Dislocation charges reveal two-dimensional topological crystalline invariants

Miert, Guido van; Ortix, Carmine

doi:10.1103/physrevb.97.201111

Cited by 35 publications

(26 citation statements)

References 43 publications

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“…This one-to-one correspondence only works in crystals possessing an even-fold rotational symmetry, and thus exclude C 3 -symmetric crystals such as the kagome lattice. We wish to remark, however, that even though the breathing kagome lattice does not display a genuine bulk-corner correspondences, its underlying crystalline topology is still reflected in the fractional charge at corners or other topological defects, such as dislocations 50 .…”

Section: Discussionmentioning

confidence: 97%

On the topological immunity of corner states in two-dimensional crystalline insulators

Miert

Ortix

2020

npj Quantum Mater.

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A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragile: the kagome lattice does not realize a higher-order topological insulator. We support this finding by introducing a criterion based on a corner charge-mode correspondence for the presence of topological midgap corner modes in n-fold rotational symmetric chiral insulators that explicitly precludes the existence of a HOTI protected by a threefold rotational symmetry.

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Section: Discussionmentioning

confidence: 97%

On the topological immunity of corner states in two-dimensional crystalline insulators

Miert

Ortix

2020

npj Quantum Mater.

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“…In some cases, such topologically nontrivial phases without protected boundary states are characterized by other observable signatures, such as the presence of boundary charges (not states! ), 51,67 or quantized electric 32,33,[68][69][70] or magnetic moments. Such sig-natures of a nontrivial bulk topology are not part of the higher-order bulk boundary correspondence that we establish here, and it is an interesting open problem how they can be incorporated.…”

Section: Discussionmentioning

confidence: 99%

Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases

2019

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We study the bulk-boundary correspondence for topological crystalline phases, where the crystalline symmetry is an order-two (anti)symmetry, unitary or antiunitary. We obtain a formulation of the bulk-boundary correspondence in terms of a subgroup sequence of the bulk classifying groups, which uniquely determines the topological classification of the boundary states. This formulation naturally includes higher-order topological phases as well as topologically nontrivial bulk systems without topologically protected boundary states. The complete bulk and boundary classification of higher-order topological phases with an additional order-two symmetry or antisymmetry is contained in this work.

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“…For instance, the electric polarization of an inversion-symmetric one-dimensional atomic chain is either integer or semi-integer, with a quantized value that does not depend upon microscopic details, but is rather encoded in a gauge-invariant topological index 28 . More recently, it has been shown that excess electronic charges localized at various topological defects, such as dislocations, can be (fractionally) quantized, thus representing yet other incarnations of bulk quantities encoded in topological invariants [29][30][31][32][33][34] . Quantized charges appearing at the corners and disclinations of two-dimensional crystals have been very recently measured in metamaterials [35][36][37] and proposed to appear in recently synthesized materials structures 38 .…”

Section: Introductionmentioning

confidence: 99%

“…This is because Kramers' theorem inevitably doubles the electronic charges, making the real-space invariants partially, often completely, trivial. Progress can be made identifying (partial) Berry phase 29 invariants and/or using Wilson loops as topological indices [45][46][47][48][49] as exemplified by the bulk-dislocation charge correspondence of rotation-symmetric two-dimensional crystals 31 . This additional knowledge, however, does not completely determine the (fractional) quantized electronic charges at the crystal boundaries.…”

Section: Introductionmentioning

confidence: 99%

The bulk-corner correspondence of time-reversal symmetric insulators

2021

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The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To do so we develop partial real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These previously unknown crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.

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Dislocation charges reveal two-dimensional topological crystalline invariants

Cited by 35 publications

References 43 publications

On the topological immunity of corner states in two-dimensional crystalline insulators

On the topological immunity of corner states in two-dimensional crystalline insulators

Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases

The bulk-corner correspondence of time-reversal symmetric insulators

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