Normal State Quantum Geometry and Superconducting Domes in (111) Oxide Interfaces

We theoretically investigate the influence of the normal state quantumgeometry on the superconducting phase in (111) oriented oxide interfaces anddiscuss some of the implications for the LaAlO_3/SrTiO_3(LAO/STO) heterostructure. From a tight-binding modeling of the interface, wederive a two-band low-energy model, allowing us to analytically compute thequantum geometry and giving us access to the superfluid weight, as well as toshowcase the role of two particular relevant energy scales. One is given by thetrigonal crystal field which stems from the local trigonal symmetry at theinterface, and the other one is due to orbital mixing at the interface. Ourcalculations indicate that the variation of the superfluid weight with thechemical potential μ is controlled by the quantum geometry in the low-μlimit where it presents a dome. At higher values of μ the conventionalcontribution dominates. In order to make quantitative comparisons between ourresults and experimental findings, we rely on an experimentally observed globalreduction of the superfluid weight that we apply to both the conventional andgeometric contributions. Furthermore, an experimentally measured non-monotonicvariation of μ with the gate voltage V_g is taken into account and yieldsa two-dome scenario for the superconducting critical temperature as a functionof V_g. The observed dome in the low-V_g regime is explained by thenon-monotonic evolution of a dominant conventional part of the superfluiddensity. In contrast, the expected second dome at larger values of V_g limitwould be due to a dominant quantum-geometric contribution.