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Chinese Physics Letters

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

彭德军, 程芳, 周光辉

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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。

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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 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.
We devise an approach to calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. The application to a semi-infinite array of chains described by Luttinger liquid models demonstrates that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wire is robust against disorder whereas bulk wires, on contrary, become insulating in some region of inter-chain interaction parameters. This result proves that the edge states may exist in disordered anisotropic strongly correlated systems without time-reversal symmetry breaking or spin-orbit interaction and provide quantized low-temperature transport.
We devise an approach to the calculation of scaling dimensions of generic operators describing scattering within multi-channel Luttinger liquid. The local impurity scattering in an arbitrary configuration of conducting and insulating channels is investigated and the problem is reduced to a single algebraic matrix equation. In particular, the solution to this equation is found for a finite array of chains described by Luttinger liquid models. It is found that for a weak inter-chain hybridisation and intra-channel electron-electron attraction the edge wires are robust against disorder whereas bulk wires, on contrary, become insulating. Thus, the edge state may exist in a finite sliding Luttinger liquid without time-reversal symmetry breaking (quantum Hall systems) or spin-orbit interaction (topological insulators).