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 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↑−K↓), resulting in a spin-polarized current. In finite, clean systems the conductance becomes different for upand down-spins as another manifestation of the electron-electron interaction. 72.15-v, 73.20.Dx, 72.10.Bg Typeset using REVTEX 1 Recent studies of quantum transport in mesoscopic systems have brought to light many unusual features unexpected for classical systems [1]. This is heightened by recent advances in fabricating nanostructure quantum wires and quasi-one-dimensional (1D) crystal structures. In 1D systems, the interactions between the electrons is so crucial due to the strong constraint in the phase space that the system becomes universally what is called the TomonagaLuttinger (TL) liquid as far as low-lying excitations are concerned no matter how small the interaction may be [2]. A most striking feature of this 1D model is the spin-charge separation. The transport properties [3] are also dominated by the spin-charge separation in the following sense. The low-temperature conductivity of the dirty TL liquid as studied by Luther and Peschel [4] exhibits a power law, σ(T ) ∼ T 2−Kρ−Kσ . The power law comes from the degraded Fermi singularity in the TL model, while the critical exponents (which are functions of the interaction) enter as a sum of Kρ for the charge phase of the system and Kσ (which is actually fixed at 1 for spin-independent interactions) for the spin phase. A recent experiment [7] for high-quality quantum wires seems to support this result. For clean systems Kane and Fisher [5] and Furusaki and Nagaosa [6] found that the conductance quantization in finite systems in the noninteracting case becomes proportional to the exponent, G = (e/π)Kρ (where h̄ = kB = 1 is assumed hereafter). Now we can raise an intriguing question: what happens if we degrade the spin-rotational (SU(2)) symmetry? Such a situation is realized by applying a magnetic field, which makes the Fermi velocities spin dependent due to the Zeeman splitting. In this paper, we show that the spin-charge separation will be then destroyed, causing even the quantities such as the density-density correlation involve spins. Thus the spin may manifest itself in the transport, leading possibly to spin-polarized currents, which is shown to be the case. The generation of spin-polarized currents has been of a long-standing interest for academic [8] as well as practical points of view, where typical applications include spin-polarized STM [9] and the Mott-detector [10]. Fasol and Sakaki [11] have suggested that in the spinorbit split bands of GaAs quantum wires the curvature in the band dispersion (as opposed 2 to the linearized dispersion in the Tomonaga-Luttinger model) will make the relaxation time due to the electron-electron interaction spin-dependent and consequently make the outgoing current spin-polarized. The mechanism proposed in this Letter is by contrast a purely electron-correlation effect, where the ratio, σ↑/σ↓, diverges toward T = 0. We start from a clean, two-band Luttinger model, which is similar to the one employed in a study for the Fermi-edge singularity in 1D [12]. The Hamiltonian is given by Hclean = H0 +Hint, (1) where the non-interacting Hamiltonian H0 is written as H0 = ∑ k,s,i vFs[(−)k − kFs]c†iksciks = 2π L ∑