Gor’kov Theory with Exact Green Function in a Magnetic Field

Abstract

The microscopic theory of superconductivity in a magnetic field has been studied for many years since the development of Gor’kov theory for a weak magnetic field. Theoretical predictions that the critical temperature in strong magnetic fields may be higher than that in zero magnetic fields has stimulated intensive theoretical study of superconductivity behavior in high magnetic fields. In the present paper, Gor’kov theory is reformulated in terms of the exact Green function in a magnetic field (i.e., the Kummer function). The linearized gap equation is solved graphically for a two-dimensional system and a critical line in the magnetic field–temperature plane is obtained. We find that a superconducting domain exists on the higher field side of the domain according to the parabolic law.