Superlattice gain in positive differential conductivity region

We analyze theoretically a superlattice structure proposed by A. Andronov et al. [JETP Lett 102, 207 (2015)] to give Terahertz gain for an operation point with positive differential conductivity. Here we confirm the existence of gain and show that an optimized structure displays gain above 20 cm$^{-1}$ at low temperatures, so that lasing may be observable. Comparing a variety of simulations, this gain is found to be strongly affected by elastic scattering. It is shown that the dephasing modifies the nature of the relevant states, so that the common analysis based on Wannier-Stark states is not reliable for a quantitative description of the gain in structures with extremely diagonal transitions.