Superpotentials, flat bands and the role of Quantum Geometry for the superfluid stiffness

TL;DR

This paper demonstrates that artificial superpotentials in 2D systems can enhance superconductivity by reconstructing electronic bands and leveraging quantum geometry, providing a tunable alternative to moire engineering.

Contribution

It introduces a method to engineer flat minibands via superpotentials, enhancing superconductivity and superfluid stiffness beyond traditional moire systems.

Findings

Superpotentials create flat minibands and increase Tc.

Superfluid stiffness arises from both quantum geometry and inherited kinetic energy.

Engineered superpotentials offer a tunable platform for high-temperature superconductivity.

Abstract

Enhancing superconductivity through material design is a central goal in quantum materials research. Moire engineering, where twisting stacked layers creates long-wavelength modulations and flat bands, has shown how electronic correlations can be amplified and eventually used to raise the superconducting critical temperature Tc. Yet this approach is largely confined to van der Waals materials and offers limited tunability. Here we explore a moire-inspired alternative: imposing artificial superpotentials on otherwise homogeneous systems to engineer flat electronic minibands. Whether such superlattice potentials can truly enhance superconductivity and sustain a finite superfluid stiffness remains, however, an open question. Our calculations show that a periodic superpotential imposed to a 2D system can indeed enhance superconductivity by reconstructing the electronic bands and creating regions of large density of states, leading to a substantial increase of Tc. In contrast to conventional flat band systems, where the superfluid stiffness arises solely from quantum geometry through the quantum metric, a modulated system inherits kinetic energy from the filled minibands below the Fermi level. This inherited component coexists with a positive quantum geometric contribution, yielding a finite and robust stiffness even when the upper band becomes nearly flat. The resulting superconducting state remains coherent and resilient against weak to moderate disorder. Our findings demonstrate that engineered superpotentials offer a tunable route to enhance superconductivity beyond twist based moire systems, unifying flat band amplification of pairing with preserved phase stiffness. They further highlight the central role of quantum geometry in shaping collective electronic phenomena and point to superlattice design as a promising platform for next-generation superconductors.