Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation, and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. The evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a
d+id superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation, and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical
Uc for the metal-insulator transition is also reduced. Our intensive numerical results reveal that twisted bilayer graphene should be a uniquely tunable platform for exploring strongly correlated phenomena.
Motivated by recent experimental studies that have found signatures of a correlated insulator phase and tuning superconductivity in twisted bilayer graphene, we study the temperature-dependent conductivity, the spin correlation and the superconducting pairing correlation within a two-orbital Hubbard model on an emergent honeycomb lattice. Evaluation of the temperature dependence of the conductivity demonstrates that there is a metal-insulator transition, and the Mott phase at strong coupling is accompanied by antiferromagnetic order. The electronic correlation drives a
d+id superconducting pairing to be dominant over a wide filling region. All of the dc conductivity, the spin correlation and the superconductivity are suppressed as the interlayer coupling strength increases, and the critical
Uc for metal-insulator transition is also reduced. Our intensive numerical results reveal that the TBG should be a uniquely tunable platform for exploring correlated states.
We investigated the honeycomb lattice using a two-orbital (α and β) Hubbard model and many-body exact calculations. The spin gap (Δ s ), charge gap (Δ c ), intrasite ( γ i i α β = ⟨ S → i α · S → i β ⟩ ), intersite ( γ i j α β = ⟨ S → i α · S → j β ⟩ ), spin–spin correlations, and orbital magnetic moments μ iα are analyzed for different band-filling ( n ), which denotes the number of electrons per site. Special attention was set in one-quarter-filled ( n = 1) and half-filled ( n = 2) bands. The results are presented by varying Coulomb repulsion ( U), Hund’s coupling ( J H ), external magnetic field ( B ), and orbital energy splitting (Δϵ). For the one-quarter-filled band, an intrasite magnetic disorder ( γ i i α β ≈ 0 ) begins to form for large values of U / t, which is interpreted as a possible signature of a resonating valence bond state. Full orbital polarization ( γ i i α β = 0.25 ) with intersite antiferromagnetic (AFM) order ( γ i j α β = − 0.25 ) was observed in the half-filled band for U / t ≫ 1, indicating that the two-orbital Hubbard model can be mapped to an AFM Heisenberg model with S = 1. The increase of J H is conductive to insulating and metallic phases for half- and one-quarter-filled bands, respectively. For a fractional n, the honeycomb lattice can exhibit spin-glass-like behavior, predominating as a disordered magnetic system characterized by random values of γ i j α β . The magnetic field induced a reduction in Δ c, which became zero at the critical external magnetic field. Twisted bilayer graphene (TBG) exhibits approximately flat electronic bands at magic angles and interesting correlated phenomena, such as unconventional superconductivity and correlated insulating states around n = 1 and n = 2, respectively. The dominance of electron–electron interactions in TBG makes the Hubbard model, in various versions (extended or multi-orbital), offer a practical, structure-scale account for investigating many-body effects in large moiré unit cells, where first-principles density-functional theory calculations are computationally challenging.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional renormalization group scheme, which allows for highly resolved calculations of wave-vector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure
nth nearest-neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when nonlocal density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough nonlocal terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semimetallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second-nearest-neighbor interactions is not realized in our results with high momentum resolution.
Mott physics in topological bands has recently attracted considerable attention, particularly in the context of twisted bilayer graphene (TBG). However, the essential ingredients for stabilizing this physics remain unclear. Here, we demonstrate a quantum Mott semimetal phase as the ground state within a one-dimensional spinful Hubbard model featuring only one orbital per unit cell, protected by inversion and particle-hole symmetries. We start from a two-orbital model where a localized
f orbital on the A sublattice hybridizes with a delocalized
c orbital on the B sublattice. Projecting the
f-orbital Hubbard
U onto the active flat band yields a lattice model with Wannier orbitals centered on the B sublattice. Similar to TBG, a momentum-space scale
k∗ emerges, setting the interaction range in the projected model to
1/k∗. While the ground state is ferromagnetic with only the Hubbard
U, introducing an inter-site antiferromagnetic spin coupling
J stabilizes a Mott semimetal
∗ phase with a central charge
c=3. Using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods, we show that this phase hosts a spinful Dirac fermion coexisting with a neutral spin mode -- analogous to the fractionalized Fermi liquid (FL
∗) phase in higher dimensions. Furthermore, breaking particle-hole (PH) symmetry via dispersion transforms the Mott semimetal into a Mott insulator, which is separated from a distinct Mott insulating phase by a continuous transition with a polarization jump of
1/2. Our work provides the first unbiased evidence of a Mott semimetal ground state and demonstrates that this 1D model captures some essential aspects of TBG physics, despite lacking a Wannier obstruction.