Transport of interacting electrons through a double barrier in quantum wires

TL;DR

This paper develops an analytical fermionic renormalization group approach to study electron transport through a double barrier in quantum wires, revealing how interactions influence conductance and tunneling regimes across temperatures.

Contribution

It introduces a systematic method to analyze renormalized scattering in double barrier systems with interactions, extending beyond single impurity models.

Findings

Weak impurities can become effectively strong due to interactions.

A sharp conductance peak can emerge even without a transmission peak.

Different transport regimes are identified depending on temperature and barrier strength.

Abstract

We generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided asymmetry is not too high.