Transport in a spin polarized Luttinger liquid in the presence of a single impurity

TL;DR

This paper investigates how a single impurity affects conductance in a spin-polarized Luttinger liquid with electron interactions and Zeeman splitting, revealing spin-dependent conductance and spin polarization effects.

Contribution

It demonstrates that in a spin-polarized Luttinger liquid with interactions, conductances for spin up and down differ, leading to spin polarization in the wire.

Findings

Conductance for spin up and down are unequal.

Spin polarization arises due to anisotropic conductance.

Luttinger liquid behavior persists with spin-dependent properties.

Abstract

The conductance for a single impurity in a one dimensional gas with electron-electron interaction and Zeeman splitting $v_F^\uparrow - v_F^\downarrow = \Delta \neq 0$ is considered. We find that for an extented Hubbard model, $\rho_\uparrow^R \rho_\uparrow^L + \rho_\downarrow^R \rho_\downarrow^L$, a Luttinger liquid for spin up and spin down is obtained. As a result the conductances for spin up $G_\uparrow$ and spin down $G_\downarrow$ are not equal. The anisotropy in the conductances $G_\uparrow \neq G_\downarrow$ gives rise to a spin polarized wire.