Spectral analysis, chiral disorder and topological edge states manifestation in open non-Hermitian Su-Schrieffer-Heeger chains

We investigate topological and disorder effects in non-Hermitian systems with chiral symmetry. The system under consideration consists in a finite Su-Schrieffer-Heeger chain to which two semi-infinite leads are attached. The system lacks the parity-time and time-reversal symmetries and is appropriate for the study of quantum transport properties. The complex energy spectrum is analyzed in terms of the chain-lead coupling and chiral disorder strength, and shows substantial differences between chains with even and odd number of sites. The mid-gap edge states acquire a finite lifetime and are both of topological origin or generated by a strong coupling to the leads. The disorder induces coalescence of the topological eigenvalues, associated with exceptional points and vanishing of the eigenfunction rigidity. The electron transmission coefficient is approached in the Landauer formalism, and an analytical expression for the transmission in the range of topological states is obtained. Notably, the chiral disorder in this non-Hermitian system induces unitary conductance enhancement in the topological phase.