Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling

Abstract

In magic angle twisted bilayer graphene (TBG), electron-electron interactions play a central role, resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question, and it is potentially linked to the relatively high-temperature superconductivity observed in the same devices. Here, we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation, which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state, which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC order exhibits a pattern of alternating circulating currents that triples the graphene unit cell, leading to an "orbital magnetization density wave." Although translation and time-reversal symmetry are broken, a combined "Kramers" timereversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate Uð4Þ × Uð4Þ symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. This low-energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry-lowering perturbations can stabilize other insulators and the semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.

Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide

“…We note that in the strong-coupling flat-band limit, recent works 44 , 45 have proposed a valley-polarized state that is competitive in energy and distinct from the intervalley exciton condensate proposed here. Experimentally, these two states can be very easily distinguished by their response to an out-of-plane magnetic field.…”

“…Details of the topological properties of the moiré band are discussed in the section "Band topology and Berry curvature". While playing an important role in the flat-band scenario in graphene-based moiré systesms [43][44][45] , the topological property does not appear to play a significant role in the weak coupling scenario considered here.…”

DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene

“…The unprecedented nature of the phenomena exhibited by twisted bilayer graphene (TBG) devices at various electron densities about charge neutrality (CN), including correlated insulated states [1][2][3] and superconductivity [4,5], has opened the door to many experimental [1][2][3][4][5][6][7] and theoretical [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] studies since their initial discovery by Y. Cao, et al [1,4] in 2018.…”

Competing zero-field Chern insulators in Superconducting Twisted Bilayer Graphene

“…In this "chiral-flat" limit, the system enjoys a large U(4)×U(4) symmetry, which allows for the exact determination of the ground-states of the Coulomb interaction Hamiltonian. Due to the single particle topology of MATBG, the two flat bands at each valley and spin bands can be labeled by a Chern number C = 1 and C = -1, related by C2 symmetry [22][23][24][46][47][48][49] . In the chiral flat limit, at each filling , the interaction favors the successive occupation of such Chern bandsreminiscent of quantum Hall ferromagnetism, leading to many-body degenerate ground states (which can be classified by U(4)×U( 4) representations) at filling  with Chern number (4 -|  |), (2 -|  |), ..., (| | -2), (| | -4).…”

“…The theoretical predictions are only as good as the region of validity of the perturbation allows. Numerical results based on exact diagonalization and DMRG 23,46,50 suggest that some of the Chern insulating ground-states, particularly at  = ±3, do not survive for realistic MATBG parameters, and that a competition occurs between (nematic) metal, momentum M (π) stripe, and K-CDW orders and metallic states with no broken symmetries.…”