Transmission across non-HermitianPT-symmetric quantum dots and ladders

A non-Hermitian (NH) region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even aPT-symmetric region that contains both a source and a sink does not lead to current conservation plainly. We propose a model and study the scattering across a NHPT-symmetric two-level quantum dot (QD) connected to two semi-infinite one-dimensional lattices in a special way so that the probability current is conserved. Aharonov-Bohm type phases are included in the model, which arise from magnetic fluxes (ℏϕL/e, ℏϕR/e) through two loops in the system. We show that whenϕL=ϕR, the probability current is conserved. We find that the transmission across the QD can be perfect in thePT-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in thePT-broken phase (corresponding to purely imaginary eigenenergies of the QD). The two transmission peaks have the same width only for special values of the fluxes (being odd multiples ofπℏ/2e). In the broken phase, the transmission peak is surprisingly not at zero energy. We give an insight into this feature through a four-site toy model. We extend the model to aPT-symmetric ladder connected to two semi-infinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to Fabry-Pérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.