Complex Wannier centers and non-reciprocal Wannier functions in non-Hermitian insulators

The non-Hermitian skin effect is the hallmark of non-Hermitian topological systems with an energy point gap. In contrast, non-Hermitian insulators with line gaps have received little attention, as they are smoothly connected to Hermitian systems.

In this talk, we systematically investigate the implications of non-Hermiticity in Wilson loops (WLs) of insulators with a line gap. We show that the WL (an intensive object) remains nonunitary in the thermodynamic limit and yields complex Wannier centers (WCs), which have observable implications on their Wannier functions. As an illustrative example, we show that for pseudo-Hermitian Hamiltonians, the WL becomes pseudo-unitary and the anti-Hermitian component of the Wannier Hamiltonian acquires chiral symmetry—yielding either static Wannier functions or counterpropagating pairs related by the pseudo-Hermitian metric.