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arXiv:0707.0784 · Physical Review B

Role of a spin-flip scatterer in a magnetized Luttinger liquid

M. A. N. Araújo, Jamal Berakdar, Vitalii K Dugaev, Vitor Rocha Vieira

Published Nov 14, 2007• 6 citations

Abstract

We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized nonhomogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform liquid, or by a transverse domain wall (DW) between two oppositely magnetized liquids. From a renormalization group treatment of the electron interactions we deduce scaling equations for the transmission and reflection amplitudes as the bandwidth is progressively reduced to an energy scale set by the temperature. The repulsive interactions dictate two possible zero temperature insulator fixed points: one in which electrons are reflected in the same spin channel and another where the electron spin is reversed upon reflection. In the latter case, a finite spin current emerges in the absence of a charge current at zero temperature and the Friedel oscillations form a transverse spiraling spin density. Adding a purely potential scattering term has no effect on the fixed points of a uniformly magnetized liquid. For a DW we find that the introduction of potential scattering stabilizes the spin-flip insulator phase even if the single-particle spin-flip scattering produced by the DW is arbitrarily weak. The potential can be induced externally, e.g., by a local gate voltage or a constriction, providing a means for controlling the transport properties of the wire.

DOI: 10.1103/physrevb.76.205107

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We study the spin-dependent scattering of charge carriers in a magnetized one dimensional Luttinger liquid from a localized nonhomogeneous magnetic field, which might be brought about by the stray field of magnetic tip near a uniform liquid, or by a transverse domain wall (DW) between two oppositely magnetized liquids. From a renormalization group treatment of the electron interactions we deduce scaling equations for the transmission and reflection amplitudes as the bandwidth is progressively reduced to an energy scale set by the temperature. The repulsive interactions dictate two possible zero temperature insulator fixed points: one in which electrons are reflected in the same spin channel and another where the electron spin is reversed upon reflection. In the latter case, a finite spin current emerges in the absence of a charge current at zero temperature and the Friedel oscillations form a transverse spiraling spin density. Adding a purely potential scattering term has no effect on the fixed points of a uniformly magnetized liquid. For a DW we find that the introduction of potential scattering stabilizes the spin-flip insulator phase even if the single-particle spin-flip scattering produced by the DW is arbitrarily weak. The potential can be induced externally, e.g., by a local gate voltage or a constriction, providing a means for controlling the transport properties of the wire.

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We study theoretically the transport of a one-channel Luttinger liquid through a weak link. For repulsive electron interactions, the electrons are completely reflected by even the smallest scatterer, leading to a truly insulating weak link, in striking contrast to that for noninteracting electrons. At finite temperature (T) the conductance is nonzero, and is predicted to vanish as a power of T. At T=0 power-law current-voltage characteristics are predicted. For attractive interactions, a Luttinger liquid is argued to be perfectly transmitted through even the largest of barriers. The role of Fermi-liquid leads is also explored.

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We review some of our recent results on the potential scattering in a weakly interacting one-dimensional(1D) electron gas. The technique we developed is a poor man's renormalization group procedure in the scattered wave basis. This technique can treat the renormalizations of the scattering on the barrier and the scattering between the electrons in a coherent way, and it allows us to find the scattering amplitudes on a localized potential of arbitrary strength for electrons at any energy. The obtained phase shifts are used to study the Fermi-edge singularity in an interacting 1D electron system, where anomalous exponent of the power-law singularity in the vicinity of the edge is found. The transmission coefficient is directly related to the conductance of a 1D channel by the Landauer formula. Simple formulas that describe the conductance at any temperature are derived. In spin-[Formula: see text] systems, the electron–electron backscattering induces renormalizations of the interaction constants, which causes the low-temperature conductance to deviate from the results of the Luttinger liquid theory. In particular, the temperature dependence of the conductance may become nonmonotonic. In the presence of a magnetic field, backscattering gives rise to a peak in the differential conductance at bias equal to the Zeeman splitting.

We develop a detailed theory for spin transport in a one-dimensional quantum wire described by Luttinger-liquid theory. A hydrodynamic description of the quantum wire is supplemented by boundary conditions, taking into account the exchange coupling between the magnetization of ferromagnetic reservoirs and the boundary magnetization in the wire. Spin-charge separation is shown to imply drastic and qualitative consequences for spin-dependent transport. In particular, the spin accumulation effect is quenched except for fine-tuned parameter regimes. We propose several feasible setups involving an external magnetic field to detect this phenomenon in transport experiments on single-wall carbon nanotubes. In addition, electron-electron backscattering processes, which do not have an important effect on thermodynamic properties or charge transport, are shown to modify spin-dependent transport through long quantum wires in a crucial way.

We investigate spin-charge mixing effect on resonant tunneling in spin-polarized Tomonaga-Luttinger liquid with double impurities. The mixing arises from Fermi velocity difference between two spin species due to Zeeman effect. Zero bias conductance is calculated as a function of gate voltage

{V}_{g}

, gate magnetic field

{B}_{g}

, temperature, and magnetic field applied to the system. Mixing effect is shown to cause rotation of the lattice pattern of the conductance peaks in

({V}_{g},{B}_{g})

plane, which can be observed in experiments. At low temperatures, the contour shapes are classified into three types, reflecting the fact that effective barrier potential is renormalized towards ``perfect reflection,'' ``perfect transmission,'' and magnetic field induced ``spin-filtering,'' respectively.