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Scientific Reports

Interaction-induced edge states in anisotropic non-Fermi liquids

I. V. Yurkevich

Published Jun 8, 2017• 10 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-017-03823-5

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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).
We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e., not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in the particular case of topological insulators realized in narrow Hall bars.
We investigate the effect of both strong and weak potential scattering caused by local impurities and extended (line) defects in the array of Luttinger liquid wires. We find that in both cases a finite range inter-wire interaction stabilises metallic state. Based on calculation of the scaling dimensions of one-particle scattering operators, we construct the phase diagram for low-temperature transport along the array. We find that unlike local impurity case where only conducting and insulating states are realised (metal-insulator transition driven by interactions), the extended line defects may bring the system into a mixed state where conducting or insulating behavior can be observed depending on bare strength of the scatterer (metal-insulator transition driven by disorder).
We investigate the effect of both strong and weak potential scattering caused by local impurities and extended (line) defects in an array of Luttinger liquid wires. We find that in both cases a finite range interwire interaction stabilizes the metallic state. Based on calculations of the scaling dimensions of one-particle scattering operators, we construct a phase diagram for low-temperature transport along the array. We find that unlike the local impurity case where only conducting and insulating states are realized (metal-insulator transition driven by interactions), the extended line defects may bring the system into a mixed state where conducting or insulating behavior can be observed depending on bare strength of the scatterer (metal-insulator transition driven by disorder).
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. 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.
Recent experiments have revealed that the temperature dependence of the conductance of quasiballistic quantum wires bears characteristic features of the Luttinger-liquid state. In this paper, the conductance of an N-channel quantum wire is calculated within the model of N coupled Luttinger liquids and under the assumption of weak disorder. It is shown that as the number of channels increases, a crossover from the Luttinger-liquid to the Fermi-liquid behavior occurs. This crossover manifests itself in the 1/N decrease of the scaling exponent of the temperature dependence. An exact expression for the scaling exponent for the case of N coupled Luttinger chains is obtained, and the large N limit is studied for the case of a quantum wire. The case of N=2 for electrons with spin is analyzed in detail, and a qualitative agreement with the experiment is achieved.