Umklapp frustration and field-theoretic approach to superconductivity

TL;DR

This paper introduces a field-theoretic approach to superconductivity, highlighting how electron pairing and umklapp scattering lead to frustration, providing a new perspective on the microscopic mechanisms behind superconductivity.

Contribution

It presents an alternative field-theoretic formulation for superconductivity that accounts for electron pairing and scattering effects, extending the Gell-Mann and Low approach.

Findings

Superconductivity arises when electron energy shifts are correlated through pairing.

Normal and umklapp scattering coexistence causes frustration in superconductivity.

The approach links microscopic scattering processes to macroscopic superconducting behavior.

Abstract

The formula of Gell-Mann and Low can be applied to both the Stark effect and superconductivity. The standard version of the field-theoretic approach fits the Stark effect, because in this version electrons have identical initial and end states, so that the energy of each and every electron orbit acquires a shift in the same direction. A preliminary alternative version of the field-theoretic approach is introduced, in which the electrons have different initial and end states, to accommodate superconductivity. Consequently the energy of the electrons acquires a random shift, which will cancel macroscopically, unless the electrons are paired. It also becomes apparent that superconductivity is frustrated when normal and umklapp scattering coexist.