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

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 the spins. Specifically, we have shown that 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, 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.