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We theoretically investigate the critical current of a thermally-biased SISJosephson junction formed by electrodes made by different BCS superconductors.The response of the device is analyzed as a function of the asymmetryparameter, $r=T_{c_1} /T_{c_2}$. We highlight the appearance of jumps in thecritical current of an asymmetric junction, namely, when $r\neq1$. In fact, insuch case at temperatures at which the BCS superconducting gaps coincide, thecritical current suddenly increases or decreases. In particular, we thoroughlydiscuss the counterintuitively behaviour of the critical current, whichincreases by enhancing the temperature of one lead, instead of monotonicallyreducing. In this case, we found that the largest jump of the critical currentis obtained for moderate asymmetries, $r\simeq3$. In view of these results, thediscussed behavior can be speculatively proposed as a temperature-basedthreshold single-photon detector with photon-counting capabilities, whichoperates non-linearly in the non-dissipative channel.

Non-linear critical current thermal response of an asymmetric Josephson tunnel junction