Reducing Electronic Transport Dimension to Topological Hinge States by Increasing Geometry Size of Dirac Semimetal Josephson Junctions

Li, Cai Zhen; Wang, An Qi; Li, Chuan; Zheng, Wen; Brinkman, Alexander; Yu, Dakuan; Liao, Zhi-Min

doi:10.1103/physrevlett.124.156601

Cited by 45 publications

(36 citation statements)

References 45 publications

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“…Our methodology can be extended to spin-density waves [69,[114][115][116] and CDWs in T -symmetric semimetals, including Dirac [97,117,118], Weyl, and nodal-line semimetals [119][120][121][122], which also exhibit signatures of higher-order topology [55,100,123,124]. Most interestingly, because rotation-and T -symmetric HOTIs [28,56] can be formed from weak stacks of 2D TIs [48,51], rotationsymmetric CDWs in T -symmetric WSMs, such as the CDW in (TaSe 4 ) 2 I [78], may also exhibit nontrivial response effects.…”

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confidence: 99%

Axionic band topology in inversion-symmetric Weyl-charge-density waves

Wieder

Lin

Bradlyn

2020

Phys. Rev. Research

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In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Rapid Communication, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion (I)-symmetric Weyl-CDWs with φ = 0, π differ by a topological axion angle δθ φ = π. However, we crucially discover that neither of the minimal Weyl-CDW phases at φ = 0, π is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-Abelian Berry phase, we demonstrate that our results generalize to multiband systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings and provide models and analysis generalizing our results to nonmagnetic Weyl-and Dirac-CDWs.

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confidence: 99%

Axionic band topology in inversion-symmetric Weyl-charge-density waves

Wieder

Lin

Bradlyn

2020

Phys. Rev. Research

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“…V A); nevertheless, Dirac HOTSMs universally host intrinsic hinge states as a topological consequence of their bulk Dirac points [93,348]. Dirac HOTSM phases have since been predicted to occur in nearly all previously identified band-inversion Dirac semimetals [93], and signatures of hinge states were recently observed in supercurrent oscillation experiments on the established Dirac semimetal Cd 3 As 2 [ICSD 609930, SG 137 (P 4 2 /nmc)] [349] (see Sec. V A).…”

Section: Higher-order Tcis and Tsmsmentioning

confidence: 99%

Topological Materials Discovery from Crystal Symmetry

Wieder,

Bradlyn,

Cano

et al. 2021

Preprint

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“…Next, if the symmetry data vector corresponds to a set of highsymmetry-point Bloch eigenstates that are implied by the compatibility relations to connect to other states outside of the symmetry data along a high-symmetry line or plane, then the system is an enforced semimetal (ES). A well-studied ES material is the archetypal higher-ordertopological Dirac semimetal Cd 3 As 2 [ICSD 107918, SG 137 (P 4 2 /nmc)] [6,19,50,51]. Conversely, if the symmetry data vector satisfies the compatibility relations along all high-symmetry lines and planes, then the bands that transform in the symmetry data either correspond to a stable TI, TCI, or TSM, or are trivial or fragile topological.…”

Section: Data Set Generation Detailsmentioning

confidence: 99%

All Topological Bands of All Stoichiometric Materials

Vergniory,

Wieder,

Elcoro

et al. 2021

Preprint

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The recently introduced theories of Topological Quantum Chemistry and Symmetry-Based Indicators (SIs) have facilitated the discovery of novel stable topological phases of matter and largescale searches for materials with experimentally accessible topological properties at the Fermi energy (EF ). In this work, we have completed the first catalog of stable and fragile topology in all of the bands both at and away from EF in the Inorganic Crystal Structure Database (ICSD), which we have made accessible through a substantial upgrade of Topological Materials Database (https://www.topologicalquantumchemistry.com/). We have computed the electronic structure, topological class, and stable and fragile SIs of all bands in the 96,196 processable ICSD entries with stoichiometric chemical formulas in the presence and absence of spin-orbit coupling, which we have grouped into 38,298 unique materials by common chemical formulas, crystal structures [space groups (SGs)], and topology at EF . Our calculations represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, and a doubling of the number of materials accessible in previous topological material catalogs. Through our calculations, we discover the existence of novel classes of topological materials, including enforced topological semimetals with energetically isolated fragile bands at EF , repeat-topological (RTopo) materials with stable topological insulating gaps at and just below EF , and supertopological (STopo) materials in which every energetically isolated set of bands above the core shell is stable topological. Our findings recontextualize several previous experimental investigations of topological materials. We find that the transition-metal chalcogenides Ta2NiSe5 in SG 15 (C/2c) and Ta2NiSe7 in SG 12 (C2/m) -respectively previously highlighted for hosting exciton-insulator and charge-density-wave phases -are 3D topological insulators (TIs) in their normal states. Additionally, we find that the higher-order TI rhombohedral bismuth in SG 166 (R 3m) and the indirect-gap TI Bi2Mg3 in SG 164 (P 3m1) are both RTopo and STopo materials. Previous ARPES investigations of Bi2Mg3 have demonstrated the presence of "surface resonance bands" below EF -in this work, we discover that the surface resonance bands are in fact RTopo Dirac-cone surface states. We present detailed statistics for our computations revealing that 52.65% of all materials are topological at EF , roughly 2/3 of bands across all materials exhibit symmetry-indicated stable topology, and that, shockingly, 87.99% of all materials contain at least one stable or fragile (crystalline) topological band in their spectrum (though potentially far from EF ). Our findings motivate the formulation of a new periodic table of chemical compounds based on the ubiquity of nontrivial electronic band topology in solid-state materials.

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Reducing Electronic Transport Dimension to Topological Hinge States by Increasing Geometry Size of Dirac Semimetal Josephson Junctions

Cited by 45 publications

References 45 publications

Axionic band topology in inversion-symmetric Weyl-charge-density waves

Axionic band topology in inversion-symmetric Weyl-charge-density waves

Topological Materials Discovery from Crystal Symmetry

All Topological Bands of All Stoichiometric Materials

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