Anapole superconductivity recently proposed for multiband superconductors [Commun. Phys. 5, 39 (2022)] is a key feature of time-reversal (T )-symmetry-broken polar superconductors. The anapole moment was shown to arise from the asymmetric Bogoliubov spectrum, which induces a finite center of mass momenta of Cooper pairs at the zero magnetic field. In this paper, we show an alternative mechanism of anapole superconductivity: the quantum geometry induces the anapole moment when the interband pairing and Berry connection are finite. Thus, the anapole superconductivity is a ubiquitous feature of T -broken multiband polar superconductors. Applying the theory to a minimal model of UTe2, we demonstrate the quantum-geometry-induced anapole superconductivity. Furthermore, we show the Bogoliubov Fermi surfaces (BFS) in an anapole superconducting state and predict an unusual temperature dependence of BFS due to the quantum geometry. Experimental verification of these phenomena may clarify the superconducting state in UTe2 and reveal the ubiquitous importance of quantum geometry in exotic superconductors.

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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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