Paper published in Nature Materials: Gap suppression at a Lifshitz transition in a multi-condensate superconductor

In a superconductor, electrons form Cooper pairs that merge to build a quantum collective state or condensate, adopting the same phase as if all the particles could be described as a unique wave with the same energy. Put in other words, all particles become identical from a physical point of view, and the whole group starts behaving as though it were a single particle. The idea of a large number of quantum particles forming a collective state was developed by Bose and Einstein in the 1920’s for the case of diluted atomic gases and the concept has been extended since then to other systems, including superconductors and superfluids.

Contrary to an ordinary metal, where a vanishingly small energy is enough to excite an electron and change its energy, a nonzero energy is required to break the electron pairs in a superconductor condensate. This is precisely why a superconductor has a zero electric resistance, since any energy below a critical value cannot break the electron pair, so that electrons cannot be scattered out of the collective quantum state. The minimum energy to break a Cooper pair is called the gap. In the simplest case, a single electronic band contributes to form the Cooper pair, and the gap is defined univocally. However, when Cooper pairs can form from different electron bands, a multi-condensate superconductor (also called multi-gapped) may emerge.

Several materials may exhibit multi-condensate behavior, including cuprates, pnictides or 2D- superconductors. A particular case is the 2D-electon gas (2DEG) at the interface between SrTiO3 (STO) and LaAlO3 (LAO). Figure 1 shows a schematic depiction of the different electronic states and bands associated with this 2DEG for two different crystallographic orientations (G. Herranz et al., Nature Communications 2015). Because of the multiple-band structure, the 2DEG at LAO/STO is a candidate for a multi-condensate state.

Figure 5

Figure 1. From  Herranz et al., Nature Comms 2015

So far, it has been predicted theoretically that the superconductivity of LAO/STO may involve two condensates and that a repulsive coupling exists between the two condensates. These predictions have awaited so far an experimental confirmation.

This is precisely the fundamental novelty of our work, namely, the first experimental demonstration of multi-condensate superconductivity in a SrTiO3-based system. We stress that SrTiO3 is a unique superconductor, as it the most dilute known superconductor, with the onset of superconductivity at carrier densities orders of magnitude lower than any other superconductor. Unsurprisingly, the origin of superconductivity in this material is still nowadays a matter of intense debate that started 50 years ago.

Our work provides novel and fundamental pieces of information relevant to this longstanding debate. A key aspect of our study is the observation, for the first time, of a transition between a regime of single-condensate superconductivity and a regime of two-condensate superconductivity. The experiments were done using resonant microwave transport characterization and were carried out in the Laboratoire de Physique et d’Etude des Matériaux, ESPCI Paris (Dr. Nicolas Bergeal), enabling continuous and reversible transitions between the two condensate regimes via electrostatic gating, which enables to control electrostatically the orbital occupation of the electronic states depicted in Figure 1. Our results can be interpreted consistently with unconventional s+-wave pairing, where the interaction between the two condensates is repulsive. This result is of broad interest for the field of superconductivity since this exotic state is the subject of considerable attention in other superconductor families including iron-pnictides and chalcogenides.

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