The stability of current filaments in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ observed via luminescent thermal microscopy

Stacks of Intrinsic Josephson Junctions (IJJs) in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ (Bi-2212) designed as emitters of THz-radiation are prone to strong self-heating and thermal instability due to the poor thermal conductivity and semiconducting resistivity along the c-axis. Recent theory and experimental evidence indicate a possible correlation between strong self-heating and THz power emission. Here we study the temperature distribution in stacks of IJJs using current-voltage (I-V) characteristics and direct thermal imaging. At low bias currents and at low temperature, we observe the nucleation of small hot-spots near the corners or edges of the sample. These hot-spots carry 20-30{\%} of the entire bias current thus forming current filaments. With increasing current and at elevated temperatures the size of the hot-spot increases and it moves to the center of the sample. These observations are in excellent agreement with theoretical analysis regarding the stability of current filaments.