Duality of Weak and Strong Scatterer in a Luttinger Liquid Coupled to Massless Bosons

Igor V. Yurkevich, Alexey Galda, Oleg M. Yevtushenko, and Igor V. Lerner

Phys. Rev. Lett. 110, 136405 – Published 28 March 2013

Abstract

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, $Δ_{WS} Δ_{WL} = 1$ , between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

Received 12 September 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.136405

Authors & Affiliations

Igor V. Yurkevich^1,2,3,4, Alexey Galda^2,5, Oleg M. Yevtushenko^6,3, and Igor V. Lerner^2,3

¹Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom
²School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
³The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, 34100 Trieste, Italy
⁴Institut für Nanotechnologie, Karlsruhe Institute of Technology, D-76021 Karlsruhe, Germany
⁵Argonne National Laboratory, Materials Science Division, Argonne, Illinois 60439, USA
⁶Arnold Sommerfeld Center and Center for Nano-Science, Ludwig Maximilians University, Munich DE-80333, Germany