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Chinese Physics Letters

Alternating-Current Conductivity for a Two-Channel Interacting Quantum Wire

Peng De-Jun, Fang Cheng, Zhou Guang-Hui

Published Jan 18, 2007• 1 citation
Publisher

Abstract

We investigate theoretically the ac conductivity of a clean two-channel spinless quantum wire in the presence of both short-ranged intra- and inter-channel electron–electron interactions. In the Luttinger-liquid regime, we formulize the action functional of the system with an external time-varying electric field. The obtained expression of ac conductivity for the system within linear response theory is generally an oscillation function of the interaction strength, the driving frequency as well as the measured position in the wire. The numerical examples demonstrate that the amplitude of ac conductivity is renormalized by the both interactions, and the dc conductivity of the system with inter-channel interaction is smaller than that without inter-channel interaction.

DOI
10.1088/0256-307x/24/2/060

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We investigate theoretically the ac conductivity of a clean two-channel spinless quantum wire in the presence of both short-ranged intra- and inter-channel electron–electron interactions. In the Luttinger-liquid regime, we formulize the action functional of the system with an external time-varying electric field. The obtained expression of ac conductivity for the system within linear response theory is generally an oscillation function of the interaction strength, the driving frequency as well as the measured position in the wire. The numerical examples demonstrate that the amplitude of ac conductivity is renormalized by the both interactions, and the dc conductivity of the system with inter-channel interaction is smaller than that without inter-channel interaction.
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.
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.
我们理论上面对 short-ranged intra-channelelectron-electron 和 inter-channelelectron-electron 相互作用调查一根干净 two-channelspinless 量电线的交流传导性。在 Luttinger 液体政体，我们 formulize 行动 functionalof 有一个外部变化时间的电场的系统。为在线性反应理论以内的系统的 acconductivity 的获得的表达式通常是在电线中的摆动函数 ofthe 相互作用力量，开车频率以及测量位置。Thenumerical 例子证明交流电导率的振幅被 bothinteractions 重新使正常化，并且没有内部隧道的相互作用，有内部隧道的相互作用的系统的电导率是更小的 thanthat。
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 use the technique of bosonization to understand a variety of recent experimental results on the conductivity of a quantum wire. The quantum wire is taken to be a finite-length Luttinger liquid connected on two sides to semi-infinite Fermi liquids through contacts. The contacts are modeled as (short) Luttinger liquids bounded by localized one-body potentials. We use effective actions and the renormalization group to study the effects of electronic interactions within the wire, the length of the wire, finite temperature, and a magnetic field, on the conductivity. We explain the deviations of the conductivity from 2Ne2/h{2Ne}^{2}/h2Ne2/h in wires that are not too short as arising from renormalization effects caused by the repulsive interactions. We also explain the universal conductance corrections observed in different channels at higher temperatures. We study the effects of an external magnetic field on electronic transport through this system and explain why odd and even spin-split bands show different renormalizations from the universal conductance values. We discuss the case of resonant transmission and of the possibility of producing a spin valve that only allows electrons of one value of the spin to go through. We compare our results for the conductance corrections with experimental observations. We also propose an experimental test of our model of the contact regions.