Magnetism and hidden quantum geometry in charge neutral twisted trilayer graphene

Abstract

Here we present a theory of mirror-symmetric magic angle twisted trilayer graphene. The electronic properties are described by a Hubbard model with long range tunneling matrix elements. The electronic properties are obtained by solving the mean field Hubbard model. We obtain the bandstructure with characteristic flat bands and a Dirac cone. At charge neutrality, turning on electron-electron interactions results in metallic to antiferomagnetic phase transition, for Hubbard interaction strength considerably smaller than in other graphene multilayers. We analyze the stability of the antiferromagnetic state against the symmetry breaking induced by hexagonal boron nitride encapsulation, and mirror symmetry breaking caused by the application of electric fields that mix the Dirac cone with the flat bands. Additionally, we explore the topological properties of the system, revealing a hidden quantum geometry. Despite the flat bands having zero Chern numbers, the multiband Berry curvature distribution over the moiré Brillouin zone exhibits a non-trivial structure. Finally, we propose a mechanism to tune this quantum geometry, providing a pathway to control the system's topological properties.

Figures (5)

• Figure 1: Structural and electronic properties of TTG. (a) Side, (b) top, and (c) 3D view of geometry. TTG consists of three layers of graphene, with the middle one twisted by $\theta$, with respect to the aligned top and bottom layers, which are relaxed out-of-plane. The system is encapsulated in aligned hBN, and a vertical electric field is applied. (d) mBZ with high symmetry points. (e) Band structure of pristine TTG. (f) Effect of non-zero electric field ($\Delta_{V} = 120$ meV) hybridizing Dirac cones with the flat band. (g) The combined effect of electric field and hBN encapsulation ($\Delta_{V}=120$meV$, \Delta_{\rm hBN}=25$meV), opening extra gaps near the Fermi level. The gaps opened by applying an electric field and hBN are marked with blue arrows.
• Figure 2: Hartree-Fock quasiparticle band structures of TTG with $\Delta_V=\Delta_{\rm hBN} = 0$. (a) Band structure in the paramagnetic state with $U=0.5t$. The insets show a schematic depiction of the spin configuration in the three layers (left) and on the honeycomb lattice of a single layer (right). Black dashed lines were added alongside the Dirac cone dispersion to improve readability. (b) Band structure of the flat band in the anti-ferromagnetic state with $U=1.1t$. Red and blue colors encode up and down spins, respectively.
• Figure 3: AF transition in various graphene-based systems. Total absolute magnetization of different graphene systems (MLG, BLG, TBG, TTG) in the units of Bohr magneton as a function of the interaction $U$ scaled by the nearest-neighbor hopping $t$.
• Figure 4: Magnetic phase diagram of TTG. (a) TTG without a substrate. AF order parameter is studied in function of interaction strength (U/t) and applied electric potential ($\Delta_V$) (b-c) Similar phase diagram for staggered potential strengths (b) $\Delta_{hBN} = 5$ meV and (c) $\Delta_{hBN} = 50$ meV. The color scale denotes the total absolute magnetization in logarithmic scale.
• Figure 5: Multiband Berry's curvature in TTG. Band structure and mBC profiles along the mBZ path for both two VBs (1+2) and two CBs (3+4) for a) $\Delta_V = 40$ meV and b) $\Delta_V = 120$ meV. Distribution of mBC on whole mBZ c) corresponding to a) and d) corresponding to b). Color scale encodes the strength of mBC. The dashed line shows the mBZ path of a) and b).