# The Geometric Field (Gravity) as an Electro-Chemical Potential in a Ginzburg-Landau Theory of Superconductivity

## TL;DR

This paper extends Ginzburg-Landau theory to include space-time curvature, proposing that gravity acts as an electro-chemical potential influencing superconductor properties and potentially linking quantum energy to space-time geometry.

## Contribution

It introduces a novel interaction between superconductor order parameters and space-time curvature, suggesting gravity can modify superconductor types and dynamics.

## Key findings

- Space-time curvature affects coherence length and Ginzburg-Landau parameter.
- Curvature acts as a chemical potential without altering ideal diamagnetism.
- Superconductor order parameter dynamics can influence space-time curvature.

## Abstract

We extend the superconductor's free energy to include an interaction of the order parameter with the curvature of space-time. This interaction leads to geometry dependent coherence length and Ginzburg-Landau parameter which suggests that the curvature of space-time can change the superconductor's type. The curvature of space-time doesn't affect the ideal diamagnetism of the superconductor but acts as chemical potential. In a particular circumstance, the geometric field becomes order-parameter dependent, therefore the superconductor's order parameter dynamics affects the curvature of space-time and electrical or internal quantum mechanical energy can be channelled into the curvature of space-time. Experimental consequences are discussed.