Regensburg 2022 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 11: Topology: Quantum Hall Systems
TT 11.3: Vortrag
Dienstag, 6. September 2022, 10:00–10:15, H10
Universal properties of boundary and interface charges in multichannel models of one-dimensional insulators — •Kiryl Piasotski1, Niklas Muller1, Dante Kennes1, 2, Herbert Schoeller1, and Mikhail Pletyukhov1 — 1Institut fur Theorie der Statistischen Physik, RWTH Aachen, 52056 Aachen, Germany — 2Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany
Generalizing our previous results on a one-dimensional single-channel continuum [1] and multichannel tight-binding [2] models, we present novel topological invariants to characterize boundary and interface charges in systems described by one-dimensional Schrödinger operators with periodic non-Abelian vector and scalar potentials. In particular, we prove that the change in boundary charge upon the continuous shift of the system towards the boundary by the distance xϕ∈[0, L] (L-period) is given by the sum of the linear function of xϕ and an integer-valued topological index I(xϕ) - the boundary invariant, and provide two equivalent representations of I(xϕ). In addition, we study translationally invariant systems interrupted by a localized impurity, we show that an excess charge on the impurity is a quantized integer quantity given by a winding number expression.
[1] Phys. Rev. B 104, 155409 (2021)
[2] Phys. Rev. B 104, 125447 (2021)