Abstract
We study analytically and numerically a problem of self-heating in small mesa structures. Our results show that the self-heating is proportional to a characteristic in-plane size of the mesa. Experimental data for small high-$T_c$ superconductor Bi2212 mesas are in qualitative agreement with our calculations. We estimate the self-heating in Bi2212 mesas with different sizes and demonstrate that the self-heating can effectively be obviated in small mesa structures.
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