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Transport and elementary excitations of a Luttinger liquid (letter to the editor)

Gianaurelio Cuniberti, Maura Sassetti, B. Krämer

Published Jan 1, 1996• 0 citations
Publisher

Abstract

The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance.

DOI
10.5283/epub.1328

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The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance.
The low-temperature AC conductance of a one-dimensional electron system with a strong interaction of finite range is calculated by using linear response theory. The conductance factorizes into parts which depend on the internal properties of the system, and the external probe. For short-range interaction, the result resembles that for non-interacting electrons, but with the zero-frequency limit and the Fermi velocity renormalized by the interaction strength. For strong and long-range interaction, the conductance shows a peak that is related to charge-wave excitations. In this limit, the AC conductance can be simulated by a quantum capacitance and a quantum inductance .
Several recent results concerning frequency dependent and nonlinear transport of one-dimensional correlated electrons are reviewed. The frequency dependent conductance of a Luttinger liquid is discussed. For zero-range interaction the conductance is similar to that of a non-interacting ideal quantum wire, with a renormalized zero-frequency limit. For a screened Coulomb potential, the conductance as a function of the frequency shows features of the elementary excitations. They can be simulated in terms of a capacitance, an inductance and a resistance. The non-linear DC-conductance of the Luttinger liquid in presence of a tunnel barrier shows Coulomb blockade if the interaction is of finite range. The capacitance scales in the same way as for the system without the tunnel barrier. The linear DC-response of a tunnel barrier as a function of the frequency and the voltage of a monochromatic driving field shows oscillations which can be interpreted as signature of a frequency-induced depinning of a charge density wave.
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g 2 , and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low-energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) β-function are identified. A universal part of the β-function is given by a ladder series and summed to all orders in g 2 . First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature-dependent conductance is solved analytically. Our result agrees with known limiting cases.
Using the equation of motion, we investigate theoretically the dynamical ac conductance of a clean Luttinger-liquid quantum wire adiabatically coupled to Fermi liquid electron reservoirs in the presence of short-ranged electron-electron interactions. For a perfect single mode quantum wire, in the limit of zero-ranged interaction we conclude that the static dc conductance of ω→0 is e 2 / h , which is independent of the electron interactions. While in the dynamical case of ω≠0, the ac conductance oscillates with the amplitude e 2 / h and the period which depends on the interaction strength and the driving frequency as well as the position in the wire.