Theory of Vortex Excitation Imaging via an NMR Relaxation Measurement

The temperature dependence of the site-dependent nuclear spin relaxation time $T_1$ around vortices is studied in $s$-wave and $d$-wave superconductors. Reflecting low-energy electronic excitations associated with the vortex core, temperature dependences deviate from those of the zero-field case, and $T_1$ becomes faster when approaching the vortex core. In the core region, $T_1^{-1\mathrm{}}$ has a new peak below $T_c$. The NMR study by the resonance field dependence may be a new method to prove the spatial resolved vortex core structure in various superconductors.