Dresden 2020 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 2: Topological Insulators 1 (jointly with DS, MA, HL, O) (joint session TT/HL)

HL 2.5: Talk

Monday, March 16, 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 Schoeller¹ — ¹RWTH Aachen University, Germany — ²University of Basel, Switzerland

We address universal properties of the boundary charge Q_B 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 Q_B via a gauge invariant decomposition in a Friedel, polarisation, and edge part. We reveal the topological nature of Q_B by proving the quantization of a topological index I=Δ Q_B − ρ, where Δ Q_B is the change of Q_B 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