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 nonzero 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 nonuniversal beyond the continuum limit, as demonstrated by self-consistent lattice Bogoliubov-de Gennes calculations.

• Received 26 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.094501