Dimensionality-driven changeover to first-order superconducting phase transitions in the Pauli paramagnetic limit

Superconducting (SC) phase transitions in strongly type-II superconductors in the Pauli paramagnetic limit are considered within the framework of the Gorkov–Ginzburg–Landau approach in the lowest Landau level approximation for both s- and d-wave electron pairings. Simple analytical expressions for the quadratic and quartic coefficients in the order parameter expansion of the SC free energy are derived without relying on gradient or wave number expansions. The existence of a changeover from continuous to discontinuous SC phase transitions that are predicted to occur in the clean limit is shown to depend on the dimensionality of the underlying electronic band structure but to be independent of the type of the electron pairing. Such a changeover can take place in the quasi-two-dimensional (2D) regime below a critical value of a three-dimensional–two-dimensional (3D-2D) crossover parameter. In the 3D limit, wherein the normal to SC phase transitions are of second order and the SC phase is spatially modulated along the field direction, the transition line to a uniform SC phase is of first order and is usually very close to the normal to SC transition line.