Quantized response and topology of magnetic insulators with inversion symmetry

By Ari M. Turner, Yi Zhang, Roger S. K. Mong, Ashvin Vishwanath. 2010

191 citations recorded by the source corpus.

We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such materials' behavior is determined by just the eigenvalues under inversion symmetry of occupied states at time reversal invariant momenta (TRIM parities). In particular, if the total number of $\ensuremath{-}1$ eigenvalues at all TRIMs is odd then the material cannot be an insulator. A likely possibility is that it is then a ``Weyl'' semimetal. Additionally if the material is an insulator and has vanishing Hall conductivity, then a magnetoelectric response, parameterized by $\ensuremath{\theta}$, can be defined, and is quantized to $\ensuremath{\theta}=0,\phantom{\rule{0.16em}{0ex}}\ensuremath{\pi}$. The value is $\ensuremath{\pi}$ if the total number of TRIM parities equal to $\ensuremath{-}1$ is twice an odd number. This generalizes the rule of Fu and Kane that applies to materials in which time reversal is unbroken. This result may be useful in the search for magnetic insulators with large $\ensuremath{\theta}$. These two results are obtained as part of a classification of the band topology of inversion-symmetric insulators. Such band structures can be classified by two sets of numbers: the TRIM parities and three Chern numbers. The TRIM parities have the physical implications just described, and additionally they constrain the values of the Chern numbers modulo 2. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground-state wave function.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/ba8ca792df364a4d1c3d5495fb0cccd65d697f5a

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In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. N. P. Armitage
3. Z. Fang
4. H. Weng
5. X. Dai
6. E. Mele
7. Chen Fang
8. T. Hughes

In Condensed Matter Physics

1. Ashvin Vishwanath
2. Luka Trifunovic
3. P. Brouwer
4. H. Weng
5. X. Dai
6. Z. Fang
7. Chen Fang
8. E. Khalaf

Citations in the corpus

• Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides (2014, background): “011029-6”
• Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, background): “[6] and by us [16] for the classification of inversion-symmetric and mirror-symmetric topological insulators and superconductors,”
• Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, background): “Thispair ofDiracnodes cannotbe removedwithoutbreaking the symmetries [35,36] or changing the symmetry class (say, by introducing spin-orbit coupling), and hence, we conclude that the 2 ∈ Z4 entry in the XBS diagnosis is enforced to be semimetallic by the symmetry representations.”
• Weyl and Dirac semimetals in three-dimensional solids (2017, background): “However, at γ = 0, the parity eigenvalue of the Γ point shows the bands are inverted and it is readily shown that this immediately implies Weyl nodes, i.e. an odd number of inverted parity eigenvalues is a diagnostic of Weyl physics (Hughes et al., 2011; Turner et al., 2012; Wang et al., 2016h).”