Quantum transport in the presence of a finite-range time-modulated potential

TL;DR

This paper investigates quantum transport through a narrow constriction with a finite-range, time-modulated potential, revealing conductance dips and peaks related to quasi-bound states, applicable in gate-controlled quantum devices.

Contribution

It introduces a detailed analysis of finite-range, time-modulated potentials in quantum transport, extending previous models to include finite spatial extent and practical potential configurations.

Findings

Conductance exhibits dips and peaks at energies nħω above subband thresholds.

Dips are narrower for smaller potential range and amplitude, indicating quasi-bound state formation.

Results connect finite-range potentials to the delta-profile limit for small parameters.

Abstract

Quantum transport in a narrow constriction, and in the presence of a finite-range time-modulated potential, is studied. The potential is taken the form $V(x,t) = V_{0} \theta(x)\theta(a-x)\cos(\omega t)$, with $a$ the range of the potential and $x$ the transmission direction. As the chemical potential $\mu$ is increasing, the dc conductance $G$ is found to exhibit dip, or peak, structures when $\mu$ is at $n\hbar\omega$ above the threshold energy of a subband. These structures in $G$ are found in both the small $a$ ($a \ll \lambda_{F}$) and the large $a$ ($a \gg \lambda_{F}$) regime. The dips, which are associated with the formation of quasi-bound states, are narrower for smaller $a$, and for smaller $V_{0}$. The locations of these dips are essentially fixed, with small shifts only in the case of large $V_{0}$. Our results can be reduced to the limiting case of a delta-profile oscillating potential when both $a$ and $V_{0}a$ are small. The assumed form of the time-modulated potential is expected to be realized in a gate-induced potential configuration.