# Gap suppression at a Lifshitz transition in a multi-condensate superconductor

## Abstract

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen–Cooper–Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

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## Data availability

All data that support the findings of this study are available from the corresponding authors on reasonable request.

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## Acknowledgements

The authors thank K. Behnia and J. Lorenzana for useful discussions. This work was supported by the Région Ile-de-France in the framework of CNano IdF, OXYMORE and Sesame programmes, by CNRS through a PICS programme (S2S) and ANR JCJC (Nano-SO2DEG). This work was supported by the Spanish MAT2017-85232-R, MAT2014-56063-C2-1-R and Severo Ochoa SEV-2015-0496 grants and the Generalitat de Catalunya (2017 SGR 1377). This work was supported by the Italian MAECI under the Italia–India collaborative project SUPERTOP-PGR04879. The authors acknowledge funding from the project Quantox of QuantERA ERA-NET Cofund in Quantum Technologies (grant agreement no. 731473) implemented within the European Union’s Horizon 2020 Programme. The authors also acknowledge the COST project Nanoscale Coherent Hybrid Devices for Superconducting Quantum Technologies–Action CA16218.

## Author information

N.B. conceived and directed the project. G.Si. and A.J. performed the measurements under the supervision of N.B. Samples were fabricated by G.H., M.S. and F.S. G.Si., A.J. and N.B. carried out analysis of the results and wrote the manuscript with the help of L.B. and J.L. G.Si.,G.Sa, G.H., S.C., M.G. and C.F.-P. contributed to discussions of the results and commented on the final manuscript.

Correspondence to N. Bergeal.

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### Competing interests

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## Supplementary information

### Supplementary Information

Supplementary Notes 1–2, Supplementary Figs. 1–7, Supplementary refs. 1–7

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• #### DOI

https://doi.org/10.1038/s41563-019-0354-z