Multicellularity of Delicate Topological Insulators

Nelson, Aleksandra; Neupert, Titus; Bzdušek, Tomáš; Alexandradinata, A.

doi:10.1103/physrevlett.126.216404

Cited by 38 publications

(52 citation statements)

References 61 publications

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“…By referring to the ∆-CSSH flat band case again, we can conclude that the topological states do not only appear because the compact Wannier functions are off-center, but also because they cannot fit inside one unit cell, and this phenomenon cannot be captured by the usual Zak phase. This situation is reminiscent to the results of a very recent work [114], in which the authors propose a 3D topological material in which the topology is also not captured by the standard tenfold classification. The reason for this is that the maximally localized Wannier functions of the system cannot fit into a single primitive unit cell, and this causes the apparition of topological surface states.…”

Section: Form Of the Caged Topological Edge Statesmentioning

confidence: 65%

Tunable zero modes and quantum interferences in flat-band topological insulators

Zurita

Creffield

Platero

2021

Quantum

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We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

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Section: Form Of the Caged Topological Edge Statesmentioning

confidence: 65%

Tunable zero modes and quantum interferences in flat-band topological insulators

Zurita

Creffield

Platero

2021

Quantum

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“…To close, we note that, in addition to the Hopf number, a returning Thouless pump invariant [43][44][45] should be present in the NHIs. Also, it will be interesting to establish the phase diagram in the vicinity of MHSMs, which may include pseudospin-s topological SMs and nodal line SMs, in analogy to recent discussions about the conversion between Weyl points, nodal lines and two-band BD singularities [45,[63][64][65].…”

mentioning

confidence: 90%

“…MHSMs as topological phase transitions. Two-band Hopf insulators (HIs) [41,42] are a well-known example of delicate topological insulators [43], a class of topological phases beyond the tenfold way classification [16]. It was recently pointed out that the topological phase transition (TPT) between such HIs is characterized by quadratic band touching points with Berry dipole structure [43][44][45].…”

mentioning

confidence: 99%

Multifold Hopf semimetals

Graf¹,

Piéchon²

2022

Preprint

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Three-dimensional topological semimetals exhibit linear energy band crossing points that act as monopole sources of Berry curvature. Here, an alternative class of semimetals is introduced, featuring linear N -fold crossing points each of which acts as a source of a Berry dipole. Continuum and lattice models for such multifold Hopf semimetals (MHSMs) are proposed for N = 3, 4, 5. Weak field magnetotransport properties of MHSMs are revealed: a single Berry dipole generates not only an anomalous Hall effect, but also dissipative current contributions to linear order in B, similar to the axial anomaly, chiral magnetic, and magnetochiral effects familiar from a pair of coupled Weyl nodes. For strong B, the Landau level spectrum highlights the importance of quantum geometry: intraband corrections to the Onsager quantization condition crucially depend on the angle between B and the Berry dipole, and interband corrections reflect the strong coupling between degenerate orbits. Finally, it is shown that MHSMs mediate topological phase transitions between N -band Hopf insulators, suggesting them as an ideal playground to explore the physics of delicate topological semimetals and insulators.

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“…For two-band spinless PT -symmetric systems, the winding number of a 2D ICR, i.e., computed on a contour around the corresponding NL, is an integer topological invariant [22]. This integer invariant is delicate [76], in the sense that it ceases to be defined in models with three or more bands. Nevertheless, we are interested in the value of this integer invariant for the 2D ICRs involved in the TPs listed in Table IV, because it determines both the Z 2 -quantized Berry phase [77] as well as the non-Abelian topological invariant [55] carried by the central nodal line in models with three or more bands [56], including the presently studied k • p models of TPs [50].…”

Section: Winding Number Of the 2d Icrsmentioning

confidence: 99%

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

Lenggenhager¹,

Liu²,

Neupert³

et al. 2022

Preprint

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We analyze triply degenerate nodal points [or triple points (TPs) for short] in energy bands of crystalline solids. Specifically, we focus on spinless band structures, i.e., when spin-orbit coupling is negligible, and consider TPs formed along high-symmetry lines in the momentum space by a crossing of three bands transforming according to a 1D and a 2D irreducible corepresentation (ICR) of the little co-group. The result is a complete classification of such TPs in all magnetic space groups, including the non-symmorphic ones, according to several characteristics of the nodal-line structure at and near the TP. We show that the classification of the presently studied TPs is exhausted by 13 magnetic point groups (MPGs) that can arise as the little co-group of a high-symmetry line and which support both 1D and 2D spinless ICRs. For 10 of the identified MPGs, the TP characteristics are uniquely determined without further information; in contrast, for the 3 MPGs containing sixfold rotation symmetry, two types of TPs are possible, depending on the choice of the crossing ICRs. The classification result for each of the 13 MPGs is illustrated with first-principles calculations of a concrete material candidate.

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Multicellularity of Delicate Topological Insulators

Cited by 38 publications

References 61 publications

Tunable zero modes and quantum interferences in flat-band topological insulators

Tunable zero modes and quantum interferences in flat-band topological insulators

Multifold Hopf semimetals

Triple nodal points characterized by their nodal-line structure in all magnetic space groups

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