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Physical Review Letters

Transport properties in the Tomonaga-Luttinger liquid

Masao Ogata, Philip Warren Anderson

Published May 17, 1993• 59 citations
Publisher

Abstract

We investigate the conductivity using Green's functions in the Tomonaga-Luttinger liquid. It is shown that the resistivity has a linear temperature dependence if we take account of the physical process that the accelerated electron decays into spinon and holon. The effect of impurity scattering becomes visible only below a crossover temperature which strongly depends on the impurity strength, energy cutoff, and spin and charge velocities. The optical conductivity is also studied and it is shown that the relaxation rate has a linear frequency dependence.

DOI
10.1103/physrevlett.70.3087

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We investigate the conductivity using Green's functions in the Tomonaga-Luttinger liquid. It is shown that the resistivity has a linear temperature dependence if we take account of the physical process that the accelerated electron decays into spinon and holon. The effect of impurity scattering becomes visible only below a crossover temperature which strongly depends on the impurity strength, energy cutoff, and spin and charge velocities. The optical conductivity is also studied and it is shown that the relaxation rate has a linear frequency dependence.
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 effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h / e 2 for spinless electrons, and the total resistance is independent of the Luttinger parameter K W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K W for one family but is independent of K W for the other family, regardless of the resistances present in the system.
We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e(2) for spinless electrons, and the total resistance is independent of the Luttinger parameter K-W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K-W for one family but is independent of K-W for the other family, regardless of the resistances present in the system. Copyright (c) EPLA, 2011
We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent $2K\ensuremath{-}1$ for spinless electrons, where KKK is the interaction parameter. For K<1∕2K<1∕2K<1∕2, the current grows large for special values of the bias. For noninteracting electrons with K=1K=1K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1∕21∕21∕2 electrons.
The transport through a barrier is studied for a Tomonaga-Luttinger liquid of finite length connected to reservoirs. An effective action for the phase variable at the barrier is derived for spatially varying electric field. In the dc limit only the total voltage drop between the left and right reservoirs appears in the action. We discuss crossovers of the renormalization group flow and hence of the temperature and wire length dependence of the conductance, taking into account the location of the barrier.