Low-coverage surface diffusion in complex periodic energy landscapes. II. Analytical solution for systems with asymmetric hops

This is part II in a series of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low coverage, single-tracer limit). While Part I [Gosalvez et al., Phys. Rev. B 93, 075429 (2016)] focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials, this report (Part II) presents a more general approach to determining the tracer diffusivity in systems where the end sites can be located asymmetrically with respect to the hop origins (asymmetric hops), as observed in reconstructed and/or chemically modified surfaces and/or bulk materials. The obtained diffusivity formulas for numerous systems are validated against kinetic Monte Carlo simulations and previously reported analytical expressions based on the continuous-time random walk (CTRW) method. The proposed method corrects some of the CTRW formulas and provides new expressions for difficult cases that have not been solved earlier. This demonstrates the ability of the proposed formalism to describe tracer diffusion.