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Physical review. B, Condensed matter

Transport properties of coupled one-dimensional interacting electron systems with impurities

T. Kimura, Kazuhiko Kuroki, Hideo Aoki

Published May 15, 1995• 8 citations
Publisher

Abstract

We consider two one-dimensional interacting electron systems that are coupled via interchain tunneling to calculate transport properties in the presence of impurities or a single barrier by using the bosonization formalisms for the non-Luttinger-liquid phases on the phase diagram obtained by Fabrizio [Phys. Rev. B 48, 15 838 (1993)]. We find for the weak- and strong-interaction phases, where the superconducting correlation dominates in the ground state, that the interchain transfer enhances the conductivity and the Anderson localization is suppressed. This shows that multichain systems can have unique transport properties.

DOI
10.1103/physrevb.51.13860

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We consider two one-dimensional interacting electron systems that are coupled via interchain tunneling to calculate transport properties in the presence of impurities or a single barrier by using the bosonization formalisms for the non-Luttinger-liquid phases on the phase diagram obtained by Fabrizio [Phys. Rev. B 48, 15 838 (1993)]. We find for the weak- and strong-interaction phases, where the superconducting correlation dominates in the ground state, that the interchain transfer enhances the conductivity and the Anderson localization is suppressed. This shows that multichain systems can have unique transport properties.
Transport through a single barrier in a one-dimensional (1D) interacting electron system is studied theoretically. By using renormalization group and duality mapping, the phase diagram of the ground state is shown to be divided into four regions in terms of the zero-temperature limits of the charge and spin conductances. The conductances are calculated perturbatively for both limits of weak and strong potential. The results are applied to clarify the crossover and scaling of the Anderson localization in a 1D system with dilute impurities. It is shown that the temperature dependence of the resistivity of the system can change significantly around a characteristic temperature corresponding to discretization energy.
We study low-temperature transport properties of a doped two-chain ladder system of interacting fermions in the presence of a barrier or of a low concentration of impurities. The conductance is suppressed above a certain value of the interaction as in a single chain, despite the presence of dominant superconducting correlations. There is, however, a region of repulsive interaction where perfect transmission across the barrier occurs unlike that in the single-chain case. We provide a possible explanation for the temperature maximum of the resistivity in the normal state of ${\mathrm{Sr}}_{0.4}{\mathrm{Ca}}_{13.6}{\mathrm{Cu}}_{24}{\mathrm{O}}_{42\ensuremath{-}\ensuremath{\delta}}$.
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.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger-liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. Two alternative approaches to the problem are developed, both combining fermionic and bosonic treatment of the underlying physics. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit. Our approach provides a framework for a systematic study of mesoscopic effects in strongly correlated electron systems.
This thesis addresses a theoretical study of the problem of a single impurity embedded in a one-dimensional system of interacting electrons in presence of electron-phonon coupling. First we consider a system with a featureless point-like potential impurity, followed by the case of a resonant level hybridised with a Luttinger Liquid. The stress is made on a more fundamental problem of a featureless scatterer, for which two opposite limits in the impurity strength are considered: a weak scatterer and a weak link. We have found that, regardless of the transmission properties of phonons through the impurity, the scaling dimensions of the conductance in these limits obey the duality condition, \\( \\triangle_{WS}\\) \\( \\triangle_{WL}\\) = 1, known for the Luttinger Liquid in the absence of phonons. However, in the case when the strength of phonon scattering is correlated with electron scattering by the impurity, we find a nontrivial phase diagram with up to three fixed points and a possibility of a metal-insulator transition. We also consider the case of a weakly interacting electron-phonon system in the presence of a single impurity of an arbitrary scattering potential. In the problem of a resonant level attached to the Luttinger Liquid we show that the electron-phonon coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant and anti-resonant transmission in the Fermi gas.