Quantum-geometry-induced anapole superconductivity

Abstract

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.

Piezoelectric effect and diode effect in anapole and monopole superconductors

“…The effective anapole moment in the superconducting state is defined by the first derivative of thermodynamic potential with respect to the Cooper pairs' momentum [37], and thus, finite anapole moment directly indicates the finite-q pairing state. As clarified in our recent work, there exist several origins of the effective anapole moment [38]. They are classified into the group velocity term and the geometric term.…”

“…states. An intriguing class is the anapole superconductivity, where Cooper pairs can get finite total momentum at zero magnetic field [37,38]. The anapole superconducting state is distinguished by the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [39,40] and the helical superconducting state [41,42] which require finite magnetic field or spin polarization.…”

“…The anapole superconducting state is distinguished by the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [39,40] and the helical superconducting state [41,42] which require finite magnetic field or spin polarization. In the anapole superconductors, the finite-q pairing state is characterized by a polar vector named the effective anapole moment, which was recently revealed to arise from various origins [37,38]. On the other hand, the other classes of P T -symmetric superconducting states are nonpolar, and Cooper pairs condensate with zero total momentum.…”

“…An important consequence of the IS and TRS breaking is the asymmetric spectrum of Bogoliubov quasiparticles, which arises from the multiband effects in anapole and monopole superconductors [37,38]. In principle, we can distinguish all the P T -symmetric superconducting phases by the asymmetric profile of the Bogoliubov spectrum.…”

“…As a link of the SCPE and SDE with Cooper pairs' momentum was shown in the helical superconductors [18-20, 25, 43], we also discuss the properties of finite-q pairing in the anapole superconducting state for comparison. It is shown that the SCPE shows distinct behaviors depending on the origin of finite-q pairing, namely, the asymmetric Bogoliubov spectrum and quantum geometry [37,38].…”