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

The large effective masses characterizing heavy-fermion metals enable, at sufficiently high magnetic fields and low temperatures, paramagnetically-driven first-order superconducting (SC) phase transitions, as well as phase transitions to non-uniform SC states with spatially modulated order parameters along the field direction. Here, we present a non-perturbative theory of these phase transitions, which reliably determines the stable SC phases, treats properly the corresponding finite jumps of the order parameter, and can account for various unusual features reported recently for some heavy-fermion superconductors. 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 compensation effect of the Fulde-Ferrel (FF) modulation is too weak to prevent a first-order phase transition from the normal to the uniform SC state. No modulated FF phase can be therefore stabilized at fields below H_c2 in this material. The calculated thermodynamic properties are in good quantitative agreement with the experimentally derived phase diagram [1] and the sharp additional damping of the de Haas-van Alphen (dHvA) oscillations observed at H_c2 in CeCoIn₅ [2]. 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. The sharp onset of the SC order parameter calculated for this double-stage scenario of the SC transition, including fluctuation effect, is found to be in good agreement with dHvA results in the SC state of URu₂Si₂ [3].