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Superconductors lacking both inversion symmetry and time-reversal symmetry have been attracting much attention as a platform for exotic superconducting phases and anomalous phenomena, including the superconducting diode effect. Recent studies revealed intrinsic phases with this symmetry, named anapole superconductivity and monopole superconductivity, which are P T -symmetric superconducting states with and without Cooper pairs' total momentum, respectively. To explore characteristic phenomena in these states, we calculate and predict the superconducting piezoelectric effect and superconducting diode effect. A close relationship with the finite-q pairing, asymmetric Bogoliubov spectrum, and quantum geometry is discussed. This study reveals the piezoelectric and diode effects as potential probes to elucidate exotic superconducting phases.

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