Superconducting-gap-node spectroscopy using nonlinear electrodynamics

We present a method to determine the nodal structure of the energy gap of unconventional superconductors such as high-(Formula presented) materials. We show how nonlinear electrodynamics phenomena in the Meissner regime, arising from the presence of lines on the Fermi surface where the superconducting energy gap is very small or zero, can be used to perform “node spectroscopy,” that is, as a sensitive bulk probe to locate the angular position of those lines. In calculating the nonlinear supercurrent response, we include the effects of orthorhombic distortion and (Formula presented)-(Formula presented) plane anisotropy. Analytic results presented demonstrate a systematic way to experimentally distinguish order parameters of different symmetries, including cases with mixed symmetry (for example, (Formula presented) and (Formula presented). We consider, as suggested by various experiments, order parameters with predominantly (Formula presented)-wave character, and describe how to determine the possible presence of other symmetries. The nonlinear magnetic moment displays a distinct behavior if nodes in the gap are absent but regions with small finite values of the energy gap exist.