Ab initio quantum embedding description of magic angle twisted bilayer graphene at even-integer fillings

Abstract

Magic angle twisted bilayer graphene (MATBG) hosts narrow moiré bands with meV-scale energy splittings, making its correlated phases sensitive to both material parameters and modeling choices in low-energy downfolding. We develop an ab initio quantum-embedding workflow that derives interacting flat-band Hamiltonians from Kohn-Sham density functional theory (KS-DFT) of a relaxed, unstrained structure. Our model combines constrained random phase approximation (cRPA) screening, controlled double-counting subtraction, and an automated gauge-fixing procedure based on the selected columns of the density matrix (SCDM) that is compatible with symmetry-resolved many-body calculations. Solving the resulting models using Hartree-Fock (HF) and coupled cluster singles and doubles (CCSD), we recover robust insulating Kramers intervalley coherent (KIVC) states at charge neutrality ($ν=0$) and at electron doping ($ν=+2$). The main new physical effect appears on the hole-doped side: at $ν=-2$ we observe a fragile semimetal with a weak $\sqrt{3}\times\sqrt{3}$ Kekulé modulation and enhanced intervalley-scattering peaks in the Fourier-transformed local density of states. Although the underlying KS-DFT band structure is nearly particle-hole symmetric, the effective interacting Hamiltonian exhibits a pronounced particle-hole asymmetry at $ν=\pm 2$ that we trace to momentum-dependent single-particle renormalizations generated by subtraction terms constructed from reference densities consistent with the KS-DFT filling. Our work provides a first-principles route for connecting microscopic electronic structure, screened interactions, subtraction choices, and scanning tunneling microscopy signatures in MATBG.

Figures (10)

• Figure 1: (\ref{['fig:val_pol_before']}) Superposition of the density of DFT band basis in $\mathbf{G}$-space. Red dots indicate the location of four significant points from SCDM and the valley $\mathbf{K}$ is specified by the highest peak in the SCDM result. Showing the graphene Brillouin zone ($\mathrm{BZ}_{\mathrm{gph}}$) and graphene lattice vectors ($\mathbf{b}^{\mathrm{gph}}_1, \mathbf{b}^{\mathrm{gph}}_2$) (\ref{['fig:val_pol_K']}) $\mathbf{K}$-valley polarized basis in $\mathbf{G}$-space (\ref{['fig:val_pol_K_zoom']}) Zoomed-in view of the $\mathbf{K}$-valley center, showing the moiré Brillouin zone ($\mathrm{BZ}_\mathrm{m}$) and reciprocal lattice vectors ($\mathbf{b}_1, \mathbf{b}_2$)
• Figure 2: (\ref{['fig:sub_pol_before']}) Superposition of the density of $\mathbf{K}$-valley polarized basis in $\mathbf{r}$-space. Red and blue atoms are $A$ and $B$ sublattices, respectively. (\ref{['fig:sub_pol_after_A']}) $A$-sublattice-polarized basis in $\mathbf{r}$-space. (\ref{['fig:sub_pol_after_B']}) $B$-sublattice-polarized basis in $\mathbf{r}$-space.
• Figure 3: (a) Density functional theory (DFT) band structure of twisted bilayer graphene (TBG) at a twist angle $\theta = 1.08^{\degree}$. (b) The primitive unit-cell Brillouin zones (BZ) of the top and bottom layers of graphene with a large twist angle $\theta = 7.34^{\degree}$ are shown in red and blue, respectively, for illustrative purposes. The moiré BZ is shown in black with various high-symmetry $k$-points.
• Figure 4: (a) Energy hierarchy of various phases of MATBG at charge neutrality at the Hartree-Fock (HF) and coupled cluster singles and doubles (CCSD) levels. (b-d) HF band structure, (e-g) Local density of states (LDOS), (h-j) The corresponding Fourier-transformed LDOS (FT-LDOS) of the KIVC, VP, and QH states, respectively. Here, $E_{\text{VBM}}$ denotes the valence band maximum. In the FT-LDOS, the Bragg peaks of the graphene lattice are denoted by blue diamonds.
• Figure 5: (a) Energy hierarchy of various phases at $\nu=+2$ at the HF and CCSD levels. (b-d) HF band structure, (e-g) LDOS, (h-j) The corresponding FT-LDOS of KIVC, VP, and VH state, respectively. Here, $E_{\text{VBM}}$ denotes the valence band maximum. In the FT-LDOS, the Bragg peaks of the graphene lattice is denoted with blue diamond.