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Progress of Theoretical Physics

Electron Conduction in a Luttinger Liquid with Asymmetric Barrier Potentials under a Weak Magnetic Field

Shogo Kawaguchi

Published Apr 1, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.115.717

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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.
We study the effect of dilute impurities on a system of interacting electrons subject to a quantizing magnetic field. For the case of point impurities, the calculation of the scattering cross section can be mapped onto a 1D problem of tunnelinng conductance through a barrier for interacting electrons. We find that the electron-electron interaction produces temperature-dependent corrections to the cross-section, and thus to the tensor of conductivities. Upon summation of the most diverging corrections in all orders of perturbation theory, a scaling behavior of the conductivities emerges. This behavior is similar to that of 1D Luttinger liquid. The scaling exponents depend on the magnetic field and are calculated explicitly in the weak-coupling limit. The limitations on the scaling behavior due to the formation of a charge-density wave are also discussed.
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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.
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.
We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter KKK, and the deviation from the resonance condition is obtained. For weak dissipation and 1/2<K<11/2<K<11/2<K<1, the conduction shows a nonmonotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.