Antiferromagnetic topological insulators

Mong, Roger S. K.; Essin, Andrew M.; Moore, Joel E.

doi:10.1103/physrevb.81.245209

Cited by 632 publications

(605 citation statements)

References 35 publications

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“…Thus far, all experimentally tested topological insulators have relied on symmorphic space groups [12][13][14][15][16][17]. Here, we propose the first nonsymmorphic theory of time-reversal-invariant insulators, which complements previous theoretical proposals with magnetic, nonsymmorphic space groups [4,5,[18][19][20]. Motivated by our recently proposed KHgX material class (X ¼ Sb, Bi, As) [21], we present here a complete classification of spin-orbit-coupled insulators with the space group (D 4 6h ) of KHgX.…”

Section: Introductionsupporting

confidence: 61%

“…The advantage of this analogy is that the Wilson bands may be interpolated [35,38] [39], and all topological insulators with robust edge states protected by space-time symmetries. Here, we refer to topological insulators with either symmorphic [1,2,8] or nonsymmorphic spatial symmetries [4,7,19,40], the time-reversal-invariant quantum spin Hall phase [25], and magnetic topological insulators [18,[41][42][43]. These case studies are characterized by extensions of G ∘ by TABLE I.…”

Section: Summary Of Resultsmentioning

confidence: 99%

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Topological Insulators from Group Cohomology

2016

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We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as "piecewise topological," in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.

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Section: Introductionsupporting

confidence: 61%

Section: Summary Of Resultsmentioning

confidence: 99%

Topological Insulators from Group Cohomology

2016

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“…Finally, notice that for a three-dimensional antiferromagnetic insulator, the Refs. [5,7] proposed a topological index involving the B-TRIM only. It would be interesting to verify whether in three dimensions the absence of symmetry between the A-TRIM could affect this result as it does in two dimensions.…”

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confidence: 99%

“…Néel antiferromagnetism explicitly violates the symmetry with respect to time reversal Θ. However, both the Θ and the translation T a by half the Néel period invert the local magnetization, and thus the combination Θ AF ≡ ΘT a of the two remains a symmetry.A number of authors [5][6][7][8][9][10][11] attempted to classify the topological phases that may appear in an antiferromagnet. However, contrary to the paramagnetic case, the relevant anti-unitary operator does not square to -1: instead, its action on a Bloch eigenstate |Ψ n,k is given by Θ 2 AF |Ψ n,k = −e i2k.a |Ψ n,k .…”

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Z 2 antiferromagnetic topological insulators with broken C 4 symmetry

2017

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A two-dimensional topological insulator may arise in a centrosymmetric commensurate Néel antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a symmetry. Fang et al., [Phys. Rev. B 88, 085406 (2013)] proposed an expression for a Z2 topological invariant to characterize such systems. Here, we show that this expression does not allow to detect all the existing phases if a certain lattice symmetry is lacking. We implement numerical techniques to diagnose topological phases of a toy Hamiltonian, and verify our results by computing the Chern numbers of degenerate bands, and also by explicitly constructing the edge states, thus illustrating the efficiency of the method.Physical phenomena, whose description involves topology, have been invariably attracting attention regardless of whether the word "topology" was actually used at the time: early examples involve topologically non-trivial stable defects such as dislocations in crystals, as well as vortices in superconductors and superfluids. Quantum Hall Effect and its remarkably precise conductance quantization [1] marked the advent of an entirely new class of phenomena, related not so much to the appearance in the sample of finite-size topological objects, but rather to the electron state of the entire sample changing its topology in a way, that could no longer be undone by a local perturbation. More recently, it was understood that, in fact, non-trivial topology may appear even in zero magnetic field: the fact that a commonplace band insulator may find itself in distinct electron states that cannot be continuously transformed one into another without a phase transition, came as a major surprise [2,3].These phenomena invite the question of classifying topologically distinct states of matter: labeling each state by a set of discrete indices in such a way as to have different sets for any two phases that cannot be continuously transformed one into another without the system undergoing a phase transition. In the general setting, the problem remains unsolved.In fact, open questions are present even in a noninteracting description of systems that are believed to admit a Z 2 ("even-odd") classification, and thus have only one topologically trivial and one topologically non-trivial phase, commonly called topological. Here, we address one such question, that has recently attracted attention: diagnosing the topological phase of a Z 2 insulating Néel antiferromagnet.To put the subsequent presentation in context, we recapitulate the key results for the prototypical Z 2 system: a paramagnetic topological insulator. Fu and Kane [4] have shown that the Z 2 invariant for such a system can be defined via the so-called sewing matrix w(k) mn :where the |Ψ n,k is the Bloch eigenstate of the n-th band at momentum k. The w(k) mn turns out to be of particular interest at special momenta Γ i such that −Γ i = Γ i + G, with G a reciprocal lattice vector. Such Γ i are now commonly called the "time reversal-i...

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Two‐Dimensional Topological States

2022

Calculations and Simulations of Low‐Dimensional Materials

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Antiferromagnetic topological insulators

Cited by 632 publications

References 35 publications

Topological Insulators from Group Cohomology

Topological Insulators from Group Cohomology

Z 2 antiferromagnetic topological insulators with broken C 4 symmetry

Two‐Dimensional Topological States

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