The influence of Joule heating on electrical properties of intrinsic Josephson junctions

The model of the process of self-heating (i.e., heating by Joule heat) of a stack containing two long Josephson junctions with the characteristic parameters of intrinsic Josephson junctions in high-temperature superconductors is developed. The current-voltage (I–V) characteristics of the non-heated stack have four steps, which appeared without applied magnetic field (the so-called zero-field steps). The coherent emission from the stack on zero-field steps was found. Joule heating appeared during the backward movement of the bias current (from large to small values) at the hysteretic branches of the I–V characteristic. To calculate the stack temperature, the quasi-one-dimensional heat-conduction equation with the preset temperatures at edges was solved. Due to small thermal conductivity, temperature of the stack increases during self-heating. The voltage positions at which zero-field steps appear are investigated for different distributions of temperatures in the stack, which appear due to Joule heating. It is found that self-heating leads to the shift of the zero-field step to smaller voltages. The shift increases with the increasing zero-field step number. It is shown that these features can be explained by the temperature dependence of the propagation velocity of electromagnetic waves in the stack. The simple equation is proposed for the rough qualitative description of step shifts due to self-heating.