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We study the phase transition between the normal and non-uniform(Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state in quasitwo-dimensional d-wave superconductors at finite temperature. We obtain anappropriate Ginzburg-Landau theory for this transition, in which thefluctuation spectrum of the order parameter has a set of minima at non-zeromomenta. The momentum shell renormalization group procedure combined withdimensional expansion is then applied to analyze the phase structure of thetheory. We find that all fixed points have more than one relevant directions,indicating the transition is of the fluctuation-driven first order type forthis universality class.Comment: 5 page

physical review letters

Fluctuation-Driven First-Order Transition in Pauli-Limited<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Wave Superconductors

Fluctuation-Driven First-Order Transition in Pauli-Limitedd-Wave Superconductors