Superfluidity and Quantum Geometry in Twisted Multilayer Systems (2111.00807v2)

Abstract: Designer 2D materials where the constituent layers are not aligned may result in band structures with dispersionless, "flat" bands. Twisted bilayer graphene has been found to show correlated phases as well as superconductivity related to such flat bands. In parallel, theory work has discovered that superconductivity and superfluidity is determined by the quantum geometry and topology of the band structure. These recent key developments are merging to a flourishing research topic: understanding the possible connection and ramifications of quantum geometry on the induced superconductivity and superfluidity in moir\'e multilayer and other flat band systems. This article presents an introduction to how quantum geometry governs superfluidity in platforms including, and beyond, graphene. We explain how a new type of topology discovered in TBG could affect superconductivity, pinpoint the geometric contribution in its Beretzinskii-Kosterlitz-Thouless (BKT) critical temperature, and mention moir\'e materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moir\'e materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.

Superfluidity and Quantum Geometry in Twisted Multilayer Systems

The research paper titled "Superfluidity and Quantum Geometry in Twisted Multilayer Systems" explores the intriguing interplay between superconductivity and quantum geometry in systems characterized by flat bands, such as twisted multilayer graphene. The paper presents a comprehensive analysis of how quantum geometry can influence superfluidity, alongside an exploration of potential pathways to achieve higher temperature superconductivity through band structure and topology design.

Flat Bands and Quantum Geometry

Flat bands in condensed matter systems refer to electronic bands where the energy dispersion is approximately constant across momentum space. These bands offer a high density of states at the Fermi energy, which can significantly increase the critical temperature $T_c$ for superconductivity due to enhanced electron-electron interactions. While flat bands facilitate the formation of Cooper pairs (bosonic pairs of electrons necessary for superconductivity), they pose challenges for achieving superfluidity, as localized particles in a flat band typically exhibit insulating behavior.

The paper elucidates that the existence of supercurrents in flat bands is contingent upon the non-trivial quantum geometry of these bands, characterized by parameters such as the quantum geometric tensor (QGT) and the Berry curvature. The quantum metric, derived from the real part of the QGT, fundamentally governs superfluidity by quantifying the overlap of Wannier functions, which are localized wave packets. A substantial overlap enabled by quantum geometric properties allows movement of particle pairs, thus facilitating supercurrents even in flat band systems.

Twisted Bilayer Graphene (TBG)

Twisted bilayer graphene, a paradigm of moiré materials, emerges when two graphene layers are rotated relative to each other by a small angle. This twist creates a superlattice that exhibits nearly flat electronic bands at certain "magic angles." TBG has demonstrated the potential for superconductivity at very low electron densities, making it a focus of contemporary research. The paper discusses how quantum geometric effects play a pivotal role in TBG's superconductive properties, particularly through a topological invariant known as the Euler class, which provides a lower bound for superfluid weight in these materials.

Contributions to Superfluid Weight

The paper distinguishes between conventional and geometric contributions to superfluid weight, deriving from diagonal and off-diagonal matrix elements of the current operator, respectively. In flat band systems, the geometric contribution can predominate, offering a compelling framework for understanding superfluidity in multilayer systems where band topology and quantum geometry are well-defined.

Implications and Innovations

The implications of this research are profound, offering pathways to engineer materials for elevated temperature superconductivity by manipulating band dispersion properties and enhancing quantum geometric effects. The findings propose theoretical frameworks for the realization of room-temperature superconductivity by leveraging topological properties inherent in flat band systems.

Future Directions

Looking ahead, this paper envisions a multidisciplinary approach encompassing advancements in both material science and ultracold gas experiments. While moiré materials provide practical avenues for enhancing superconductivity, ultracold gas systems offer a clean and highly tunable platform to simulate and explore underlying quantum effects. The synergistic exploration of moiré platforms alongside ultracold gases might unravel novel insights into quantum geometric influences on superfluidity, possibly heralding breakthroughs in the quest for practical high-temperature superconductors.