Dresden 2020 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 1: Topological Insulators 1 (joint session TT/HL)

TT 1.5: Vortrag

Montag, 16. März 2020, 10:30–10:45, HSZ 03

Topological invariants to characterize universality of boundary charge in one-dimensional insulators beyond symmetry constraints — •Mikhail Pletyukhov1, Dante Kennes1, Jelena Klinovaja2, Daniel Loss2, and Herbert Schoeller11RWTH Aachen University, Germany — 2University of Basel, Switzerland

We address universal properties of the boundary charge QB for a wide class of tight-binding models with non-degenerate bands in one dimension [1]. We provide a precise formulation of the bulk-boundary correspondence by splitting QB via a gauge invariant decomposition in a Friedel, polarisation, and edge part. We reveal the topological nature of QB by proving the quantization of a topological index IQBρ, where Δ QB is the change of QB when shifting the lattice by one site towards a boundary and ρ is the average charge per site. For a single band we find this index to be given by the winding number of the fundamental phase difference of the Bloch wave function between two adjacent sites. For a given chemical potential we establish a central topological constraint I∈{−1,0} related to charge conservation and particle-hole duality.

[1] M. Pletyukhov et al, arXiv: 1911.06886, 1911.06890

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