Theory of NMR as a local probe for the electronic structure in the mixed state of the high-Tccuprates

We argue that nuclear-magnetic-resonance experiments are a site-sensitive probe for the electronic spectrum in the mixed state of the high-$T_c$ cuprates. Within a spin-fermion model, we show that the Doppler-shifted electronic spectrum arising from the circulating supercurrent changes the low-frequency behavior of the imaginary part of the spin susceptibility. For a hexagonal vortex lattice, we predict that these changes lead to (i) a unique dependence of the ${}^{63}\mathrm{Cu}$ spin lattice relaxation rate, ${1/T}_1,$ on resonance frequency, and (ii) a temperature dependence of $T_1$ which varies with frequency. We propose a nuclear quadrupole experiment to study the effects of a uniform supercurrent on the electronic structure and predict that $T_1$ varies with the direction of the supercurrent.