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arXiv:cond-mat/0109116 · Physical review. B, Condensed matter

Conductance renormalization and conductivity of a multisubband Tomonaga-Luttinger model

T. Kimura

Published Nov 15, 2001• 1 citation
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Abstract

We studied the conductance renormalization and conductivity of multisubband Tomonaga-Luttinger models with intersubband interactions. We found that, as in single-band systems, the conductance of a multisubband system with an arbitrary number of subbands is not renormalized due to interaction between electrons. We derived a formula for the conductivity in multisubband models. We applied it to a simplified case and found that intersubband interaction enhances the conductivity, which is contrary to the intrasubband repulsive interaction, and that the conductivity is further enhanced for a larger number of subbands.

DOI
10.1103/physrevb.64.233306

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We studied the conductance renormalization and conductivity of multisubband Tomonaga-Luttinger models with intersubband interactions. We found that, as in single-band systems, the conductance of a multisubband system with an arbitrary number of subbands is not renormalized due to interaction between electrons. We derived a formula for the conductivity in multisubband models. We applied it to a simplified case and found that intersubband interaction enhances the conductivity, which is contrary to the intrasubband repulsive interaction, and that the conductivity is further enhanced for a larger number of subbands.
Conductivity of a coupled two-channel dirty Tomonaga-Luttinger model is calculated from the Mori formalism. We find that the conductivity becomes enhanced as the interchannel interaction is turned on even when the interaction is repulsive. This effect is opposite to those from the 2KF{\mathit{K}}_{\mathit{F}}KF​ charge-fluctuation coupling in systems with the channel separation 1/kF{\mathit{k}}_{\mathit{F}}kF​, and is considered to come from the suppressed charge-density-wave fluctuations.
The Kondo effect in a repulsively interacting electron system (Tomonaga-Luttinger liquid) is studied. By using the poor man's scaling method it is shown that the Kondo coupling in this model flows to the strong-coupling regime not only for the antiferromagnetic but also for the ferromagnetic case. The ground state is governed by stable strong-coupling fixed points where the impurity spin is completely screened; the fixed-point Hamiltonian consists of two semi-infinite Tomonaga-Luttinger liquids and a spin singlet. Specific heat, susceptibility, and conductance are calculated for low temperatures.
The finite-size Tomonaga-Luttinger Hamiltonian with an arbitrary potential is mapped onto a noninteracting Fermi gas with renormalized potential. This is done by means of flow equations for Hamiltonians and is valid for small electron-electron interaction. This method also yields an alternative bosonization formula for the transformed field operator which makes no use of Klein factors. The two-terminal conductance can then be evaluated using the Landauer formula. We obtain similar results for infinite systems at finite temperature by identifying the flow parameter with the inverse squared temperature in the asymptotic regime.
Scattering from a localized potential of arbitrary strength is found for weakly interacting electrons. Poor man's renormalization group procedure allows us to calculate the renormalized transmission amplitudes at any energies. Simple formulas that describe the conductance at any temperature are derived. In the presence of the electron-electron backscattering, the low-temperature conductance deviates from the results of 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.