| 1. |
- Autieri, Carmine, et al.
(author)
-
Gap opening and large spin–orbit splitting in MX2 (M = Mo,W; X = S,Se,Te) from the interplay between crystal field and hybridisations : insights from ab-initio theory
- 2017
-
In: Philosophical Magazine. - : Informa UK Limited. - 1478-6435 .- 1478-6443. ; 97:35, s. 3381-3395
-
Journal article (peer-reviewed)abstract
- By means of first-principles density functional calculations, we study the maximally localised Wannier functions for the 2D transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te). We have found that part of the energy gap is opened by the crystal field splitting induced by the X-2-like atoms. The inversion of the band character between the Gamma and the K points of the Brillouin zone is due to the M-M hybridisation. The consequence of this inversion is the closure of the gap in absence of the M-X hybridisation. The M-X hybridisation is the only one that tends to open the gap at every k-point. It is found that the change in the M-X and M-M hybridisation is the main responsible for the difference in the gap between the different dichalcogenide materials. The inversion of the bands gives rise to different spinorbit splitting at Gamma and K point in the valence band. The different character of the gap at Gamma and K point offers the chance to manipulate the semiconducting properties of these compounds. For a bilayer system, the hybridisation between the out-of-plane orbitals and the hybridisation between the in-plane orbitals split the valence band respectively at the Gamma and K point. The splitting in the valence band is opened also without spin-orbit coupling and occurs due to the M-M and X-X hybridisation between the two monolayers. The transition from direct to indirect band gap is governed by the hybridisation between out-of-plane orbitals of different layers and in-plane orbitals of different layers.
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| 2. |
- Awoga, Oladunjoye A., et al.
(author)
-
Domain walls in a chiral d-wave superconductor on the honeycomb lattice
- 2017
-
In: Physical Review B. - 2469-9950 .- 2469-9969. ; 96:1
-
Journal article (peer-reviewed)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.
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| 3. |
- Bouhon, Adrien, et al.
(author)
-
Geometric approach to fragile topology beyond symmetry indicators
- 2020
-
In: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 102:11
-
Journal article (peer-reviewed)abstract
- We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on C2T-symmetric systems that have gained recent attention, for example, in the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Plucker embedding, to induce windings in the band structure necessary to facilitate nontrivial topology. Specifically, this directly relates to the parametrization of the Grassmannian, which describes partitioning of an arbitrary band structure and is embedded in a better manageable exterior product space. From a physical perspective, our construction encapsulates and elucidates the concepts of fragile topological phases beyond symmetry indicators as well as non-Abelian reciprocal braiding of band nodes that arises when the multiple gaps are taken into account. The adopted geometric viewpoint most importantly culminates in a direct and easily implementable method to construct model Hamiltonians to study such phases, constituting a versatile theoretical tool.
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| 4. |
- Bouhon, Adrien, et al.
(author)
-
Global band topology of simple and double Dirac-point semimetals
- 2017
-
In: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 95:24
-
Journal article (peer-reviewed)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.
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| 5. |
- Bouhon, Adrien, et al.
(author)
-
Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe
- 2020
-
In: Nature Physics. - : Springer Science and Business Media LLC. - 1745-2473 .- 1745-2481. ; 16, s. 1137-1143
-
Journal article (peer-reviewed)abstract
- Weyl points in three-dimensional systems with certain symmetry carry non-Abelian topological charges, which can be transformed via non-trivial phase factors that arise upon braiding these points inside the reciprocal space. Weyl semimetals in three-dimensional crystals provide the paradigm example of topologically protected band nodes. It is usually taken for granted that a pair of colliding Weyl points annihilate whenever they carry opposite chiral charge. In stark contrast, here we report that Weyl points in systems that are symmetric under the composition of time reversal with a pi rotation are characterized by a non-Abelian topological invariant. The topological charges of the Weyl points are transformed via braid phase factors, which arise upon exchange inside symmetric planes of the reciprocal momentum space. We elucidate this process with an elementary two-dimensional tight-binding model that is implementable in cold-atom set-ups and in photonic systems. In three dimensions, interplay of the non-Abelian topology with point-group symmetry is shown to enable topological phase transitions in which pairs of Weyl points may scatter or convert into nodal-line rings. By combining our theoretical arguments with first-principles calculations, we predict that Weyl points occurring near the Fermi level of zirconium telluride carry non-trivial values of the non-Abelian charge, and that uniaxial compression strain drives a non-trivial conversion of the Weyl points into nodal lines.
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| 6. |
- Bouhon, Adrien, et al.
(author)
-
Topological correspondence between magnetic space group representations and subdimensions
- 2021
-
In: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:24
-
Journal article (peer-reviewed)abstract
- The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored in the pertinent context of magnetic structures. We report on a general class of electronic configurations within a set of antiferromagnetic-compatible space groups that are necessarily topological. Interestingly, we find a systematic correspondence between these antiferromagnetic phases to necessarily nontrivial topological ferro/ferrimagnetic counterparts that are readily obtained through physically motivated perturbations. Addressing the exhaustive list of magnetic space groups in which this mechanism occurs, we also verify its presence on planes in 3D systems that were deemed trivial in existing classification schemes. This leads to the formulation of the concept of subdimensional topologies, featuring nontriviality within part of the system that coexists with stable Weyl points away from these planes, thereby uncovering novel topological materials in the full 3D sense that have readily observable features in their bulk and surface spectrum.
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| 7. |
- Bouhon, Adrien, et al.
(author)
-
Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
- 2018
-
In: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:10
-
Journal article (peer-reviewed)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.
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| 8. |
- Bouhon, Adrien, et al.
(author)
-
Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry
- 2019
-
In: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 100:19
-
Journal article (peer-reviewed)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.
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| 9. |
- Chen, Siyu, et al.
(author)
-
Non-Abelian braiding of Weyl nodes via symmetry-constrained phase transitions
- 2022
-
In: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 105:8
-
Journal article (peer-reviewed)abstract
- Weyl semimetals are arguably the most paradigmatic form of a gapless topological phase. While the stability of Weyl nodes, as quantified by their topological charge, has been extensively investigated, recent interest has shifted to the manipulation of the location of these Weyl nodes for non-Abelian braiding. To accomplish this braiding it is necessary to drive significant Weyl node motion using realistic experimental parameter changes. We show that a family of phase transitions characterized by certain symmetry constraints impose that the Weyl nodes have to reorganize by a large amount, shifting from one high-symmetry plane to another. Additionally, for a subset of pairs of nodes with nontrivial Euler class topology, this reorganization can only occur through a braiding process with adjacent nodes. As a result, the Weyl nodes are forced to move a large distance across the Brillouin zone and to braid, all driven by small temperature changes, a process we illustrate with Cd2Re2O7.
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| 10. |
- Chen, Xin, et al.
(author)
-
PAI-graphene : A new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones
- 2020
-
In: Carbon. - : Elsevier BV. - 0008-6223 .- 1873-3891. ; 170, s. 477-486
-
Journal article (peer-reviewed)abstract
- Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most of the reported 2D allotropes of graphene. Crucially, the crystal structure realizes a nonsymmorphic layer group that enforces a nontrivial global topology of the band structure with two Dirac cones lying perfectly at the Fermi level. The absence of electron/hole pockets makes PAI-graphene a pristine crystalline topological semimetal having anisotropic Fermi velocities with a high value of 7.0×105" role="presentation"> m/s. We show that while the semimetallic property of the allotrope is robust against the application of strain, the positions of the Dirac cone and the Fermi velocities can be modified significantly with strain. Moreover, by combining strain along both the x- and y-directions, two band inversions take place at Γ" role="presentation"> leading to the annihilation of the Dirac nodes demonstrating the possibility of strain-controlled conversion of a topological semimetal into a semiconductor. Finally we formulate the bulk-boundary correspondence of the topological nodal phase in the form of a generalized Zak-phase argument finding a perfect agreement with the topological edge states computed for different edge-terminations.
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| 11. |
- Davoyan, Zory, et al.
(author)
-
Three-dimensional ??-symmetric topological phases with a Pontryagin index
- 2024
-
In: Physical Review B. - 2469-9950 .- 2469-9969. ; 109:16
-
Journal article (peer-reviewed)abstract
- We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless ?? symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multigap topology, providing a realization of a single ℤ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes Belavin-Polyakov-Schwartz-Tyupkin (BPST) instantons in particle physics contexts and corresponds to a three-sphere winding number. We study naturally arising multigap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally recast the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully nondegenerate multigap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states, and linked nodal structures in acoustic metamaterials and trapped-ion experiments.
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| 12. |
- Etter, Sarah B., et al.
(author)
-
Spontaneous surface flux pattern in chiral p-wave superconductors
- 2018
-
In: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 97:6
-
Journal article (peer-reviewed)abstract
- In chiral p-wave superconductors, magnetic flux patterns may appear spontaneously when translational symmetry is broken such as at surfaces, domain walls, or impurities. However, in the candidate material Sr2RuO4 no direct signs of such magnetic fields have been detected experimentally. In this paper, the flux pattern at the edge of a disk-shaped sample is examined using the phenomenological Ginzburg-Landau approach. The detailed shape of the flux pattern, including self-screening, is computed numerically for different surface types by systematically scanning a range of boundary conditions. Moreover, specific features of the electronic structure are included qualitatively through the coefficients in the Ginzburg-Landau functional. Both the shape and the magnitude of the flux pattern are found to be highly sensitive to all considered parameters. In conclusion, such spontaneous magnetic flux patterns are not a universal feature of chiral p-wave superconductors.
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| 13. |
- Geilhufe, R. Matthias, et al.
(author)
-
Data Mining for Three-Dimensional Organic Dirac Materials : Focus on Space Group 19
- 2017
-
In: Scientific Reports. - : Springer Science and Business Media LLC. - 2045-2322. ; 7
-
Journal article (peer-reviewed)abstract
- We combined the group theory and data mining approach within the Organic Materials Database that leads to the prediction of stable Dirac-point nodes within the electronic band structure of three-dimensional organic crystals. We find a particular space group P2(1)2(1)2(1) (#19) that is conducive to the Dirac nodes formation. We prove that nodes are a consequence of the orthorhombic crystal structure. Within the electronic band structure, two different kinds of nodes can be distinguished: 8-fold degenerate Dirac nodes protected by the crystalline symmetry and 4-fold degenerate Dirac nodes protected by band topology. Mining the Organic Materials Database, we present band structure calculations and symmetry analysis for 6 previously synthesized organic materials. In all these materials, the Dirac nodes are well separated within the energy and located near the Fermi surface, which opens up a possibility for their direct experimental observation.
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| 14. |
- Geilhufe, R. Matthias, et al.
(author)
-
Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry : A data mining approach
- 2017
-
In: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 95:4
-
Journal article (peer-reviewed)abstract
- A datamining study of electronic Kohn-Sham band structures was performed to identify Dirac materials within the Organic Materials Database. Out of that, the three-dimensional organic crystal 5,6-bis(trifluoromethyl)-2-methoxy-1H-1,3-diazepine was found to host different Dirac-line nodes within the band structure. From a group theoretical analysis, it is possible to distinguish between Dirac-line nodes occurring due to twofold degenerate energy levels protected by the monoclinic crystalline symmetry and twofold degenerate accidental crossings protected by the topology of the electronic band structure. The obtained results can be generalized to all materials having the space group P2(1)/c (No. 14, C-2h(5)) by introducing three distinct topological classes.
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| 15. |
- Guan, Yifei, et al.
(author)
-
Landau levels of the Euler class topology
- 2022
-
In: Physical Review Research. - : American Physical Society (APS). - 2643-1564. ; 4:2
-
Journal article (peer-reviewed)abstract
- Two-dimensional systems with C2T (PT) symmetry exhibit the Euler class topology E is an element of Z in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating phases in the presence of an external magnetic field, we reveal the robust gaplessness of the Hofstadter butterfly spectrum in the flat-band limit, while for the dispersive bands the gapping of the Landau levels is controlled by a hidden symmetry. We also find that the Euler class E of a two-band subspace gives a lower bound for the Chern numbers of the magnetic subgaps. Our study provides new fundamental insights into the fragile topology of flat-band systems going beyond the special case of E = 1 as, e.g., in twisted bilayer graphene, thus opening the way to a very rich, still mainly unexplored, topological landscape with higher Euler classes.
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| 16. |
- Jiang, Bin, et al.
(author)
-
Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions
- 2021
-
In: Nature Physics. - : Springer Science and Business Media LLC. - 1745-2473 .- 1745-2481. ; 17, s. 1239-1246
-
Journal article (peer-reviewed)abstract
- Topological phases of matter connect mathematical principles to real materials, and may shape future electronic and quantum technologies. So far, this discipline has mostly focused on single-gap topology described by topological invariants such as Chern numbers. Here, based on a tunable kagome model, we observe non-Abelian band topology and its transitions in acoustic semimetals, in which the multi-gap Hilbert space plays a key role. In non-Abelian semimetals, the topological charges of band nodes are converted through the braiding of nodes in adjacent gaps, and their behaviour cannot be captured by conventional topological band theory. Using kagome acoustic metamaterials and pump–probe measurements, we demonstrate the emergence of non-Abelian topological nodes, identify their dispersions and observe the induced multi-gap topological edge states. By controlling the geometry of the metamaterials, topological transitions are induced by the creation, annihilation, merging and splitting of band nodes. This reveals the underlying rules for the conversion and transfer of non-Abelian topological charges in multiple bandgaps. The resulting laws that govern the evolution of band nodes in non-Abelian multi-gap systems should inspire studies on multi-band topological semimetals and multi-gap topological out-of-equilibrium systems.
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| 17. |
- Jiang, Bin, et al.
(author)
-
Observation of an acoustic topological Euler insulator with meronic waves
- 2024
-
In: Science Bulletin. - : Elsevier BV. - 2095-9273. ; 69:11, s. 1653-1659
-
Journal article (peer-reviewed)abstract
- Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.
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| 18. |
- König, J. Lukas K.
(author)
-
Non-Hermitian Symmetric Nodal Phases
- 2024
-
Licentiate thesis (other academic/artistic)abstract
- I den här avhandlingen introducerar vi ämnen som är centrala för de bifogade artiklarna [Art. I, Art. II, Art. III]. Alla tre handlar om degenererade faser i icke-hermitska system. I kapitel 1 inleder vi med att introducera experimentella plattformar för icke-hermitska system, och skillnaderna i deras matematiska hantering gentemot hermitska system. I [Art. I] undersökte vi tvådimensionella icke-hermitska system under periodiska randvillkor, och fann att nielsen-ninomiyas teorem inte kan tillämpas trivialt i detta fall. Vi visar hur detta teorem fungerar för hermitska system i kapitel 2, och förklarar varför det misslyckas för icke-hermitska system. I detta kapitel förklaras även den allmänna metoden för homotopiklassificering utifrån begreppet degenererad hamiltonian. Slutligen diskuterar vi diskreta symmetrier i kapitel 3, med utgångspunkt i kristallina symmetrier. Dessa är centrala för [Art. II], där vi visade att en hamiltonian som beskriver kristaller med specifika symmetri-grupper måste ha degenererade punkter. Fortsättningsvis diskuterar vi anti-unitära och partikel-hål-symmetrier, vilket leder till den tiofaldiga klassificeringen av symmetrier. Vi betonar betydelsen av tidsomvändningssymmetri och PT-symmetri, en kombination av tidsomvändning och rumslig inversion. Denna symmetri förstärker ytterligare den degenererade struktur som vi fann i [Art. II], vilket leder till exceptionella linjer, ett fenomen som är omöjligt i hermitska system. PT-symmetrin är också central för [Art. III], där vi klassificerade homotopistrukturen för PT-symmetriska system i allmänhet och fann ett antal intressanta topologiska invarianter.
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| 19. |
- Könye, Viktor, et al.
(author)
-
Chirality flip of Weyl nodes and its manifestation in strained MoTe2
- 2021
-
In: Physical Review Research. - 2643-1564. ; 3:4
-
Journal article (peer-reviewed)abstract
- Due to their topological charge, or chirality, the Weyl cones present in topological semimetals are considered robust against arbitrary perturbations. One well-understood exception to this robustness is the pairwise creation or annihilation of Weyl cones, which involves the overlap in energy and momentum of two oppositely charged nodes. Here we show that the topological charge can in fact change sign, in a process that involves the merging of not two, but three Weyl nodes. This is facilitated by the presence of rotation and time-reversal symmetries, which constrain the relative positions of Weyl cones in momentum space. We analyze the chirality flip process, showing that transport properties distinguish it from the conventional, double Weyl merging. Moreover, we predict that the chirality flip occurs in MoTe2, where experimentally accessible strain leads to the merging of three Weyl cones close to the Fermi level. Our work sets the stage to further investigate and observe such chirality flipping processes in different topological materials.
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| 20. |
- Lange, Gunnar F., et al.
(author)
-
Spin texture as a bulk indicator of fragile topology
- 2023
-
In: Physical Review Research. - 2643-1564. ; 5:3
-
Journal article (peer-reviewed)abstract
- We study the relationship between momentum-space spin textures projected onto the occupied bands and Wilson loop winding, proving a map between band topology and spin topology in certain restricted symmetry settings relevant to fragile topology. Our results suggest that, in specific scenarios, the spin gap may act as a smoking gun bulk indicator for fragile topology.
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| 21. |
- Lange, Gunnar F., et al.
(author)
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Subdimensional topologies, indicators, and higher order boundary effects
- 2021
-
In: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:19
-
Journal article (peer-reviewed)abstract
- The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features. Within this context we recently reported on a class of unexplored topological structures that thrive on the concept of subdimensional topology. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within subdimensional spaces, such as planes or lines. This perspective does not just refine classification pursuits, but can result in observable features in the full dimensional sense. In three spatial dimensions (3D), for example, subdimensional topologies can be characterized by nontrivial planes, having general topological invariants that coexist with Weyl nodes away from these planes. As a result, such phases have 3D stable characteristics such as Weyl nodes, Fermi arcs and edge states that can be systematically predicted by subdimensional analysis. Within this work we further elaborate on these concepts. We present refined representation counting schemes and address distinctive bulk-boundary effects, that include momentum depended (higher order) edge states that have a signature dependence on the perpendicular momentum. As such, we hope that these insights might spur on new activities to further deepen the understanding of these unexplored phases.
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| 22. |
- Lange, Gunnar F., et al.
(author)
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Topological continuum charges of acoustic phonons in two dimensions and the Nambu-Goldstone theorem
- 2022
-
In: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 105:6
-
Journal article (peer-reviewed)abstract
- We analyze the band topology of acoustic phonons in 2D materials by considering the interplay between spatial/internal symmetries and additional constraints that arise from the physical context. These supplemental constraints trace back to the Nambu-Goldstone theorem and the requirements of structural stability. We show that this interplay can give rise to previously unaddressed nontrivial nodal charges that are associated with the crossing of the acoustic phonon branches at the center (Γ point) of the phononic Brillouin zone. We moreover apply our perspective to the concrete context of graphene, where we demonstrate that the phonon spectrum harbors these kinds of nontrivial nodal charges. Apart from its fundamental appeal, this analysis is physically consequential and dictates how the phonon dispersion is affected when graphene is grown on a substrate. Given the generality of our framework, we anticipate that our strategy, which thrives on combining physical context with insights from topology, should be widely applicable in characterizing systems beyond electronic band theory.
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| 23. |
- Morris, Arthur S., et al.
(author)
-
Andreev reflection in Euler materials
- 2024
-
In: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 26:2
-
Journal article (peer-reviewed)abstract
- Many previous studies of Andreev reflection have demonstrated that unusual effects can occur in media which have a nontrivial bulk topology. Following this line of investigation, we study Andreev reflection by analysing a simple model of a bulk node with a generic winding number n > 0, where the even cases directly relate to topological Euler materials. We find that the magnitudes of the resultant reflection coefficients depend strongly on whether the winding is even or odd. Moreover this parity dependence is reflected in the differential conductance curves, which are highly suppressed for n even but not n odd. This gives a possible route through which the recently discovered Euler topology could be probed experimentally.
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| 24. |
- Peng, Bo, et al.
(author)
-
Multigap topology and non-Abelian braiding of phonons from first principles
- 2022
-
In: Physical Review B. - : American Physical Society (APS). - 2469-9950 .- 2469-9969. ; 105:8
-
Journal article (peer-reviewed)abstract
- Non-Abelian states of matter, in which the final state depends on the order of the interchanges of two quasipar-ticles, can encode information immune from environmental noise with the potential to provide a robust platform for topological quantum computation. We demonstrate that phonons can carry non-Abelian frame charges at the band-crossing points of their frequency spectrum, and that external stimuli can drive their braiding. We present a general framework to understand the topological configurations of phonons from first-principles calculations using a topological invariant called Euler class, and provide a complete analysis of phonon braiding by combining different topological configurations. Taking a well-known dielectric material Al2O3 as a representative example, we demonstrate that electrostatic doping gives rise to phonon band inversions that can induce redistribution of the frame charges, leading to non-Abelian braiding of phonons. Our work provides a quasiparticle platform for realizable non-Abelian braiding in reciprocal space, and expands the tool set for studying braiding processes.
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| 25. |
- Peng, Bo, et al.
(author)
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Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
- 2022
-
In: Nature Communications. - : Springer Nature. - 2041-1723. ; 13:1
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Journal article (peer-reviewed)abstract
- Multi-gap topology is a new avenue in topological phases of matter but it remains difficult to verify in real materials. Here, the authors predict multi-gap topologies and associated phase transitions driven by braiding processes in the phonon spectra of monolayer silicates, providing clear signatures for experimental verification. Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that the band inversion processes at the Gamma point can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of the band inversion accompanied by the braiding process.
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