Coulomb blockade in a quantum wire with long-range Coulomb interactions

TL;DR

This paper investigates how long-range Coulomb interactions affect electron transport in a one-dimensional quantum wire with impurities, revealing that conductance diminishes rapidly at low temperatures and resonant tunneling is suppressed.

Contribution

It introduces a detailed analysis of Coulomb blockade effects in quantum wires considering long-range interactions, showing deviations from standard Luttinger liquid behavior.

Findings

Conductance decreases faster than any power law as temperature approaches zero.

Long-range Coulomb interactions cause barriers to become effectively stronger at low temperatures.

Resonant tunneling is suppressed at zero temperature due to Coulomb blockade effects.

Abstract

We study the transport through two impurities or ``barriers'' in a one-dimensional quantum wire, taking into account the long-range $\frac1r$ Coulomb interactions. We compute the temperature-dependent conductance $G(T)$ of this system. Long-range forces lead to a dramatic increase of weak barrier potentials with decreasing temperature, even in the ``resonant'' case. The system thus always reaches a ``strong barrier'' regime in which only charge is pinned, contrary to the standard LL case. $G(T)$ vanishes faster than any power as $T$ goes to zero. In particular, resonant tunneling is suppressed at zero temperature.