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Physical Review B

Spin Coulomb drag in a spin-polarized Luttinger liquid

P. Schlottmann

Published Nov 10, 2009• 10 citations
Publisher

Abstract

The spin Coulomb drag is a distinctive feature of spin-polarized transport. The current of majority spins can induce a current of minority-spin carriers via the transconductivity. The friction is caused by the Coulomb interaction between up and down spin. This interaction reduces the current but does not change the spin polarization. We calculate the conductivities and the transconductivity for a spin-polarized interacting one-dimensional electron gas with nonmagnetic impurities using the Kubo formalism. Due to the Luttinger-liquid properties, the temperature dependence of the transport correlation functions follow power laws of $T$ with nonuniversal exponents.

DOI
10.1103/physrevb.80.205110

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The spin Coulomb drag is a distinctive feature of spin-polarized transport. The current of majority spins can induce a current of minority-spin carriers via the transconductivity. The friction is caused by the Coulomb interaction between up and down spin. This interaction reduces the current but does not change the spin polarization. We calculate the conductivities and the transconductivity for a spin-polarized interacting one-dimensional electron gas with nonmagnetic impurities using the Kubo formalism. Due to the Luttinger-liquid properties, the temperature dependence of the transport correlation functions follow power laws of TTT with nonuniversal exponents.
The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. This interaction reduces the spin current but does not change the spin-polarization. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of TTT with nonuniversal exponents.
The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. This interaction reduces the spin current but does not change the spin-polarization. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of TTT with nonuniversal exponents.
The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe Ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follows power laws of T with nonuniversal exponents.
The spin transport as the current flows through an impurity in a one-dimensional conductor is analyzed. The interacting electrons are described in terms of the Luttinger liquid theory. Both the Coulomb and short-range interactions are considered; the latter appears when the gate screens the long-range part of the Coulomb potential. The cases of magnetic and nonmagnetic impurities are considered. It has been revealed that, for a magnetic impurity, the electric current flow induces the generation of the spin current, which has direct and alternating components. At low temperatures and voltages, the current can be completely spin-polarized. For a nonmagnetic impurity, the spin current generation is absent. The spin current flowing though the wire affects the current-voltage characteristic for both magnetic and nonmagnetic impurities. The results have been obtained for a rather strong electron-electron interaction.
One-dimensional (1D) quantum wires provide a versatile platform for studying strong electron-electron interactions and collective excitations under confinement. Coulomb drag between 1D systems offers a powerful probe of Tomonaga-Luttinger liquid (TLL) physics, with theoretical predictions suggesting distinct power-law in temperature dependencies between the spin-full and the spin-polarized regimes. However, experimental verification has thus far remained limited. Here, we report measurements of reciprocal and nonreciprocal Coulomb drag between vertically coupled quasi-1D quantum wires in the spin-polarized regime. Clear signatures of spin splitting are observed in both the wires conductance and the drag signal. We observed a connection between electron-hole asymmetry and negative drag, and demonstrated different power-law behaviors in spin-full and spin-polarized regimes, yielding consistent TLL interaction parameters. These results validate the theoretical predictions for backscattering induced drag in the reciprocal regime and extend them to the nonreciprocal and the multiple subband regimes. Furthermore, the nonmonotonic density dependence of the reciprocal interaction parameter correlates with the subband occupation of the drag wire, revealing the complexity of the scattering mechanisms in multichannel systems.
The exact solution of the one-dimensional Hubbard model, the supersymmetric $t\ensuremath{-}J$ model, and the gas of fermions interacting via a $\ensuremath{\delta}$-function potential is used to calculate the drag current between two parallel quantum wires. The critical exponent for the drag current at low temperatures is obtained by means of the mesoscopic energy spectrum and conformal field theory. For a repulsive interaction between the carriers the drag current is opposite to the driving current, while for attractive potentials the two currents are parallel.