Interacting electrons with spin in a one-dimensional wire connected to leads

TL;DR

This paper studies the effects of electron interactions and spin in a one-dimensional wire connected to leads, analyzing correlation functions, proximity effects, conductance, and fluctuations across different regimes of temperature and interaction strength.

Contribution

It provides a detailed analysis of correlation functions, proximity effects, and conductance in interacting spinful electrons in a 1D wire with leads, including effects of backscattering and impurities.

Findings

Charge and spin separation persists in the wire.

Proximity effect related to Andreev reflection is studied.

Conductance fluctuations depend on interactions and temperature.

Abstract

We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of an incident electron even in the noninteracting leads. The Fourier transform of nonlocal correlation functions are computed for $T\gg \omega$. In particular, this allows us to study the proximity effect, related to the Andreev reflection. A new type of proximity effect emerges when the wire has normally a tendency towards Wigner crystal formation. The latter is suppressed by the leads below a space--dependent crossover temperature; it gets dominated everywhere by the $2k_F$ CDW at $T<L^{3/2 (K-1)}$ for short range interactions with parameter $K<1/3$. The lowest--order renormalization equations of a weak backscattering potential are derived explicitly at finite temperature. A perturbative expression for the conductance in the presence of a potential with arbitrary spatial extension is given. It depends on the interactions, but is also affected by the noninteracting leads, especially for very repulsive interactions, $K<1/3$. This leads to various regimes, depending on temperature and on $K$. For randomly distributed weak impurities, we compute the conductance fluctuations, equal to that of $R=g-2e^2 /h$. While the behavior of $Var(R)$ depends on the interaction parameters, and is different for electrons with or without spin, and for $K<1/3$ or $K>1/3$, the ratio $Var(R)/R^2$ stays always of the same order: it is equal to $L_T/L\ll 1$ in the high temperature limit, then saturates at 1/2 in the low temperature limit, indicating that the relative fluctuations of $R$ increase as one lowers the temperature.