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arXiv:cond-mat/0411600 · Physical Review B

Spin-charge mixing effects on resonant tunneling in a polarized Luttinger liquid

Kenji Kamide, Yuji Tsukada, Susumu Kurihara

Published Jun 15, 2006• 7 citations
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Abstract

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.

DOI
10.1103/physrevb.73.235326

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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 Vg{V}_{g}Vg​, gate magnetic field Bg{B}_{g}Bg​, temperature, and magnetic field applied to the system. Mixing effect is shown to cause rotation of the lattice pattern of the conductance peaks in (Vg,Bg)({V}_{g},{B}_{g})(Vg​,Bg​) 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.
The resonant tunneling through a double-barrier structure in a one-dimensional system of interacting spinless fermions is studied. The conductance is calculated as a function of gate voltage and temperature. It is shown that even in Luttinger liquids the line shape of resonances is almost the same as that of the noninteracting Fermi liquid provided that the temperature is not too low. The temperature dependence, on the other hand, is drastically changed by the interaction, and the height of the conductance peak is a nonmonotonic function of temperature for weak repulsive interaction.
In this paper, we study the effect of a weak magnetic field and the charging energy on electron conduction in a Luttinger liquid with two impurities. We consider the situation in which the two potential barriers are different in the symmetric tunneling and asymmetric tunneling limits. We focus on the dependence of the charge conductance on the temperature, the charging energy and the magnetic field. It is shown that the asymmetry of the potential barrier obstructs the resonant conduction in the symmetric tunneling limit. On the other hand, in the asymmetric tunneling limit, we treat the cases of excitation both with and without a gap. For excitation without a gap, the charging energy changes the exponent of the temperature dependence of the conductance, and there appears resonant conduction under zero magnetic field. Contrastingly, for excitation with a gap, the charging energy does not change the exponent of the conductance, and there appears resonant conduction unrelated to the magnetic field. Our results suggest that there is no spin-filter phase in the asymmetric tunneling limit.
We have calculated the two-probe Landauer conductance of a one-channel quantum wire containing a Luttinger liquid and connected to two noninteracting leads through tunnel barriers. The tunneling conductance shows broad resonances as a function of the bias voltage, this being a manifestation of the spin-charge separation. In the limit of zero bias and zero barrier, the tunneling conductance reduces to the ballistic contact value e2h\frac{{e}^{2}}{h}he2​ per channel.
Using bosonization and path-integral methods, we study general low-temperature behavior of nonmagnetic and magnetic impurity scattering in Tomonaga-Luttinger liquid, and calculate the electron Green function for a general backward scattering potential. We demonstrate that the electron density of state near the impurity site is suppressed by backward scattering, but it mainly remains invariant far away from the impurity, and that at zero temperature the electrons are completely reflected on the impurity site; the system breaks into two subsystems, but right- and left-moving electron fields have a twisted boundary condition. We also show that a testing charge can only be partially screened by conduction electrons, and in a strong interaction region the impurity susceptibility has a 1/T1/T1/T-type low-temperature behavior.
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.
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. \textcopyright{} 1996 The American Physical Society.