A Theory of a Strange Metal in a Quantum Superconductor to Metal Transition

Recent experiments with nano-patterned cuprate films show a quantum superconductor to metal phase transition exhibiting linear in T resistivity at the critical point, in constrast to the standard expectation of a constant sheet resistance of order R_Q = h/e². We explain the linear in T resistivity using an effective model of the disordered superconductor that can be solved in the large N limit. The key ingredient is a frustrating disordered pairing interaction that would lead to a superconducting phase with trapped π vortices. Adding usual diagonal disorder to the model leads to a very small residual resistance much below the normal state resistance or R_Q. We further predict anomalous Hall resistivity ρ_xy~1/T. Together with linear in T resistivity this leads to scaling of the inverse Hall angle as cot θ_H ∝ T², which has long been a puzzling feature of cuprate phenomenology.