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Parity violation effects in the Josephson junction of a $p$-wave superconductor

The phenomenon of the parity violation due to weak interaction may be studied with superconducting systems. Previous research considered the case of conventional superconductors. We here theoretically investigate the parity violation effect in an unconventional $p$-wave ferromagnetic superconductor, and find that its magnitude can be increased by three orders of magnitude, as compared to results of earlier studies. For potential experimental observations, the superconductor UGe$_2$ is suggested, together with the description of a possible experimental scheme allowing one to effectively measure and control the phenomenon. Furthermore, we put forward a setup for a further significant enhancement of the signature of parity violation in the system considered.