We investigate the critical current in microwave-irradiated Josephson junctions hosting Yu-Shiba-Rusinov states due to magnetic impurities. Under two conditions, namely (i) the breaking of particle-hole symmetry in the normal sense by nonzero potential scattering and (ii) the breaking of inversion symmetry either by unequal magnitudes of potential scattering and/or magnetic moments, microwave irradiation induces an additional phase-independent contribution to the current. This leads to asymmetric critical currents for opposite current polarities, an effect absent in the same junction without microwave irradiation. The asymmetry is highly tunable via the microwave amplitude and frequency, and we may even achieve perfect asymmetry where the critical current vanishes for one polarity, akin to a perfect diode. While Yu-Shiba-Rusinov states provide the ideal platform for a pronounced asymmetry, we find that as long as the two conditions (i) and (ii) above are met, our proposal does not necessarily depend upon them.

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• Critical current
• Josephson effect
• Superconductivity
• Superconductors
• BCS theory
• Discrete symmetries in condensed matter
• Green's function methods
• Methods in superconductivity
• Microwave techniques
• Symmetries in condensed matter