Symmetry of Two- and Four- Electron States in Solids. Application to Unconventional Superconductors

TL;DR

This paper develops a group theoretical method to construct two- and four-electron wavefunctions in solids, analyzing their symmetry and nodal structures, with implications for understanding unconventional superconductors.

Contribution

It introduces a novel group theoretical approach using the Mackey theorem to construct and analyze two- and four-electron states in solids, linking symmetry properties to superconducting behavior.

Findings

Constructed two-electron wavefunctions with zero total momentum.

Analyzed the nodal structure and compared with experimental data.

Proposed a connection between four-electron states and experimental observations.

Abstract

Group theoretical technique for construction of two-electron wavefunctions with zero total momentum in solids based on the Mackey theorem on symmetrized squares is developed. These states correspond to singlet and triplet Cooper pairs. The nodal structure of these states is investigated group theoretically and compared with experimental data for unconventional superconductors. It is shown that when the Mackey theorem is applied twice, the main four-electron states in solids can be constructed. Possible connection of these states with experimental data is discussed.