Bulk-boundary correspondence and infernal points in the non-Hermitian trimer Su-Schrieffer-Heeger model

We investigated a one-dimensional non-Hermitian trimer Su-Schrieffer-Heeger (SSH) model with nonreciprocal intercell couplings. By constructing the non-Bloch Hamiltonian and analyzing the non-Hermitian skin effect, we demonstrated that the boundary states exhibit qualitative similarities to those in the Hermitian case, albeit emerging at distinct locations. We established the bulk-boundary correspondence through numerical calculations of the non-Hermitian sublattice Zak phase. Furthermore, we extended the concept of the sublattice winding number to define the non-Hermitian sublattice winding number and derived its exact analytical expression. The role of the non-Hermitian sublattice winding number in characterizing topological properties is analogous to that of the non-Hermitian sublattice Zak phase. The non-Hermitian sublattice winding number provides a different approach to characterizing the bulk-boundary correspondence in non-Hermitian systems lacking chiral symmetry. Finally, by applying the criterion for the infernal points (IPs) in non-Hermitian systems, the IPs in the non-Hermitian trimer SSH model are identified.