Correspondence between winding numbers and skin modes in non-hermitian systems

2019/10/31 by Kai Zhang, Zhesen Yang, Chen Fang · 5 citations
Physics and Astronomy · #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.125.126402

published as Phys. Rev. Lett. 125, 126402 (2020) · 22 pages, 10 figures. To appear in Physical Review Letters

arxiv created 2020/08/25 · arxiv updated 2020/09/23

Abstract

We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary condition in non-hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the non-vanishing current through the system.

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