Electric field effects in ultrathin metallic superconductors

Understanding the interplay of electricity and superconductivity is a fundamental problem that stands out for its general relevance, the great impact it can have for accessing, controlling or driving new phases of quantum matter, and the enticing perspectives for the development of future quantum technologies. Electric field effects have been mostly employed to drive or control the superconducting phase by gating materials in a low-to-moderate density regime and thin enough to avoid shielding of the electric field. However, the recent discovery of unconventional gating effects in elemental metallic superconductors [1] is challenging the current view of how electric field can impact on superconductivity. The major experimental findings demonstrate a rich variety of effects [1,2,3,4,5]: reduction or full suppression of the critical supercurrent, also for suspended nanostructures and through ionic-gating, manipulation of the superconducting phase in interferometric setups, enhancement of phase fluctuations, and weak interrelation between the critical magnetic field and the critical voltage related to the suppression of the supercurrent. In this context, we have theoretically investigated the physical mechanisms for achieving an electrical control of conventional spin-singlet superconductivity in thin films by focusing on the role of surface orbital polarization as due to the electrically induced orbital-Rashba coupling at the surface of the superconductor. Assuming a realistic multi-orbital description of the metallic state, due to screening effects the electric field is shown to act by essentially modifying the strength of the surface potential. The resulting orbital polarization at the surface and in its close proximity is found to have a dramatic impact on superconductivity. We demonstrate that, by varying the strength of the electric field, the superconducting phase can be either suppressed, i.e. turned into normal metal, or undergo a 0−$\pi$ transition with the $\pi$-phase being marked by non-trivial sign change of the superconducting order parameter between different bands [6]. The occurrence of orbital dependent phase frustration can naturally account for the observation of the suppression of the critical supercurrent without change in the critical temperature. Remarkably, we have also demonstrated that the phases with $\pi$-pairing are robust to the application of external magnetic fields [7] in agreement with the experimental observations [7]. At last, tunnel spectroscopic signatures are analyzed in the phase space of the electrically driven superconducting states [8]. We determine the tunneling conductance of superconductor-insulator-normal metal (SIN) and superconductor-insulator-superconductor (SIS) heterostructures with one superconducting side of the junction that is subjected to an external electric field. The distinctive marks for spectroscopically distinguishing the various electrically driven phases are highlighted for both SIN and SIS geometries. The overall findings unveil a rich scenario to design heterostructures with superconducting orbitronics effects for the achievement of all-electric superconducting devices.

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[2] F. Paolucci et al., AVS Quantum Science 1, 016501 (2019).
[3] M. F. Ritter et al., Nat. Commun. 12, 1266 (2021).
[4] F. Paolucci et al., arXiv:2107.00935 (2021).
[5] F. Paolucci et al., Nano Lett. 19, 96263 (2019).
[2] M. T. Mercaldo, P. Solinas, F. Giazotto, and M. Cuoco, Phys. Rev. Applied 14, 034041 (2020).
[3] L. Bours, M. T. Mercaldo, M. Cuoco, E. Strambini, and F. Giazotto, Phys. Rev. Research 2, 033353 (2020).
[4] M. T. Mercaldo, F. Giazotto, and M. Cuoco, arXiv:2012.01490 (2020).

We acknowledge support by the EU’s Horizon 2020 research and innovation program under Grant Agreement nr. 964398 (SUPERGATE).