Transmission across non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric quantum dots and ladders
Abstract
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. 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 focus on the case $\phi_L=\phi_R$, for which 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 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-Pérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2022
- arXiv:
- arXiv:2205.08859
- Bibcode:
- 2022arXiv220508859S
- Keywords:
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- Condensed Matter - Mesoscale and Nanoscale Physics;
- Physics - Optics;
- Quantum Physics
- E-Print:
- 10 pages, 10 captioned figures, 1 table. Comments are welcome