Dear friends, please join my talk and webinar hosted by Wolfram Research, Inc.:
Unravelling the Edge Spectra of Non-Hermitian Chern Insulators
Wednesday DEC 14 at 7:00 PM EET (GMT +2:00)
PRESENTER: Dr. James Bartlett
Department of Physics and Astronomy, George Mason University.
REGISTER HERE: https://wolfr.am/ChernInsulators
About This Webinar
Learn about innovative scientific research that offers insightful analysis and applies Wolfram Language as an important investigative tool. At this webinar, James Bartlett will talk about the research behind his recent paper, including phase diagrams and visualizations of Generalized Brillouin Zone surfaces.
Research summary
ARTICLE: https://doi.org/10.48550/arXiv.2209.06774
DISCUSSION: https://community.wolfram.com/groups/-/m/t/2739305
ABSTRACT: Non-Hermitian Chern insulators differ from their Hermitian cousins in one key aspect: their edge spectra are incredibly rich and confounding. For example, even in the simple case where the bulk spectrum consists of two bands with Chern number ±1, the edge spectrum in the slab geometry may have one or two edge states on both edges, or only at one of the edges, depending on the model parameters. This blatant violation of the familiar bulk-edge correspondence casts doubt on whether the bulk Chern number can still be a useful topological invariant, and demands a working theory that can predict and explain the myriad of edge spectra from the bulk Hamiltonian to restore the bulk-edge correspondence. We outline how such a theory can be set up to yield a thorough understanding of the edge phase diagram based on the notion of the generalized Brillouin zone (GBZ) and the asymptotic properties of block Toeplitz matrices. The procedure is illustrated by solving and comparing three non-Hermitian generalizations of the Qi-Wu-Zhang model, a canonical example of two-band Chern insulators. We find that, surprisingly, in many cases the phase boundaries and the number and location of the edge states can be obtained analytically. Our analysis also reveals a non-Hermitian semimetal phase whose energy-momentum spectrum forms a continuous membrane with the edge modes transversing the hole, or genus, of the membrane. Subtleties in defining the Chern number over GBZ, which in general is not a smooth manifold and may have singularities, are demonstrated using examples. The approach presented here can be generalized to more complicated models of non-Hermitian insulators or semimetals in two or three dimensions.
