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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 conditions 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 nonvanishing current through the system.
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Kai Zhang
Zhesen Yang
Chen Fang
Physical Review Letters
Chinese Academy of Sciences
University of Chinese Academy of Sciences
Institute of Physics
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Zhang et al. (Tue,) studied this question.
www.synapsesocial.com/papers/69d77fd13fae90fd6048f83d — DOI: https://doi.org/10.1103/physrevlett.125.126402