Local impurity in multichannel Luttinger liquid

Abstract

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 particular case of topological insulators realized in narrow Hall bars.

11 pages, 4 figures

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Cited by in corpus (7)

• Stability of a topological insulator: interactions, disorder and parity of Kramers doublets
• Berezinskii-Kosteriltz-Thouless transition in disordered multi-channel Luttinger liquids
• Metal-insulator transition in a sliding Luttinger liquid with line defects
• Two-channel Kondo problem in coupled interacting helical liquids
• Sliding Luttinger liquid with alternating interwire couplings
• Instability of sliding Luttinger liquid
• Dominant superconducting correlations in a Luttinger liquid induced by spin fluctuations