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arXiv:0905.4665 · Physical Review B

Pumping current and conductance of a Luttinger liquid in the presence of two time-dependent impurities at finite temperatures

Mariano J. Salvay

Published Jun 9, 2009• 7 citations
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Abstract

We study the pumping current and the conductance in a Tomonaga-Luttinger liquid in the presence of two time-dependent pointlike weak impurities, taking into account finite-temperature effects. We investigate the different regimes which can be established as functions of the frequency, the temperature, and the separation between the impurity potentials. We show how the previous zero-temperature or single-impurity results are distorted.

DOI
10.1103/physrevb.79.235405

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We study the pumping current and the conductance in a Tomonaga-Luttinger liquid in the presence of two time-dependent pointlike weak impurities, taking into account finite-temperature effects. We investigate the different regimes which can be established as functions of the frequency, the temperature, and the separation between the impurity potentials. We show how the previous zero-temperature or single-impurity results are distorted.
We study the backscattered current in a Luttinger liquid in the presence of a pointlike weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter ${\ensuremath{\tau}}_{R}$ as a function of the electron-electron interaction and the temperature, such that for ${\ensuremath{\tau}}_{R}<1$ (>1)(>1)(>1) the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter KKK through time measurements in transport experiments at fixed voltage.
We study the transport properties of a Luttinger liquid in the presence of several time-dependent weak pointlike impurities. Our starting point is the bosonized form of the Luttinger liquid Hamiltonian with a potential introduced by the impurities. We find the correction to the total current due to the backscattering of the electrons by the impurities in first order of perturbation theory for a general time-dependent impurity potential. We then apply this result to a single time-dependent impurity, and show that it reproduces the result obtained by Feldman and Gefen [Phys. Rev. B 67, 115337 (2003)], in particular that the current enhancement occurs only for strong repulsive electron-electron interactions. For the case of two impurities oscillating with the same frequency, we find that the dc component of the backscattering current is positive even for weak repulsive interactions, due to the presence of the interference term induced by spatial correlations in the Luttinger liquid. We show that the impurity frequencies at which the enhancement takes place form a bandlike structure. In the case of several impurities, the bands become broader, because of interference effects.
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.
We study theoretically the transport properties of an interacting quantum wire in the presence of a time-dependent point impurity. Using the Keldysh formalism within the framework of Luttinger liquid model, we calculate and analyze the dc contribution of the backscattered current and the shot noise of the system with arbitrary Luttinger interaction strength and impurity position. From some numerical examples, we find that the time-dependent point impurity in the wire can enhance the total current in the strongly interaction regime, and the total current enhancement is dependent on both the impurity potential frequency and the equivalent frequency in relation to the drain-source voltage VVV. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with VVV. However, the final current-noise relation is similar to that in the case of a static point impurity.
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.
The nonlinear transport in a Luttinger liquid with finite-range interaction is considered for a general time-dependent driving electric field, in the presence of an impurity. In the static limit, the nonlinear current-voltage characteristic depends only on the integral of the driving field. For a time-dependent field, a relation between the currents at different sites is derived which depends only on the nonlocal ac conductivity of the Luttinger system without impurity, but is independent of the strength and the shape of the electric field. Experimental consequences are discussed.