Transmission across nonHermitian $\mathcal{P}\mathcal{T}$symmetric quantum dots and ladders
Abstract
We propose a model and study the scattering across a nonHermitian $\mathcal{P}\mathcal{T}$symmetric twolevel quantum dot (QD) connected to two semiinfinite onedimensional lattices. AharonovBohm 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 foursite toy model. We extend the model to a $\mathcal{P}\mathcal{T}$symmetric ladder connected to two semiinfinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to FabryPérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08859
 Bibcode:
 2022arXiv220508859S
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Physics  Optics;
 Quantum Physics
 EPrint:
 10 pages, 10 captioned figures, 1 table. Comments are welcome