Assesing the effect of Coulomb repulsion asymmetry on electron pairing

TL;DR

This paper investigates how relativistic effects induce anisotropic Coulomb repulsion, leading to an angular-dependent attraction potential that could facilitate electron pairing and superconductivity in anisotropic materials.

Contribution

It introduces a novel relativistic correction to Coulomb repulsion, revealing an angular-dependent attraction potential that may enable superconductivity under certain conditions.

Findings

Relativistic effects cause Coulomb repulsion to become anisotropic.

An angular-dependent attraction potential emerges in the presence of a uniform positive ion background.

Superconducting states may occur if the density of states is anisotropic.

Abstract

Coulomb repulsion between two moving electrons loses its spherical symmetry due to relativistic effects. In presence of a uniform positive ion background this asymmetry uncovers an angular dependent attraction potential in the direction of motion. The quantum mechanical response to such an attraction potential is obtained through perturbation. It is shown that the transition amplitude between states with the symmetry of the attraction potential becomes negative and if the density of states is anisotropic, occurrence of a superconducting state becomes possible.