The geometric field (gravity) as an electro-chemical potential in a Ginzburg-Landau theory of superconductivity

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.