Antiferromagnetically ordered Mott insulator and $d+id$ superconductivity in twisted bilayer graphene: A quantum Monte carlo study

Abstract

Using exact quantum Monte Carlo method, we examine the recent novel electronic states seen in magic-angle graphene superlattices. From the Hubbard model on a double-layer honeycomb lattice with a rotation angle $\theta =1.08^{\circ }$, we reveal that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half filling, and with a small doping, the pairing with $d+id$ symmetry dominates over other pairings at low temperature. The effective $d+id$ pairing interaction strongly increase as the on-site Coulomb interaction increases, indicating that the superconductivity is driven by electron-electron correlation. Our non-biased numerical results demonstrate that the twisted bilayer graphene share the similar superconducting mechanism of high temperature superconductors, which is a new and idea platform for further investigating the strongly correlated phenomena.

6 pages, 7 figures. A very careful revision on finite-size scaling analysis and sign problem are made, and some more references are added

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• Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
• Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• The pseudo-Landau-level representation of twisted bilayer graphene: band topology and the implications on the correlated insulating phase
• Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems
• Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
• Phonon-induced giant linear-in-$T$ resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity
• Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model
• Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene
• Flatbands in twisted double bilayer graphene
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• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene
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• Strong electron-phonon coupling, electron-hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
• Twisted bilayer graphene.VI. An Exact Diagonalization Study of Twisted Bilayer Graphene at Non-Zero Integer Fillings
• Twisted bilayer graphene I. Matrix elements, approximations, perturbation theory and a $k\cdot p$ 2-Band model
• Flat bands and perfect metal in trilayer moiré graphene
• The Landau Level of Fragile Topology
• Is magic-angle twisted bilayer graphene near a quantum critical point?
• Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices
• Topological flat bands in twisted trilayer graphene
• Pairing symmetry and spontaneous vortex-antivortex lattice in superconducting twisted-bilayer graphene: Bogoliubov-de Gennes approach
• Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
• Wannier Pairs in the Superconducting Twisted Bilayer Graphene and Related Systems
• Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
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• Topological chiral superconductivity with spontaneous vortices and supercurrent in twisted bilayer graphene
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• Spectroscopy of Twisted Bilayer Graphene Correlated Insulators
• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
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• Dynamical correlations and order in magic-angle twisted bilayer graphene
• TSTG I: Single-Particle and Many-Body Hamiltonians and Hidden Non-local Symmetries of Trilayer Moiré Systems with and without Displacement Field
• Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
• Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: Applications to twisted double-bilayer graphene
• Twistronics in graphene-based van der Waals structures
• TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters
• Lattice relaxation, mirror symmetry and magnetic field effects on ultraflat bands in twisted trilayer graphene
• TSTG II: Projected Hartree-Fock Study of Twisted Symmetric Trilayer Graphene
• Spin polarized nematic order, quantum valley Hall states, and field tunable topological transitions in twisted multilayer graphene systems
• Degradation of phonons in disordered moiré superlattices
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• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Electric-field-tunable electronic nematic order in twisted double-bilayer graphene
• Mott insulating state and $d+id$ superconductivity in an ABC graphene trilayer
• Spin density wave and electron nematicity in magic-angle twisted bilayer graphene
• Metal-insulator transition and dominant $d+id$ pairing symmetry in twisted bilayer graphene
• Harmonic Fingerprint of Unconventional Superconductivity in Twisted Bilayer Graphene
• Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field
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• Towards holographic flat bands
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• Charge order and Mott insulating ground states in small-angle twisted bilayer graphene
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• Charge Stripe Manipulation of Superconducting Pairing Symmetry Transition
• Site-selective insulating phase in twisted bilayer Hubbard model
• Strong ferromagnetic fluctuations in a doped checkerboard lattice
• Magnon bands in twisted bilayer honeycomb quantum magnets
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• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• In-Depth Investigation of Phase Transition Phenomena in Network Models Derived from Lattice Models
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• Particle-hole asymmetric phases in doped twisted bilayer graphene
• Exotic Topological Phenomena in Chiral Superconducting States on Doped Quantum Spin Hall Insulators with Honeycomb Lattices