Generation of spin-polarized currents in Zeeman-split Tomonaga-Luttinger models

TL;DR

This paper investigates how a magnetic field affects one-dimensional interacting electron gases, leading to spin-polarized currents due to Zeeman splitting disrupting spin-charge separation in Tomonaga-Luttinger models.

Contribution

It introduces a detailed analysis of spin-dependent conductivities and correlations in Zeeman-split Tomonaga-Luttinger models, revealing mechanisms for spin polarization.

Findings

Conductivity ratio diverges at low temperatures, indicating spin polarization.

Electron-electron interactions cause different conductance for up- and down-spins.

Spin-charge separation is destroyed by Zeeman splitting in the model.

Abstract

In a magnetic field an interacting electron gas in one dimension may be described as a Tomonaga-Luttinger model comprising two components with different Fermi velocities due to the Zeeman splitting. This destroys the spin-charge separation, and even the quantities such as the density-density correlation involve spin and charge critical exponents (K). Specifically, the ratio of the up-spin and down-spin conductivities in a dirty system diverges at low temperatures like an inverse power of the temperature, $T^{-(K_{\uparrow}-K_{\downarrow})}$, resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for up- and down-spins as another manifestation of the electron-electron interaction.