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Electronic properties of Luttinger Liquid with electron-phonon interaction

Galda, Alexey (2013)
Ph.D. thesis, University of Birmingham.

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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: Ph.D. thesis. Lerner, Igor V. and Yurkevich, Igor Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Physics and Astronomy QC PhysicsTK Electrical engineering. Electronics Nuclear engineering University of Birmingham 4293
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