Wavefront depinning in semiconductor superlattices due to discrete-mapping failure

We investigate the wavefronts depinning in current biased,infinitely long semiconductor superlattice systems by the method ofdiscrete mapping and show that the wavefront depinning correspondsto the discrete mapping failure. For parameter values near the lowercritical current in both discrete drift model (DD model) anddiscrete drift--diffusion model (DDD model), the mapping failure isdetermined by the important mapping step from the bottom of branch$gamma$ to branch $alpha$. For the upper critical parameters inDDD model, the key mapping step is from branch $gamma$ to the topof the corresponding branch $alpha$, and we may need several activewells to describe the wavefronts.