First-order quantum breakdown of superconductivity in amorphous superconductors

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait involves scaling laws governing a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here, we show a departure from this paradigm, showcasing that amorphous superconducting films of indium oxide undergo a distinctive, discontinuous first-order quantum phase transition tuned by disorder. Through systematic measurements of the plasmon spectrum in superconducting microwave resonators, we provide evidence for a marked jump of both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the previously overlooked role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, our investigation shows that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions into the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits.