Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene

Abstract

The recent observation of superconductivity in proximity to an insulating phase in twisted bilayer graphene (TBG) at small "magic" twist angles has been linked to the existence of nearly-flat bands, which make TBG a fresh playground to investigate the interplay between correlations and superconductivity. The low-energy narrow bands were shown to be well-described by an effective tight-binding model on the honeycomb lattice (the dual of the triangular Moiré superlattice) with a local orbital degree of freedom. In this paper, we perform a strong-coupling analysis of the proposed (px, py) two-orbital extended Hubbard model on the honeycomb lattice. By decomposing the interacting terms in the particle-particle and particle-hole channels, we classify the different possible superconducting, magnetic, and charge instabilities of the system. In the pairing case, we pay particular attention to the two-component (d-wave) pairing channels, which admit vestigial phases with nematic or chiral orders, and study their phenomenology. Furthermore, we explore the strong-regime by obtaining a simplified spin-orbital exchange model which may describe a putative Mott-like insulating state at quarter-filling. Our mean-field solution reveals a rich intertwinement between ferro-and antiferro-magnetic orders with different types of nematic and magnetic orbital orders. Overall, our work provides a solid framework for further investigations of the phase diagram of the two-orbital extended Hubbard model in both strong-and weak-coupling regimes.arXiv:1808.10416v3 [cond-mat.supr-con]

SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators

“…3(a), which extends the result of Ref. [24] by including nonzero orbital-dependent hopping t . We shall then analyze the stability of the ordered states against quantum fluctuations using LFWT [42].…”

“…In the physically more relevant regime ξ < 1, we observe a competition between two states with AFOxz order distinguished by the FM or AFM spin order. In agreement with [24], the FM state has lower energy for ξ → 0 at any fixed η. The transition from AFOxz to the orbital vortex states across the line ξ = 1 can be attributed to a six-sublattice orbital rota-tion symmetry of the model discussed in [31], which maps H(ξ, η) → H(1/ξ, η) and connects the collinear orbital phases in Figs.…”

“…We present a detailed analysis of a KK model derived independently in Refs. [24] and [31] using mean-field theory (MFT), linear flavor-wave theory (LFWT) (complemented by a variational study considering the Huse-Elser wavefunction [39,40]) and VMC. Our main results are summarized in (Color online) Phase diagram of the Kugel-Khomskii model as a function of the ratio of hopping parameters ξ = t /t and the dimensionless Hund's coupling parameter η = JH /U .…”

Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

“…Such considerations hint that, even if the physical system is ultimately in an intermediate coupling regime, a strong coupling approach may be more successful in capturing the nature of the correlated phases. In this approach the interaction-only Hamiltonian is minimized first, and the kinetic energy term is then treated as a perturbation [7,[10][11][12][13][14][15][16][17][18][19].…”

Spin-Orbital Density Wave and a Mott Insulator in a Two-Orbital Hubbard Model on a Honeycomb Lattice

“…As a result of the reduced kinetic energy, the correlation effect becomes significant and most likely is the driving force for the MIT. The nature of the insulating states is now under intensive study [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. A paradigmatic theoretical model for MIT is the Hubbard model and its various generalizations to include multiple orbits and extended interactions.…”