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From the photoluminescence of SiC microcrystals uniformly covering arectangular mesa of the high transition temperature $T_c$ superconductorBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the local surface temperature $T({\bm r})$was directly measured during simultaneous sub-THz emission from the $N\sim10^3$intrinsic Josephson junctions (IJJs) in the mesa. At high bias currents $I$ andlow bath temperatures $T_{\rm bath}\lesssim~35$ K, the center of a largeelliptical hot spot with $T({\bm r})> T_c$ jumps dramatically with littlecurrent-voltage characteristic changes. The hot spot doesn't alter theubiquitous primary and secondary emission conditions: the ac Josephson relationand the electromagnetic cavity resonance excitation, respectively. Since theintense sub-THz emission was observed for high $T_{\rm bath}\gtrsim~50$ K inthe low $I$ bias regime where hot spots are absent, hot spots can not providethe primary mechanisms for increasing the output power, the tunability, or forpromoting the synchronization of the $N$ IJJs for the sub-THz emission, but canat best coexist non-mutualistically with the emission. No $T({\bm r})$ standingwaves were observed.

physical review. b, condensed matter and materials physics

Local SiC photoluminescence evidence of non-mutualistic hot spot  formation and sub-THz coherent emission from a rectangular  Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ mesa