Local impurity in a multichannel Luttinger liquid

V. Kagalovsky, Igor V. Lerner, Igor V. Yurkevich

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    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.
    Original languageEnglish
    Article number205122
    Number of pages10
    JournalPhysical Review B
    Issue number20
    Publication statusPublished - 15 May 2017


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