On non-Riemannian Superconductors and torsion loops

TL;DR

This paper explores the role of torsion in superconductors by extending electrodynamics geometrically, showing torsion's effects on symmetry breaking, and relating torsion to supercurrents and the Meissner effect.

Contribution

It introduces a geometric framework incorporating torsion into superconductivity theory, revealing its influence on vacuum symmetry and supercurrent behavior.

Findings

Torsion causes a shift in the symmetry breaking vacuum.

Torsion loops are related to geometrical phases outside superconductors.

Inside superconductors, torsion vanishes, indicating a torsion-based Meissner effect.

Abstract

The geometrization of electrodynamics is obtained by performing the complex extension of the covariant derivative operator to include the Cartan torsion vector and applying this derivative to the Ginzburg-Landau equation of superfluids and Superconductors.It is shown that the introduction of torsion makes a shift in the symmetry breaking vacuum.Torsion loops are computed from geometrical phases outside the superconductor.Inside the superconductor the torsion vanishes which represents the Meissner effect for torsion geometry. Torsion in general equals the London supercurrent.It is possible to place a limit on the size of superconductor needed to give an estimate to torsion.