Spontaneous Edge Current in Higher Chirality Superconductors

The effects of finite temperature, Meissner screening and surface roughness on the spontaneous edge current for higher chirality quasi-two dimensional superconductors are studied in the continuum limit using the quasiclassical Eilenberger equations. We find that the total spontaneous current is non-zero at finite temperature T and maximized near T=T_c/2, where T_c is the transition temperature, although it vanishes at T=0. In the presence of surface roughness, we observe a surface current inversion in the chiral d-wave case that can be understood in terms of a disorder induced s-wave pairing component in the rough surface regime. This conclusion is supported by a Ginzburg-Landau analysis. However, this current inversion is non-universal beyond the continuum limit as demonstrated by self-consistent lattice Bogoliubov-de Gennes calculations.