Proposal to detect emergent gauge field and its Meissner effect in spin liquids using NV centers

Abstract

We show that nitrogen-vacancy (NV) centers could provide distinct signatures of emergent gauge fields in certain phase transitions in spin liquids. We consider the relaxation rate $1/{T}_{1}$ of a diamond NV center placed a distance ${z}_{0}$ above a crystal consisting of two-dimensional layers which hosts a U(1) quantum spin liquid with spinon Fermi surface. We show that, during a spinon pairing transition from a U(1) to a Z2 spin liquid, the relaxation rate exhibits a rapid fall just below the pairing transition. The drop is much faster than what can be accounted for by the opening of the energy gap. Instead, the rapid fall with a unique ${z}_{0}$ dependence of its height and width is the signature of the Meissner effect of the gauge field. We identify the organic ET compound which has a phase transition at 6 K as a candidate for the experimental observation of this phenomenon.