Single-spin qubit magnetic spectroscopy of two dimensional superconductivity

A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its $1/T_1$ relaxation rate due to magnetic noise created by electric current fluctuations in the material. We analyze this technique as a wireless probe of superconductivity in atomically thin two dimensional materials. At temperatures $T \lesssim T_c$, the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations. We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature. We show that scaling of the noise with sample-probe distance provides a window into the non-local quasi-static conductivity of superconductors, both clean and disordered. At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers. Potential experimental implications are discussed.