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TT: Fachverband Tiefe Temperaturen

TT 28: Topology: Other Topics

TT 28.1: Vortrag

Dienstag, 19. März 2024, 09:30–09:45, H 3025

Theory of local Z₂ topological markers for finite and periodic systems — •Nicolas Baù and Antimo Marrazzo — Dipartimento di Fisica, Università degli Studi di Trieste, Strada Costiera 11, Trieste, I-34151, Italy

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers have been introduced, allowing to probe the topological order locally in real space even for disordered and inhomogeneous systems [1]. In this talk, I will address time-reversal symmetric systems in two dimensions and introduce two local Z₂ topological markers [2]. The first formulation is based on a generalization of the spin-Chern number [3] while the second one is based solely on time-reversal symmetry [4]. Then, I will introduce a formulation of the local Chern marker for extended systems with periodic boundary conditions [5], and I extend it to the aforementioned Z₂ markers [2]. Finally, I will show numerical simulations to validate the approach, including pristine disordered and inhomogeneous systems, such as topological/trivial heterojunctions.

[1] R. Bianco, R. Resta, Phys. Rev. B 84 (2011) 241106(R)

[2] N. Baù, A. Marrazzo, in preparation

[3] E. Prodan, Phys. Rev. B 80 (2009) 125327

[4] A. A. Soluyanov, D. Vanderbilt, Phys. Rev. B 85 (2012) 115415

[5] N. Baù, A. Marrazzo, arXiv:2310.15783 (2023)

Keywords: Topological invariant; Quantum spin Hall insulators; Local markers; Z2; Disorder