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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 moiré 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 moiré materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moiré materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.
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 moiré 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 moiré materials beyond TBG. Ultracold gases are introduced as a complementary platform for quantum geometric effects and a comparison is made to moiré materials. An outlook sketches the prospects of twisted multilayer systems in providing the route to room temperature superconductivity.
Although evidence of inter-valley attraction-mediated by phonon or topological fluctuations is accumulating, the origin of superconductivity in the flat-band quantum moiré materials remains an open question. Here, instead of attempting to pinpoint the origin of the superconductivity, we aim at identifying nontrivial phenomena that emerge in the presence of inter-valley attractions, in addition to the superconducting dome. We show that by matching the interaction strength of inter-valley attraction with intra-valley repulsion, the flat-band limit becomes exactly solvable. Away from the flat-band limit, the system can be simulated via quantum Monte Carlo (QMC) methods without sign problem for any fillings. Combining analytic solutions with large-scale numerical simulations, we show that upon increasing temperature, the superconducting phase melts into a bosonic fluid of Cooper pairs with large/diverging compressibility, in strong analogy to flat bands in attractive Hubbard models. At higher temperature, the boson fluid phase gives its way to a pseudo gap phase, where some Cooper pairs are torn apart by thermal fluctuations, resulting in fermion density of states inside the gap. In contrast to the superconducting transition temperature, which is very sensitive to doping and twisting angles, the gap and the temperature scale of the boson fluid phase and the pseudo gap phase are found to be nearly independent of doping level and/or flat-band bandwidth. The relevance of these phases with experimental discoveries in the flat band quantum moiré materials is discussed.
Studies of twisted morie systems have been mainly focused on 2D materials like graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a new twisted bilayer of 2D systems which feature quadratic-band-touching points and find exotic physics different from previously studied twisted morie systems. Specifically, we show that exactly flat bands can emerge at magic angles and, more interestingly, each flat band exhibits a high Chern number (C = ±2) which was not realized in bilayer morie systems before. We further consider the effect of Coulomb interactions in such magic-angle twisted system and find that the ground state supports the quantum anomalous Hall effect with quantized Hall conductivity 2 e 2 hc at certain filling. Furthermore, possible physical realization of such twisted bilayer systems will be briefly discussed.
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