Temperature distribution in large Bi2212 mesas

I numerically analyze Joule heating in large Bi2212 mesas while taking into account typical thermal conductivities and their temperature dependencies of all the materials involved in the heat dissipation and its removal. Such mesas are used in experiments on THz-range radiation. The analysis shows that the temperature increases with bias current and is distributed unevenly along the mesas. The temperature of the mesa's middle part can even exceed $T_c$ at sufficiently high bias. The non-uniform temperature distribution can possibly be important for synchronization of emission from different junctions in the mesas. The overall current-voltage characteristics are also calculated self-consistently showing a negative differential conductance in a wide range of currents.