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

TL;DR

This paper demonstrates that NMR can serve as a site-sensitive probe of the electronic spectrum in the mixed state of high-$T_c$ cuprates, revealing how supercurrents influence local electronic properties.

Contribution

It introduces a theoretical framework showing how NMR measurements can detect supercurrent-induced changes in the electronic spectrum of high-$T_c$ cuprates.

Findings

Frequency-dependent $1/T_1$ relaxation rate predictions

Frequency-dependent temperature variation of $T_1$

Proposal of a nuclear quadrupole experiment to study supercurrent effects

Abstract

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 {\it (a)} a unique dependence of the $^{63}$Cu spin lattice relaxation rate, $1/T_1$, on resonance frequency, and {\it (b)} 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.