Discontinuous Transition to Superconducting Phase

We discuss the instability of uniform superconducting states that contain the pairing correlations belonging to the odd-frequency symmetry class. The instability originates from the paramagnetic response of odd-frequency Cooper pairs and is considerable at finite temperatures. As a result, the pair potential varies discontinuously at the transition temperature when the amplitude of the odd-frequency pairing correlation functions is sufficiently large. The discontinuous transition to the superconducting phase is a general feature of superconductors that include odd-frequency Cooper pairs.