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

• URL: http://arxiv.org/abs/2205.08859v2
• Date: Mon, 7 Nov 2022 12:52:29 GMT
• Title: Transmission across non-Hermitian $\mathcal{PT}$-symmetric quantum dots and ladders
• Authors: Abhiram Soori, M. Sivakumar, V. Subrahmanyam
• Abstract summary: We study the scattering across a non-Hermitian $mathcalPmathcalT$-symmetric two-level quantum dot(QD) connected to two semi-infinite one-dimensional lattices. We find that the transmission across the QD can be perfect in the $mathcalPmathcalT$-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the $mathcalPmathcalT$-broken phase (corresponding to purely
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• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 ($\hbar\phi_{L} /e,~\hbar\phi_{R} /e$) through two loops in the system. We show that when $\phi_L=\phi_R$, 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 $\pi\hbar/2e$). 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-P\'erot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.

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