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

We show that NV centers could provide distinct signatures of emergent gauge fields in certain phase transitions in spin liquids. We consider the relaxation rate $1\mathrm{/}{T}_1$ 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 ${\mathbb{Z}}_2$ 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 6K as a candidate for the experimental observation of this phenomenon.