Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders

Abstract

A non-Hermitian 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 a $\mathcal{P}\mathcal{T}$-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 non-Hermitian $\mathcal{P}\mathcal{T}$-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 ($\hslash {\varphi }_L/e,\hslash {\varphi }_R/e$) through two loops in the system. We show that when ${\varphi }_L={\varphi }_R$, the probability current is conserved. We find that the transmission across the QD can be perfect in the $\mathcal{P}\mathcal{T}$-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the $\mathcal{P}\mathcal{T}$-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 of $\pi \hslash /2e$). 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 a $\mathcal{P}\mathcal{T}$-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.

11 pages, 10 captioned figures, 1 table

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Cited by in corpus (4)

• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Floquet Exceptional Topological Insulator
• Fabry-Pérot interference in Josephson junctions
• Transverse currents in spin transistors