Space group constraints on weak indices in topological insulators

Varjas, Dániel; Juan, Fernando de; Lü, Yuan

doi:10.1103/physrevb.96.035115

Cited by 13 publications

(13 citation statements)

References 54 publications

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“…The above picture is, in fact, quite general: it applies to a large class of DSTIs arising in settings where the realspace deformation of "weak-0" to "weak-1/2" is forbidden by symmetry, as in the case when inversion [24] and/ or nonsymmorphic [14][15][16]42] symmetries are present. In particular, we note that the glide-protected TCI showcasing the "hourglass fermion" surface states also falls into this category [14,15,42].…”

Section: Stable Topological Phasesmentioning

confidence: 99%

“…Such bulkboundary correspondence is an important attribute of such topological phases, and it plays a key role in their classification, which has been achieved in arbitrary spatial dimensions [2][3][4]. Crystals, however, frequently exhibit a far richer set of spatial symmetries, like lattice translations, rotations, and reflections, which can also protect new topological phases of matter [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

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confidence: 99%

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Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators

et al. 2018

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The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the symmetries at hand. While isolated examples of TCI have been identified and studied, the same variety demands a unified theoretical framework. In this work, we show how the surfaces of TCIs can be analyzed within a general surface theory with multiple flavors of Dirac fermions, whose mass terms transform in specific ways under crystalline symmetries. We identify global obstructions to achieving a fully gapped surface, which typically lead to gapless domain walls on suitably chosen surface geometries. We perform this analysis for all 32 point groups, and subsequently for all 230 space groups, for spin-orbit-coupled electrons. We recover all previously discussed TCIs in this symmetry class, including those with "hinge" surface states. Finally, we make connections to the bulk band topology as diagnosed through symmetry-based indicators. We show that spin-orbit-coupled band insulators with nontrivial symmetry indicators are always accompanied by surface states that must be gapless somewhere on suitably chosen surfaces. We provide an explicit mapping between symmetry indicators, which can be readily calculated, and the characteristic surface states of the resulting TCIs. arXiv:1711.11589v3 [cond-mat.str-el]

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Section: Stable Topological Phasesmentioning

confidence: 99%

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confidence: 99%

Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators

et al. 2018

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“…Spatial symmetries have enriched the topological classification of insulators and superconductors [1][2][3][4][5][6][7][8][9][10]. A basic geometric property that distinguishes spatial symmetries regards their transformation of the spatial origin: symmorphic symmetries preserve the origin, while nonsymmorphic symmetries unavoidably translate the origin by a fraction of the lattice period [11].…”

Section: Introductionmentioning

confidence: 99%

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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“…However, these bands are generally not separated from each other, instead they are entangled due to certain symmetries. In our case of space group P4 1 32, non-symmorphic screw symmetry S 4 dictates that bands always appear in quadruplets that cannot be disentangled [38][39][40][41]. Meanwhile, time reversal symmetry T leads to an extra 2-fold band degeneracy at high symmetry points in k-space.…”

Section: A Gapped Vs Gapless Statesmentioning

confidence: 80%

Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na4Ir3O8

2017

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Na 4 Ir 3 O 8 provides a material platform to study three-dimensional quantum spin liquids in the geometrically frustrated hyperkagome lattice of Ir 4+ ions. In this work, we consider quantum spin liquids on hyperkagome lattice for generic spin models, focusing on the effects of anisotropic spin interactions. In particular, we classify possible Z 2 and U(1) spin liquid states, following the projective symmetry group analysis in the slave-fermion representation. There are only three distinct Z 2 spin liquids, together with 2 different U(1) spin liquids. The nonsymmorphic space group symmetry of hyperkagome lattice plays a vital role in simplifying the classification, forbidding "π-flux" or "staggered-flux" phases in contrast to symmorphic space groups. We further prove that both U(1) states and one Z 2 state among all 3 are symmetry-protected gapless spin liquids, robust against any symmetry-preserving perturbations. Motivated by the "spin-freezing" behavior recently observed in Na 4 Ir 3 O 8 at low temperatures, we further investigate the nearest-neighbor spin model with dominant Heisenberg interaction subject to all possible anisotropic perturbations from spin-orbit couplings. We found a U(1) spin liquid ground state with spinon fermi surfaces is energetically favored over Z 2 states. Among all spin-orbit coupling terms, we show that only Dzyaloshinskii-Moriya (DM) interaction can induce spin anisotropy in the ground state when perturbing from the isotropic Heisenberg limit. Our work paves the way for a systematic study of quantum spin liquids in various materials with a hyperkagome crystal structure.

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Space group constraints on weak indices in topological insulators

Cited by 13 publications

References 54 publications

Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators

Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators

Topological Insulators from Group Cohomology

Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na4Ir3O8

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