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

TL;DR

This paper develops an ab initio quantum-embedding approach to derive and solve effective Hamiltonians for magic angle twisted bilayer graphene, revealing correlated insulating and semimetal states with particle-hole asymmetry.

Contribution

It introduces a first-principles workflow combining DFT, cRPA, gauge fixing, and many-body methods to accurately model MATBG's electronic phases.

Findings

Robust insulating KIVC states at charge neutrality and electron doping.

Discovery of a fragile semimetal with Kekulé modulation at hole doping.

Pronounced particle-hole asymmetry in the effective Hamiltonian.

Abstract

Magic angle twisted bilayer graphene (MATBG) hosts narrow moir\'e 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 ($\nu=0$) and at electron doping ($\nu=+2$). The main new physical effect appears on the hole-doped side: at $\nu=-2$ we observe a fragile semimetal with a weak $\sqrt{3}\times\sqrt{3}$ Kekul\'e 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 $\nu=\pm 2$ 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.