Theory of Unusual Superconducting Phase Transitions in Heavy Fermion Metals at High Magnetic Fields

We present a non-perturbative theory of paramagnetically-driven superconducting (SC) phase transitions in heavy-fermion metals, which reliably determines their stable SC phases, treats properly the corresponding finite jumps of the order parameter, and can account for unusual features reported recently for this type of materials. It is found that for quasi-2D heavy-fermion metals, such as CeCoIn₅, at high magnetic fields oriented perpendicular to the highly conducting planes, the effect of the Fulde-Ferrel (FF) modulation is too weak to prevent a direct first-order phase transition from the normal to the uniform SC state. For 3D heavy-fermion metals, such as URu₂Si₂, the FF modulation stabilizes, under a decreasing magnetic field, a non-uniform SC state via a second-order phase transition from the normal state. However, at a slightly lower field the modulated phase becomes unstable, transforming to a uniform SC state via a first-order transition.