Generalized bulk-edge correspondence for non-hermitian topological systems

Ken-Ichiro Imura (Hiroshima U.)

Non-hermitian topological phases attract much attention recently. Primarily in theory, 
but some experiments have been already done in photonic and phononic systems. 
Yet, non-hermitian (topological) systems are still enigmatic in many respects. For example, 
in the presence of anisotropic hopping [1,2], non-hermitian skin effect makes the concept 
of bulk and edge ambiguous. As a result, the bulk-edge correspondence [3], the defining 
property of topological quantum phases, does not stand on its own, as it usually does in 
hermitian systems.

In the standard bulk-edge correspondence, a bulk topological number is first defined and 
calculated for a purely bulk system, which is realized (at least in theory) by employing a 
periodic boundary condition. This topological number is used for predicting what happens 
(whether topological edge states appear or not) in the actual bulk (+ possibly edge) system 
under an open boundary. This simple scenario breaks down in non-hermitian topological 
systems, because the spectrum (and the corresponding wave function also) of the periodic 
system is very different from those under open boundary. The underlying reason is again the 
non-hermitian skin effect. Here, we propose a recipe to deal with this non-hermitian skin 
effect, in the form of <<modified periodic boundary condition>> [4], which makes possible a 
smooth evolution from a purely bulk to bulk+edge system.

[1] S. Yao and Z. Wang, Phys. Rev. Lett. 121, 086803 (2018).
[2] K. Yokomizo, S. Murakami, arXiv:1902.10958.
[3] Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[4] K.-I. Imura, Y. Takane, arXiv:1908.xxxxx