| 1. |
- Björnson, Kristofer, et al.
(författare)
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Majorana fermions at odd junctions in a wire network of ferromagnetic impurities
- 2016
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 94:10
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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.
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| 2. |
- Björnson, Kristofer, et al.
(författare)
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Probing vortex Majorana fermions and topology in semiconductor/superconductor heterostructures
- 2015
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 91:21
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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.
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| 3. |
- Björnson, Kristofer, et al.
(författare)
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Skyrmion spin texture in ferromagnetic semiconductor-superconductor heterostructures
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 89:13, s. 134518-
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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.
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| 4. |
- Björnson, Kristofer, et al.
(författare)
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Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors
- 2015
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : American Physical Society. - 1098-0121 .- 1550-235X. ; 92:21
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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.
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| 5. |
- Björnson, Kristofer, et al.
(författare)
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Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:2, s. 024501-
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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.
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| 6. |
- Black-Schaffer, Annica M.
(författare)
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Chiral d-wave superconducting state in the core of a doubly quantized s-wave vortex in graphene
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:10, s. 104506-
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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.
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| 7. |
- Black-Schaffer, Annica M., et al.
(författare)
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Chiral d-wave superconductivity on the honeycomb lattice close to the Mott state
- 2014
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 90:5, s. 054521-
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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.
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| 8. |
- Black-Schaffer, Annica M., et al.
(författare)
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Filling of magnetic-impurity-induced gap in topological insulators by potential scattering
- 2015
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 91:20
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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.
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| 9. |
- Black-Schaffer, Annica M., et al.
(författare)
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Majorana fermions in spin-orbit-coupled ferromagnetic Josephson junctions
- 2011
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 84:18, s. 180509(R)-
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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.
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| 10. |
- Black-Schaffer, Annica M., et al.
(författare)
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Odd-frequency superconducting pairing in multiband superconductors
- 2013
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 88:10, s. 104514-
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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.
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