Transition metal dichalcogenide (TMD) bilayers are a new class of tunable moiré systems attracting interest as quantum simulators of strongly-interacting electrons in two dimensions. In particular, recent theory predicts that the correlated insulator observed in WSe$_2$/WS$_2$ at half filling is a charge-transfer insulator similar to cuprates and, upon further hole doping, exhibits a transfer of charge from anion-like to cation-like orbitals at different locations in the moiré unit cell. In this work, we demonstrate that in this doped charge-transfer insulator, tightly-bound charge-2e excitations can form to lower the total electrostatic repulsion. This composite excitation, which we dub a trimer, consists of a pair of holes bound to a charge-transfer exciton. When the bandwidth of doped holes is small, trimers crystallize into insulating pair density waves at a sequence of commensurate doping levels. When the bandwidth becomes comparable to the pair binding energy, itinerant holes and charge-2e trimers interact resonantly, leading to unconventional superconductivity similar to superfluidity in an ultracold Fermi gas near Feshbach resonance. Our theory is broadly applicable to strongly-interacting charge-transfer insulators, such as WSe$_2$/WS$_2$ or TMD homobilayers under an applied electric field.
We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. W…
Gossamer Superconductivity in Moiré WSe$_2$ Bilayer
ShanghaiTech University（上海科技大学）；Peking University（北京大学）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论科学研究中心）
It has long been speculated that quasi-two-dimensional superconductivity can reappear above its semiclassical upper critical field due to Landau quantization, yet this reentrant property has never been observed. Here, we argue that twisted bilayer graphene at a magic angle (MATBG) is an ideal system in which to search for this phenomenon because its Landau levels are doubly degenerate, and its superconductivity appears already at carrier densities small enough to allow the quantum limit to be reached at relatively modest magnetic fields. We study this problem theoretically by combining a simpl…
The moiré Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. In this attractive regime, we stud…
Driven-dissipative superconductivity in moiré heterostructure without attraction
Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科技大学光子科学研究所）；Institute of Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
Recently, superconductivity was discovered at very low densities in slightly misaligned graphene multilayers. Surprisingly, despite extremely low electronic density (about $10^{-4}$ electrons per unit cell), these systems realize strong-coupling superconductivity, with the transition temperature being a large fraction of the Fermi energy ($T_c\sim 0.1 ε_F$). Here we propose a qualitative explanation for this remarkable phenomenon, highlighting similarities and qualitative differences with the conventional uniform high-density superconductivity. Most importantly, we find that periodic superimpo…
We construct a van der Waals heterostructure consisting of three graphene layers stacked with alternating twisting angles $\pmθ$. At the average twist angle $θ\sim 1.56^{\circ}$, a theoretically predicted magic angle for the formation of flat electron bands, narrow conduction and valence moiré bands appear together with a linearly dispersing Dirac band. Upon doping the half-filled moiré valence band with holes, or the half-filled moiré conduction band with electrons, displacement field tunable superconductivity emerges, reaching a maximum critical temperature of 2.1 K at optimal doping and dis…
Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model on a honeycomb lattice. We find that the $f$-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and non-topological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply quali…
Collective plasma excitations in moiré flat bands display unique properties reflecting strong electron-electron interactions and unusual carrier dynamics in these systems. Unlike the conventional two-dimensional plasmon modes, dispersing as $\sqrt{k}$ at low frequencies and plunging into particle-hole continuum at higher frequencies, the moiré plasmons pierce through the flat-band continuum and acquire a strong over-the-band character. Due to the complex structure of the moiré superlattice unit cell, the over-the-band plasmons feature several distinct branches connected through zone folding in…
Moiré superlattices have recently emerged as a novel platform where correlated physics and superconductivity can be studied with unprecedented tunability. Although correlated effects have been observed in several other moiré systems, magic-angle twisted bilayer graphene (MATBG) remains the only one where robust superconductivity has been reproducibly measured. Here we realize a new moiré superconductor, mirror symmetric magic-angle twisted trilayer graphene (MATTG) with dramatically richer tunability in electronic structure and superconducting properties. Hall effect and quantum oscillations m…
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 universal properties of moiré flat bands that shall emerge in the presence of inter-valley attractions. 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 sy…
Experimental demonstrations of tunable correlation effects in magic-angle twisted bilayer graphene have put two-dimensional moiré quantum materials at the forefront of condensed-matter research. Other twisted few-layer graphitic structures, boron-nitride, and homo- or hetero-stacks of transition metal dichalcogenides (TMDs) have further enriched the opportunities for analysis and utilization of correlations in these systems. Recently, within the latter material class, strong spin-orbit coupling or excitonic physics were experimentally explored. The observation of a Mott insulating state and ot…
Exciton-roton mode in moiré fractional Chern insulators
Tsinghua University（清华大学）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Frontier Science Center for Quantum Information, Beijing（北京量子前沿科学中心）
Understanding the mechanism of high temperature (high Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high Tc superconductivity arises from a doped Mott insulator as described by the Hubbard model. An exact solution of the Hubbard model, however, is extremely challenging due to the strong electron-electron correlation. Therefore, it is highly desirable to experimentally study a model Hubbard system in which the unconventional superconductivity can be continuously tuned by varying the Hubbard parameters. Here we report signatures of tunable su…
The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) has established moiré quantum matter as a new platform to explore interaction-driven and topological quantum phenomena. Multitudes of phases have been realized in moiré systems, but surprisingly, robust superconductivity has been one of the least common of all, initially found in MATBG and only more recently also in magic-angle twisted trilayer graphene (MATTG). While MATBG and MATTG share some similar characteristics, they also exhibit substantial differences, such as in their response to …
We discover chiral phonons at the lowest-energy bands in moiré superlattices. The moiré chiral phonons we uncover are the collective excitations of the stacking domains. Their origin is uniquely attributed to the stacking configurations whose interlayer binding energy breaks the $C_{2z}$ symmetry on the moiré length scale. Within elastic theory, we use a general symmetry analysis to provide a complete classification of van der Waals heterostructures in respect to hosting moiré chiral phonons and show the calculation for twisted MoS$_2$ as an example. We present a low-energy effective model to …
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 su…
Twisted bilayer graphene (TBG) develops large moiré patterns at small twist angles with flat energy bands hosting domes of superconductivity. The large system size and intricate band structure have however hampered investigations into the superconducting state. Here, using full-scale atomistic modelling with local electronic interactions, we find at and above experimentally relevant temperatures a highly inhomogeneous superconducting state with nematic ordering on both atomic and moiré length scales. The nematic state has a locally anisotropic real-valued d-wave pairing, with a nematic vector …
Extended strange metal and superconductivity in partially filled moiré Hubbard bands
Cornell University（康奈尔大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）；University of Delaware（特拉华大学）；National Institute for Materials Science（日本国立材料研究所）
Superconductivity Proximate to Non-Abelian Fractional Spin Hall Insulator in Twisted Bilayer MoTe$_2$
Pohang University of Science and Technology（浦项科技大学）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究院）
When layers of graphene are rotationally misaligned by the magic angle, the moiré superlattice features extremely flat bands. Due to the enhanced density of states, the Coulomb interaction induces a variety of instabilities. The most prominent occur at integer filling and are therefore commonly attributed to spontaneous polarization of the moiré unit cell's `flavor' degrees of freedom -- spin, valley, and the flat-band degeneracy. As the dominant member of the hierarchy, these correlated states are thought to crucially determine further instabilities at lower energy scales, such as superconduc…
Collective Spin Excitations in Correlated Moiré Chern Ferromagnets
Condensed Matter Theory Center, Department of Physics, University of Maryland（马里兰大学凝聚态理论中心）；Department of Physics, The University of Texas at Dallas（德克萨斯大学达拉斯分校物理系）
Extended s-wave superconductivity in M-point twisted bilayer SnSe2
University of Würzburg（维尔茨堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马克斯·普朗克研究所）；The Flatiron Institute（平顿研究所）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics, Princeton University（普林斯顿大学物理系）；ITAMP, Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Harvard University
Strong Correlations and Superconductivity in the Supermoiré Lattice
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院物理研究所）；Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin（柏林自由大学复杂量子系统达勒姆中心及物理系）；Research Center for Functional Materials, National Institute for Materials Science（国立材料科学研究所功能材料研究中心）；International Center for Materials Nanoarchitectonics, National Institute for Materials Science（国立材料科学研究所国际纳米材料架构中心）；National High Magnetic Field Laboratory（国家高磁场实验室）；Department of Physics, Florida State University（佛罗里达州立大学物理系）；Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院量子科学与工程中心）
Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling…
Moiré quantum matter has emerged as a novel materials platform where correlated and topological phases can be explored with unprecedented control. Among them, magic-angle systems constructed from two or three layers of graphene have shown robust superconducting phases with unconventional characteristics. However, direct evidence for unconventional pairing remains to be experimentally demonstrated. Here, we show that magic-angle twisted trilayer graphene (MATTG) exhibits superconductivity up to in-plane magnetic fields in excess of 10 T, which represents a large ($2\sim3$ times) violation of th…
Spinless and spinful charge excitations in moiré Fractional Chern Insulators
Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Department of Physics, University of Florida（佛罗里达大学物理系）；Department of Physics, University of Washington（华盛顿大学物理系）；Department of Materials Science and Engineering, University of Washington（华盛顿大学材料科学与工程系）；Pacific Northwest National Laboratory（太平洋西北国家实验室）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基克，巴斯克科学基金会）；Center for Computational Quantum Physics, Flatiron Institute（西蒙斯平顿研究所计算量子物理中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学）
Bilayer Moiré structures are a highly tunable laboratory to investigate the physics of strongly correlated electron systems. Moiré transition metal dichalcogenides at low-energies, in particular, are believed to be described by a single narrow band Hubbard model on a triangular lattice with spin-orbit coupling. Motivated by recent experimental evidence for superconductivity in twisted bilayer materials, we investigate the possible superconducting pairings in a two-dimensional single band Rashba-Hubbard model. Using a random-phase approximation in the presence of nearest and next-nearest neighb…
