Renormalization of impurity scattering in one-dimensional interacting electron systems in magnetic field

TL;DR

This paper investigates how magnetic fields influence impurity scattering in one-dimensional interacting electron systems, revealing that strong magnetic fields can suppress backscattering for majority spins, leading to potential spin-filtering effects.

Contribution

It demonstrates that magnetic fields can alter the renormalization of impurity scattering, showing suppression of backscattering for majority spins in 1D systems, a novel insight into spin-dependent transport.

Findings

Magnetic field suppresses backscattering of majority-spin electrons.

Impurity becomes nearly transparent for majority spins in certain conditions.

Potential for strong spin-filtering effects in 1D electron systems.

Abstract

We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.