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TT: Fachverband Tiefe Temperaturen

TT 12: Topological Insulators 2 (joint session TT/HL)

TT 12.5: Vortrag

Montag, 16. März 2020, 16:00–16:15, HSZ 103

Analytic continuation of Bloch states and the significance for universal boundary physics — Mikhail Pletyukhov¹, Dante Kennes¹, Jelena Klinovaja², Daniel Loss², and •Herbert Schoeller¹ — ¹RWTH Aachen University, Germany — ²University of Basel, Switzerland

For generic tight-binding models in one dimension with non-degenerate bands we present an analytic continuation of Bloch states to complex quasimomentum [1], useful for an understanding of boundary physics in half-infinite systems. We show that the pole positions provide the oscillation frequency and localization length of edge states and the branching points define the corresponding quantities for the total density. Each edge state is shown to have a fingerprint in the bulk density which cancels exactly the edge state density. The remaining part of the density is shown to have a pre-exponential power-law with universal exponent -1/2. Introducing a phase variable which continuously shifts the boundary, we derive topological constraints for the edge modes and show that the pole positions oscillate around the branch cuts. We find that the phase dependence of the model parameters can always be chosen such that no edge mode crosses the chemical potential when shifting the boundary by one lattice site. This provides a rigorous proof for universal properties of the boundary charge found in Ref.[2].

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

[2] M. Pletyukhov et al., arXiv:1911.06890.