Influence of capacitance and thermal fluctuations on the Josephson diode effect in asymmetric higher-harmonic SQUIDs

Asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics, demonstrate a flux-tunable Josephson diode effect (asymmetry between currents flowing in the opposite directions, which can be tuned by the magnetic flux through the interferometer loop). We theoretically investigate influence of junction capacitance and thermal fluctuations on performance of such Josephson diodes. Our main focus is on the ``minimal model'' with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. Capacitance generally weakens the diode effect in the resistive branch (R state) of the current-voltage characteristic (CVC) both in the absence and in the presence of external ac irradiation. At the same time, it leads to qualitatively new features of the Josephson diode effect such as asymmetry of the retrapping currents (which are a manifestation of hysteretic CVC). In particular, the limiting case of the single-sided hysteresis becomes accessible. In its turn, thermal fluctuations are known to lead to nonzero average voltages at any finite current, even below the critical value. We demonstrate that in the diode regime, the fluctuation-induced voltage can become strongly (exponentially) asymmetric. In addition, we find asymmetry of the switching currents arising both due to thermal activation and due to Josephson plasma resonances in the presence of ac irradiation.