Magnetic field effects on low dimensional electron systems: Luttinger liquid behaviour in a Quantum Wire

TL;DR

This paper explores how strong magnetic fields influence electron interactions and transport in quantum wires, revealing modifications in Luttinger liquid behavior, reduced backward scattering, and induced spin polarization.

Contribution

It demonstrates how magnetic fields alter electron-electron interactions and correlation functions in quantum wires, highlighting effects on Luttinger liquids and conductance properties.

Findings

Magnetic field reduces backward scattering in quantum wires.

Magnetic field induces spin polarization similar to quantum dots.

Correlation functions exhibit modified power-law behavior under magnetic influence.

Abstract

We discuss the effects of a strong magnetic field in Quantum Wires. We show how the presence of a magnetic field modifies the role played by % which %coefficients corresponding to electron electron interaction % and the Fermi velocity producing a strong reduction of the backward scattering corresponding to the Coulomb repulsion. We discuss the consequences of this and other effects of magnetic field on the Tomonaga-Luttinger liquids and especially on their power-law behaviour in all correlation functions. The focal point is the rescaling of all the repulsive terms of the interaction between electrons with opposite momenta, due to the edge localization of the electrons and to the reduction of the length scale. Because of the same two reasons there are some interesting effects of the magnetic field concerning the backward scattering due to the presence of one impurity and the corresponding conductance. As an effect of the magnetic field we find also a spin polarization induced by a combination of electrostatic forces and the Pauli principle, quite similar to the one observed in large Quntum Dots.