Orbital effects in spin-singlet superconductors: π-pairing, Edelstein effect, and orbital vortex phase

Maria Teresa Mercaldo

The breaking of point-group spatial symmetries can have a profound impact on superconductivity. We consider a multi-orbital spin-singlet superconductor without inversion symmetry, e.g. due to crystalline asymmetry as well as to electric field or mechanical strain. The lack of inversion symmetry yields orbital-Rashba couplings that can turn the superconductor into normal metal, or induce 0−π transition, with the π phase being marked by a sign change of the superconducting order parameter between different bands [1-2]. The occurrence of orbital dependent phase frustration can account for the observation of the suppression of the critical supercurrent without change in the critical temperature, observed in recent experiments [3-4]. Furthermore, in superconductors that lack inversion symmetry, the flow of supercurrent can induce a non-vanishing magnetization, a phenomenon which is at the heart of non-dissipative magneto-electric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments a question of fundamental relevance deals with the orbital nature of magneto-electric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than one order of magnitude greater than that due to the spin, giving rise to a colossal magneto-electric effect [5]. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone and in the presence of superconducting phase inhomogeneities, yielding domains with opposite orbital moment orientation. Finally, we show that in two-dimensional spin-singlet superconductors with very low degree of spatial symmetry content, vortices with neutral supercurrents carrying angular momentum around the core can form and be energetically stable [6]. The vortex has zero net magnetic flux since it is made up of counterpropagating Cooper pairs with opposite orbital moments. The overall findings unveil a rich scenario to design heterostructures with superconducting orbitronics effects for the achievement, for instance, of all-electric superconducting devices.

[1] M. T. Mercaldo, P. Solinas, F. Giazotto, and M. Cuoco, Phys. Rev. Applied 14, 034041 (2020)
[2] M. T. Mercaldo, F. Giazotto, and M. Cuoco, Phys. Rev. Research 3, 043042 (2021).
[3] G. De Simoni, et al., Nat. Nanotechnol. 13, 802 (2018).
[4] L. Bours, M. T. Mercaldo, M. Cuoco, E. Strambini, and F. Giazotto, Phys. Rev. Research 2, 033353 (2020).
[5] L. Chirolli, M.T. Mercaldo, C. Guarcello, F. Giazotto, and M. Cuoco, arXiv:2107.07476, Phys. Rev. Lett. (2022), to be published.
[6] M. T. Mercaldo, C. Ortix, F. Giazotto, and M. Cuoco, Phys. Rev. B 105, L140507 (2022).