Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators

By Chen Fang, M. Gilbert, Bogdan Andrei Bernevig. 2012

337 citations recorded by the source corpus.

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number of a Cn-invariant insulator can be determined, up to a multiple of n, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a Cn-invariant insulator is also determined, up to a multiple of n ,b y theCn eigenvalue of the Slater determinant of a noninteracting many-body system; and (iii) the Chern number vanishes in insulators with dihedral point groups Dn, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that (i) only insulators with point groups Cn, Cnh ,a nd Sn PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization P3 in the term P3E · B, the axion term in the electrodynamics of the insulator (medium).

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/54801f98211fd11082f4985dbd564a7828bdfb43

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. E. Khalaf
3. Hsin Lin
4. H. Po
5. Arun Bansil
6. Tanmoy Das
7. T. Hughes
8. Wladimir A. Benalcazar

In Materials Chemistry

1. Ashvin Vishwanath
2. E. Khalaf
3. Hsin Lin
4. Arun Bansil
5. H. Po
6. Tanmoy Das
7. T. Hughes
8. Ze-Guo Chen

Citations in the corpus

• Topological Classification of Crystalline Insulators through Band Structure Combinatorics (2016, neutral): “For the specific case of the space group p 4 mm , there are no Chern numbers [20] because of the reflection symmetry in D 4 , so its topological phases within class A are completely specified once the representation of the set of valence bands is known.”
• Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi2Te4 (2019, background): “[7] C.”
• Triple Point Topological Metals (2016, methodology): “If the Hamiltonian has a symmetry R, it can be shown that [73]”
• Tunable topological phononic crystals (2015, background): “Recently, the Chern number was found to be constrained by the symmetry properties of the eigenstates at high symmetry points [34].”
• Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, methodology): “The eigenvalues of the fourfold rotation determine Cðkz1⁄40Þ M mod 4 [37].”
• Quantization of fractional corner charge in Cn -symmetric higher-order topological crystalline insulators (2018, methodology): “where a1 and a2 are primitive unit lattice vectors and the components p1 and p2 are topological indices that correspond to quantized Berry phases along the noncontractible loops of the Brillouin zone (BZ) [6, 10, 11, 44].”
• Colloquium : Topological band theory (2016, background): “(Hasan and Kane 2010; Kitaev 2009; Schnyder et al. 2008; Fang, Gilbert, and Bernevig 2012; Slager et al. 2013; Chiu, Yao, and Ryu 2013; Hughes, Prodan, and Bernevig 2011; Shiozaki and Sato 2014)”