2010/10/31 by Ari M. Turner, Yi Zhang, Roger S. K. Mong +1 · 284 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Combinatorics #Computer science #Geometry #Homogeneous space #Mathematics #Modulo #Parameterized complexity #Physics #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topology (electrical circuits) #Trim #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.85.165120
published in Physical Review B 85(16) (American Physical Society) · 12 pages main text; 12 pages appendices; 11 figures. Added new refs. in 2nd version
arxiv created 2010/12/04 · openalex publication_date 2012/04/12 · arxiv updated 2012/09/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \ensuremathθ, can be defined, and is quantized to \ensuremathθ=0,\phantom\rule0.16em0ex\ensuremathπ. The value is \ensuremathπ 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 \ensuremathθ. 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.