On the Fulde-Ferrell State in Spatially Isotropic Superconductors

TL;DR

This paper investigates the stability of the Fulde-Ferrell state in isotropic superconductors under magnetic fields, revealing that fluctuations prevent long-range order and significantly affect the phase transition near the critical field.

Contribution

It provides a microscopic analysis of the Fulde-Ferrell state stability considering superconducting fluctuations, extending previous phenomenological results.

Findings

Superconducting fluctuations suppress the long-range order of the FF state.

Even weak pairing interactions lead to a shift in chemical potential affecting the phase transition.

No second-order phase transition occurs for the FF state in this context.

Abstract

Effects of superconducting fluctuations on the Fulde-Ferrell (FF) state are discussed in a spatially isotropic three-dimensional superconductor under a magnetic field. For this system, Shimahara recently showed that within the phenomenological Ginzburg-Landau theory, the long-range order of the FF state is suppressed by the phase fluctuation of the superconducting order parameter. [H. Shimahara: J. Phys. Soc. Jpn. {\bf 67} (1998) 1872, Physica B {\bf 259-261} (1999) 492] In this letter, we investigate this instability of the FF state against superconducting fluctuations from the microscopic viewpoint, employing the theory developed by Nozi\'eres and Schmitt-Rink in the BCS-BEC crossover field. Besides the absence of the second-order phase transition associated with the FF state, we show that even if the pairing interaction is weak, the shift of the chemical potential from the Fermi energy due to the fluctuations is crucial near the critical magnetic field of the FF state obtained within the mean-field theory.