Recent experiments with nanopatterned thin films revealed an unusual quantum superconductor to metal phase transition (QSMT) with a linear-in-temperature resistivity. In contrast, most known examples of such transitions and standard theoretical considerations predict a temperature-independent sheet resistance of order $R_Q=\hslash /e^2$. We propose an effective theory of a disordered superconductor which features a QSMT with robust $T$-linear resistivity at the critical point. The crucial ingredient in our model is spatial disorder in the pairing interaction. Such random pairing mirrors the emergent phase disorder seen in a recent mean-field study of a microscopic $d$-wave superconductor subject to potential disorder. We also make the prediction that in such systems the diamagnetic susceptibility diverges as $ln\mathrm{\Lambda }/T$, which starkly differs from the power-law divergence in standard XY transitions.

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• Electrical conductivity
• Quantum phase transitions
• Cuprates
• Disordered systems
• Thin films
• Unconventional superconductors
• Effective field theory
• Green's function methods