Moir\'e heterostructures: a condensed matter quantum simulator

We propose twisted van der Waals heterostructures as an efficient, reliable and scalable quantum platform that enables the seamless realization and control of a plethora of interacting quantum models in a solid state framework. These new materials hold great promise to realize novel and elusive states of matter in experiment. Going one step beyond, in this paper we propose these systems as a robust quantum simulation platform to study strongly correlated physics and topology that is notoriously difficult to study computationally. Among the features that make these materials a versatile toolbox are (i) tunability of properties via readily accessible external parameters (such as gating, straining, packing and twist angle), (ii) ability to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed matter physics and beyond and (iii) state-of-the-art experimental readouts exist to directly map out their rich phase diagrams in and out of equilibrium. This general framework, besides unravelling new phases of matter, permits to identify their key microscopic ingredients and therefore to robustly realize and functionalize those new phases in other material systems, deepening our fundamental understanding and holding many promises for future technological applications.

[1]  Mit H. Naik,et al.  Ultraflatbands and Shear Solitons in Moiré Patterns of Twisted Bilayer Transition Metal Dichalcogenides. , 2018, Physical review letters.

[2]  Kenji Watanabe,et al.  Observation of fractional Chern insulators in a van der Waals heterostructure , 2017, Science.

[3]  One-dimensional flat bands in twisted bilayer germanium selenide , 2019, Nature Communications.

[4]  R. Averitt,et al.  Towards properties on demand in quantum materials. , 2017, Nature materials.

[5]  Unconventional critical behaviour in a quasi-two-dimensional organic conductor , 2005, Nature.

[6]  J. Shan,et al.  Evidence of high-temperature exciton condensation in two-dimensional atomic double layers , 2019, Nature.

[7]  J. Hone,et al.  Excitonic Phase Transitions in MoSe2/WSe2 Heterobilayers , 2020, 2001.03812.

[8]  G. Refael,et al.  Helical liquids and Majorana bound states in quantum wires. , 2010, Physical review letters.

[9]  Interfacial Charge Transfer Circumventing Momentum Mismatch at Two-Dimensional van der Waals Heterojunctions. , 2017, Nano letters.

[10]  A. Reina,et al.  Observation of Van Hove singularities in twisted graphene layers , 2009, 0912.2102.

[11]  T. Koretsune,et al.  Maximally Localized Wannier Orbitals and the Extended Hubbard Model for Twisted Bilayer Graphene , 2018, Physical Review X.

[12]  N. Yuan,et al.  Model for the metal-insulator transition in graphene superlattices and beyond , 2018, Physical Review B.

[13]  J. Shan,et al.  Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices , 2020, Nature.

[14]  E. Kaxiras,et al.  Collective excitations in twisted bilayer graphene close to the magic angle , 2019, 1910.07893.

[15]  Fengcheng Wu,et al.  Topological Exciton Bands in Moiré Heterojunctions. , 2016, Physical review letters.

[16]  Á. Rubio,et al.  Cavity Control of Excitons in Two-Dimensional Materials , 2018, Nano letters.

[17]  Hemant Kumar,et al.  Tunable strain soliton networks confine electrons in van der Waals materials , 2019, 1910.14231.

[18]  Kenji Watanabe,et al.  Moiréless correlations in ABCA graphene , 2019, Proceedings of the National Academy of Sciences.

[19]  Yulin Chen,et al.  Interaction effects and superconductivity signatures in twisted double-bilayer WSe$_2$ , 2019, 1907.03966.

[20]  Cheng-Cheng Liu,et al.  Chiral Spin Density Wave and d+id Superconductivity in the Magic-Angle-Twisted Bilayer Graphene. , 2018, Physical review letters.

[21]  Takashi Taniguchi,et al.  Unconventional superconductivity in magic-angle graphene superlattices , 2018, Nature.

[22]  D. K. Efimkin,et al.  Helical network model for twisted bilayer graphene , 2018, Physical Review B.

[23]  A. Vishwanath,et al.  Flat band in twisted bilayer Bravais lattices , 2019, Physical Review Research.

[24]  M. Katsnelson,et al.  Magnetic Two-Dimensional Chromium Trihalides: A Theoretical Perspective. , 2020, Nano letters.

[25]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[26]  S. Larentis,et al.  Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene , 2017, Proceedings of the National Academy of Sciences.

[27]  S. Trebst,et al.  Realization of nearly dispersionless bands with strong orbital anisotropy from destructive interference in twisted bilayer MoS2 , 2020, Nature Communications.

[28]  E. Kaxiras,et al.  Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene , 2018, Nature Materials.

[29]  P. Kim,et al.  Photonic crystals for nano-light in moiré graphene superlattices , 2018, Science.

[30]  Á. Rubio,et al.  Multiflat Bands and Strong Correlations in Twisted Bilayer Boron Nitride: Doping-Induced Correlated Insulator and Superconductor , 2019, Nano letters.

[31]  T. Taniguchi,et al.  Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect , 2019, Nature.

[32]  M. Lukin,et al.  Electrical control of interlayer exciton dynamics in atomically thin heterostructures , 2018, Science.

[33]  M. Hafezi,et al.  Cavity Quantum Eliashberg Enhancement of Superconductivity. , 2018, Physical review letters.

[34]  F. Guinea,et al.  Polaritons in layered two-dimensional materials. , 2016, Nature materials.

[35]  A. Millis,et al.  Evidence of an Improper Displacive Phase Transition in Cd_{2}Re_{2}O_{7} via Time-Resolved Coherent Phonon Spectroscopy. , 2018, Physical review letters.

[36]  D. Mandrus,et al.  A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd2Re2O7 , 2017, Science.

[37]  Á. Rubio,et al.  Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity , 2018, Science Advances.

[38]  Y. Nishio,et al.  Electronic phases in an organic conductor α-(BEDT-TTF)2I3 : Ultra narrow gap semiconductor, superconductor, metal, and charge-ordered insulator , 2006 .

[39]  Kenji Watanabe,et al.  Visualization of moiré superlattices , 2020, Nature Nanotechnology.

[40]  S. Das Sarma,et al.  Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. , 2010, Physical review letters.

[41]  Kenji Watanabe,et al.  Topologically Protected Helical States in Minimally Twisted Bilayer Graphene. , 2018, Physical review letters.

[42]  L. Balents,et al.  Superconductivity and strong correlations in moiré flat bands , 2020 .

[43]  E. Tutuc,et al.  Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands. , 2018, Physical review letters.

[44]  J. Lischner,et al.  Strong correlations and d+id superconductivity in twisted bilayer graphene , 2018, Physical Review B.

[45]  Feng Wang,et al.  Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice , 2018, Nature Physics.

[46]  D. Graf,et al.  Tuning superconductivity in twisted bilayer graphene , 2018, Science.

[47]  Kenji Watanabe,et al.  Signatures of tunable superconductivity in a trilayer graphene moiré superlattice , 2019, Nature.

[48]  M. Beck,et al.  Magneto-transport controlled by Landau polariton states , 2018, Nature Physics.

[49]  Kenji Watanabe,et al.  Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene , 2020, Nature.

[50]  K. L. Shepard,et al.  Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices , 2013, Nature.

[51]  Hao Wang,et al.  Soliton superlattices in twisted hexagonal boron nitride , 2019, Nature Communications.

[52]  L. Balents,et al.  Noncollinear phases in moiré magnets , 2020, Proceedings of the National Academy of Sciences.

[53]  G. Refael,et al.  Author Correction: Electronic correlations in twisted bilayer graphene near the magic angle , 2019, Nature Physics.

[54]  T. Taniguchi,et al.  Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene , 2019, Nature.

[55]  Kenji Watanabe,et al.  Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene , 2019, Nature.

[56]  R. Bistritzer,et al.  Moiré bands in twisted double-layer graphene , 2010, Proceedings of the National Academy of Sciences.

[57]  Sefaattin Tongay,et al.  Ultrafast charge transfer in atomically thin MoS₂/WS₂ heterostructures. , 2014, Nature nanotechnology.

[58]  P. Kim,et al.  Tunable spin-polarized correlated states in twisted double bilayer graphene , 2020, Nature.

[59]  Garnet Kin-Lic Chan,et al.  Stripe order in the underdoped region of the two-dimensional Hubbard model , 2016, Science.

[60]  M. Kastner,et al.  Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene , 2019, Science.

[61]  Kenji Watanabe,et al.  Untying the insulating and superconducting orders in magic-angle graphene , 2020, Nature.

[62]  S. Banerjee,et al.  Evidence for moiré excitons in van der Waals heterostructures , 2018, Nature.

[63]  J. Dalibard,et al.  Quantum simulations with ultracold quantum gases , 2012, Nature Physics.

[64]  Kenji Watanabe,et al.  Correlated Insulating States in Twisted Double Bilayer Graphene. , 2019, Physical review letters.

[65]  K. Shepard,et al.  Boron nitride substrates for high-quality graphene electronics. , 2010, Nature nanotechnology.

[66]  J. Hone,et al.  Disassembling 2D van der Waals crystals into macroscopic monolayers and reassembling into artificial lattices , 2020, Science.

[67]  L. Balents Spin liquids in frustrated magnets , 2010, Nature.

[68]  L Li,et al.  Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet. , 2015, Nature Materials.

[69]  T. Taniguchi,et al.  Tunable crystal symmetry in graphene–boron nitride heterostructures with coexisting moiré superlattices , 2019, Nature Nanotechnology.

[70]  Kenji Watanabe,et al.  Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene , 2019, Nature.

[71]  P. Kim,et al.  Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene , 2019, Nature Communications.

[72]  D. Basov,et al.  Nanoscale electrodynamics of strongly correlated quantum materials , 2017, Reports on progress in physics. Physical Society.

[73]  T. Taniguchi,et al.  Maximized electron interactions at the magic angle in twisted bilayer graphene , 2018, Nature.

[74]  Yang Wang,et al.  Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene , 2015, 1510.02888.

[75]  Gate-dependent Pseudospin Mixing in Graphene/boron Nitride Moire Superlattices , 2014, 1405.2032.

[76]  L. Fu,et al.  Superconducting proximity effect and majorana fermions at the surface of a topological insulator. , 2007, Physical review letters.

[77]  Xiaodong Xu,et al.  Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions , 2020, Nature Materials.

[78]  T. Taniguchi,et al.  Strongly correlated electrons and hybrid excitons in a moiré heterostructure , 2020, Nature.

[79]  A. Millis,et al.  Three-dimensional metallic and two-dimensional insulating behavior in octahedral tantalum dichalcogenides , 2014, 1401.0246.

[80]  A. Georges,et al.  Superradiant Quantum Materials. , 2018, Physical review letters.

[81]  Kenji Watanabe,et al.  Observation of moiré excitons in WSe2/WS2 heterostructure superlattices , 2018, Nature.

[82]  Juwon Lee,et al.  Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures , 2019, Nature.

[83]  Xiaodong Xu,et al.  Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers , 2018, Nature.

[84]  Xiaodong Xu,et al.  Tunable correlation-driven symmetry breaking in twisted double bilayer graphene , 2020 .

[85]  E. Kaxiras,et al.  Correlated insulator behaviour at half-filling in magic-angle graphene superlattices , 2018, Nature.

[86]  J. Zhu,et al.  Intrinsic quantized anomalous Hall effect in a moiré heterostructure , 2019, Science.

[87]  K. T. Law,et al.  Ising pairing in superconducting NbSe2 atomic layers , 2015, 1507.08731.

[88]  A. Cavalleri,et al.  Cavity-Mediated Electron-Photon Superconductivity. , 2018, Physical review letters.

[89]  Á. Rubio,et al.  Universal optical control of chiral superconductors and Majorana modes , 2018, Nature Physics.

[90]  Xiaodong Xu,et al.  Superconductivity in metallic twisted bilayer graphene stabilized by WSe2 , 2020, Nature.

[91]  S. Louie,et al.  Strong correlations and orbital texture in single-layer 1T-TaSe2 , 2020 .

[92]  L. Balents,et al.  Topological Superconductivity in Twisted Multilayer Graphene. , 2018, Physical review letters.

[93]  G. Ma,et al.  Observation of Dicke cooperativity in magnetic interactions , 2018, Science.

[94]  L. Fu,et al.  Quantum spin Hall effect in two-dimensional transition metal dichalcogenides , 2014, Science.

[95]  Angel Rubio,et al.  From a quantum-electrodynamical light–matter description to novel spectroscopies , 2018 .

[96]  Y. Shimizu,et al.  Spin liquid state in an organic Mott insulator with a triangular lattice. , 2003, Physical review letters.

[97]  A. Vishwanath,et al.  Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene , 2018, Physical Review X.

[98]  R. Feynman Simulating physics with computers , 1999 .

[99]  Vinod M. Menon,et al.  Optical control of room-temperature valley polaritons , 2017, Nature Photonics.

[100]  W. Yao,et al.  Skyrmions in the Moiré of van der Waals 2D Magnets. , 2018, Nano letters.