-Dimensional Systems : Solving Higher-Dimensional Systems Combining Matrix-Product-State Methods and Mean-Field Theory 2023 Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract Since their discovery the understanding of unconventional superconductors (USCs) has posed a great challenge in condensed matter physics. One central problem, both of theory and experiment, lies in determining the microscopic origin of electron pairing in such systems. Partly, the difﬁculty lies in numerically simulating systems hypothesized to represent USCs. In particular, it remains an open question whether the ground state of the two-dimensional Hubbard model realizes an USC. This system epitomizes the combined difﬁculty of ﬁnding both whether electrons form pairs and whether they condense into an USCs phase.Conversely, the one-dimensional (1D) Hubbard ladder is readily solved numerically using matrix-product state (MPS) methods. Doped away from a half-ﬁlled lattice repulsively mediated electron pairing is realized in the system. However, quantum ﬂuctuations hinder ordering in such systems even at zero temperature viz. continuous symmetries cannot be spontaneously broken. Instead, quasi-one-dimensional (Q1D) systems featuring arrays of one-dimensional (1D) chains weakly coupled into a higher-dimensional system can be studied. While pairing is resolved in each 1D system using MPS the condensation of such pairs into a superconductor may be treated using mean-ﬁeld (MF) theory. The subject of this thesis is the development of the MPS+MF framework: An algorithm utilizing MPS and MF theory capable of solving Q1D systems.Developing new methods requires comparison with known solutions to learn of their potential inaccuracies. Thus, development is split into three steps: i) Simulation of bosons to test the basic approach, ii) simulation of attractive fermions, iii) simulation of an USC composed of repulsive Hubbard ladders. The ﬁrst two targets admit comparison to quantum Monte Carlo simulations and, for some parameters, analytical methods. The MPS+MF framework is found to simulate the critical temperature of condensation with a ﬁxed ratio to the true critical temperature, independent of Q1D coupling. Additionally, the framework is found capable of resolving competition of insulating and USC phases.Utilizing the possibility of evolving states in time using MPS numerics, MPS+MF is extended to perform self-consistent time evolution. We ﬁnd that this method allows the detection of superconductivity out of equilibrium and, in particular, dynamically induced superconductivity.
41.	Borla, Umberto, et al. (författare) Tuning Majorana zero modes with temperature in pi-phase Josephson junctions 2018 Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:1 Tidskriftsartikel (refereegranskat)abstract We study a superconductor-normal-state-superconductor Josephson junction along the edge of a quantum spin Hall insulator with a superconducting pi phase across the junction. We solve self-consistently for the superconducting order parameter and find both real junctions, where the order parameter is fully real throughout the system, and junctions where the order parameter has a complex phase winding. Real junctions host two Majorana zero modes (MZMs), while phase-winding junctions have no subgap states close to zero energy. At zero temperature we find that the phase-winding solution always has the lowest free energy, which we establish as being due to a strong proximity effect into the N region. With increasing temperature this proximity effect is dramatically decreased and we find a phase transition into a real junction with two MZMs.
42.	Bouhon, Adrien, et al. (författare) Global band topology of simple and double Dirac-point semimetals 2017 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 95:24 Tidskriftsartikel (refereegranskat)abstract We combine space group representation theory together with the scanning of closed subdomains of the Brillouin zone with Wilson loops to algebraically determine the global band-structure topology. Considering space group No. 19 as a case study, we show that the energy ordering of the irreducible representations at the high-symmetry points {Gamma, S, T, U} fully determines the global band topology, with all topological classes characterized through their simple and double Dirac points.
43.	Bouhon, Adrien, et al. (författare) Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice 2018 Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:10 Tidskriftsartikel (refereegranskat)abstract We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice, and we derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find a line-nodal state dominating at low doping levels that is topologically nontrivial and exhibits surface Majorana flatbands, which we show perfectly match the bulk-boundary correspondence using the Berry phase approach. At higher doping levels, we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the nodal lines, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice are present. Adding simple energy arguments, we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this fully gapped state to be topologically trivial, while we find an additional point-nodal state at very low doing levels that also break time-reversal symmetry and has nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and we show how all but the point-nodal state are reasonably stable.
44.	Bouhon, Adrien, et al. (författare) Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry 2019 Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 100:19 Tidskriftsartikel (refereegranskat)abstract We present a general methodology toward the systematic characterization of crystalline topological insulating phases with time-reversal symmetry. In particular, taking the two-dimensional spinful hexagonal lattice as a proof of principle, we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries. Our approach finds a prominent use in elucidating and quantifying the recently proposed "topological quantum chemistry" concept. Namely, we prove that the split of an elementary band representation (EBR) by a band gap must lead to a topological phase. For this we first show that in addition to the Fu-Kane-Mele Z(2) classification, there is C2T-symmetry-protected Z classification of two-band subspaces that is obstructed by the other crystalline symmetries, i.e., forbidding the trivial phase. This accounts for all nontrivial Wilson loop windings of split EBRs that are independent of the parametrization of the flow of Wilson loops. Then, by systematically embedding all combinatorial four-band phases into six-band phases, we find a refined topological feature of split EBRs. Namely, we show that while Wilson loop winding of split EBRs can unwind when embedded in higher-dimensional band space, two-band subspaces that remain separated by a band gap from the other bands conserve their Wilson loop winding, hence revealing that split EBRs are at least "stably trivial," i.e., necessarily nontrivial in the nonstable (few-band) limit but possibly trivial in the stable (many-band) limit. This clarifies the nature of fragile topology that has appeared very recently. We then argue that in the many-band limit, the stable Wilson loop winding is only determined by the Fu-Kane-Mele Z(2) invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.
45.	Cayao, Jorge, et al. (författare) Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states 2018 Ingår i: Beilstein Journal of Nanotechnology. - : BEILSTEIN-INSTITUT. - 2190-4286. ; 9, s. 1339-1357 Tidskriftsartikel (refereegranskat)abstract Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of p, a wellvisible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2 pi-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of pi when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.
46.	Cayao, Jorge, et al. (författare) Bulk Bogoliubov Fermi arcs in non-Hermitian superconducting systems 2023 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 107:10 Tidskriftsartikel (refereegranskat)abstract We consider a non-Hermitian superconducting system by coupling a conventional superconductor to a ferromagnet lead and demonstrate the emergence of exceptional points when an external Zeeman field is applied. We discover that, depending on the non-Hermiticity and the Zeeman field, the exceptional points mark the ends of lines with zero real energy, thus giving rise to topologically protected and highly tunable bulk Fermi arcs, which we coin bulk Bogoliubov Fermi arcs due to their superconducting nature. We show that these bulk Bogoliubov Fermi arcs are the non-Hermitian counterparts of the Hermitian topological phase transition but are much more prevalent and also experimentally detectable through large spectral signatures.
47.	Cayao, Jorge, et al. (författare) Distinguishing trivial and topological zero-energy states in long nanowire junctions 2021 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 104:2 Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract The emergence of zero-energy states in nontopological superconductors represents an inevitable problem that obscures the proper identification of zero-energy Majorana bound states (MBSs) and prevents their use as topologically protected qubits. In this Research Letter we investigate long superconductor-normal-superconductor junctions where trivial zero-energy states, robust over a large range of parameters, appear as a result of helicity and confinement in the normal region. We demonstrate that both equilibrium supercurrents and critical currents are sensitive to variations in the length of the superconductor regions in the topological phase hosting MBSs but, remarkably, no such length dependence exists when robust, but trivial, zero-energy states are present. This strikingly different response originates from the nonlocal nature of the MBSs, and we therefore propose it as a simple protocol for distinguishing between trivial and topological zero-energy states.
48.	Cayao, Jorge, et al. (författare) Exceptional odd-frequency pairing in non-Hermitian superconducting systems 2022 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 105:9 Tidskriftsartikel (refereegranskat)abstract We first show the realization of exceptional points in a non-Hermitian superconducting system based on a conventional superconductor and then demonstrate that, surprisingly, the system hosts odd-frequency pairing, solely generated by the non-Hermiticity. While there is a coexistence of even- and odd-frequency pairs under general conditions, we find that the even-frequency term vanishes at the exceptional degeneracies, leaving only odd-frequency pairing. This exceptional odd-frequency pairing is directly given by the imaginary part of the eigenvalues at the exceptional points and can be measured from the spectral function. Our results thus put forward non-Hermitian systems as a powerful platform to realize odd-frequency superconducting pairing.
49.	Cayao, Jorge, et al. (författare) Finite length effect on supercurrents between trivial and topological superconductors 2018 Ingår i: The European Physical Journal Special Topics. - : Springer Science and Business Media LLC. - 1951-6355 .- 1951-6401. ; 227:12, s. 1387-1396 Tidskriftsartikel (refereegranskat)abstract We numerically analyze the effect of finite length of the superconducting regions on the low-energy spectrum, current-phase curves, and critical currents in junctions between trivial and topological superconductors. Such junctions are assumed to arise in nanowires with strong spin-orbit coupling under external magnetic fields and proximity-induced superconductivity. We show that all these quantities exhibit a strong dependence on the length of the topological sector in the topological phase and serve as indicators of the topological phase and thus the emergence of Majorana bound states at the end of the topological superconductor.
50.	Cayao, Jorge, et al. (författare) Floquet engineering bulk odd-frequency superconducting pairs 2021 Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:10 Tidskriftsartikel (refereegranskat)abstract We introduce the concept of Floquet odd-frequency superconducting pairs and establish their emergence in time-periodic conventional superconductors. We show that these exotic Cooper pairs are possible because the Floquet modes in time-periodic systems provide an additional index (a Floquet index) that broadens the classification of superconducting pair symmetries, with no analog in the static regime. Our results thus put forward a different route for odd-frequency superconducting pairs, and pave the way for Floquet engineered dynamical superconducting states.

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