# Electronic properties of Luttinger Liquid with electron-phonon interaction

Galda, Alexey (2013). Electronic properties of Luttinger Liquid with electron-phonon interaction. University of Birmingham. Ph.D.

 Preview
Galda13PhD.pdf
PDF - Accepted Version

## Abstract

This thesis addresses a theoretical study of the problem of a single impurity embedded in a one-dimensional system of interacting electrons in presence of electron-phonon coupling. First we consider a system with a featureless point-like potential impurity, followed by the case of a resonant level hybridised with a Luttinger Liquid. The stress is made on a more fundamental problem of a featureless scatterer, for which two opposite limits in the impurity strength are considered: a weak scatterer and a weak link. We have found that, regardless of the transmission properties of phonons through the impurity, the scaling dimensions of the conductance in these limits obey the duality condition, $$\triangle_{WS}$$ $$\triangle_{WL}$$ = 1, known for the Luttinger Liquid in the absence of phonons. However, in the case when the strength of phonon scattering is correlated with electron scattering by the impurity, we find a nontrivial phase diagram with up to three fixed points and a possibility of a metal-insulator transition. We also consider the case of a weakly interacting electron-phonon system in the presence of a single impurity of an arbitrary scattering potential. In the problem of a resonant level attached to the Luttinger Liquid we show that the electron-phonon coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant and anti-resonant transmission in the Fermi gas.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Lerner, Igor V.UNSPECIFIEDUNSPECIFIED
Yurkevich, IgorUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Physics and Astronomy
Funders: None/not applicable
Subjects: Q Science > QC Physics
T Technology > TK Electrical engineering. Electronics Nuclear engineering
URI: http://etheses.bham.ac.uk/id/eprint/4293

### Actions

 Request a Correction View Item