Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field

Abstract

Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional for the case of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature as a function of the magnetic field. This extends the previous works [17,18] of Frank, Hainzl, Seiringer and Solovej to the case of external magnetic fields with non-vanishing magnetic flux through the unit cell.

Enhanced pairing mechanism in Cuprate-type crystals

“…A particular weakness of our approach is the loss of phase dependence, since the solution of ( 9) is determined only up to an arbitrary phase function e iθ(k) . It should be mentioned that in recent years the mathematical properties of conventional BCS theory have been intensively studied [23][24][25][26][27][28][29] with sometimes rather surprising insights [30,31].…”

Differential Equations of Quantum Mechanics

“…In particular, Theorem 6.2 was proven in [74]. An asymptotic behaviour of critical temperature in weak magnetic fields was established in [131,102].…”