Inversion-symmetric topological insulators
By T. Hughes, E. Prodan, Bogdan Andrei Bernevig. 2010
366 citations recorded by the source corpus.
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer $\mathcal{N}$, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is ``topological.'' We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion symmetric points and charge polarization. In two dimensions, we prove a link between the product of the inversion eigenvalues and the parity of the Chern number of the occupied bands. In three dimensions, we find a topological constraint on the product of the inversion eigenvalues thereby showing that some $3$D materials are protected topological metals; we show the link between the inversion eigenvalues and the $3$D Quantum Hall Effect, and analyze the magnetoelectric polarization ($\ensuremath{\theta}$ vacuum) in the absence of time-reversal symmetry.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/0d9408b4acd6ed0da94dfe93a3cd14a35a5da9fd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Topological Semimetals from First Principles (2018, methodology): “Specific cases where such an approach applies were known, as for instance the inversion-eigenvalue formula for detecting Weyl points (166), and the methods relying on symmetry indicators promote these specific examples to a comprehensive and systematic framework.”
- 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).”
- A quantized microwave quadrupole insulator with topologically protected corner states (2017, background): “The simplest model of a system with a quantized dipole moment is a two-band insulator in 1D [12] which, due to the presence of chiral or inversion symmetries [13, 14], exhibits quantized fractional edge charges of ±e/2 when its band structure is topological.”
- Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides (2014, background): “011029-6”
- Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, background): “A nontrivial classifying group KðdÞ indicates the existence of multiple topologically distinct atomic-limit phases [22,50,51].”
- Topological crystalline insulators in the SnTe material class (2012, background): “…Bansil,2 and Liang Fu1, ∗ 1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 2Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA 3Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics,Tsinghua University,…”