Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Journal Article · Tue May 11 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.103.205416· OSTI ID:1852147

Xie, Fang ^[1]; Cowsik, Aditya ^[2]; Song, Zhi-Da ^[2]; Lian, Biao ^[2]; Bernevig, B. Andrei ^[2]; Regnault, Nicolas ^[3]

---

1. Princeton Univ., NJ (United States); OSTI
2. Princeton Univ., NJ (United States)
3. Princeton Univ., NJ (United States); Sorbonne Univ., Paris (France); University Paris-Diderot (France)

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w₀/w₁ = 0, where w₀ (w₁) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν_C = ±1 at w₀/w₁ ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w₀/w₁ ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w₀/w₁ is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M_M (π) stripe and K_M-CDW orders at large w₀/w₁.

• Research Organization: Princeton University, NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0016239
• OSTI ID: 1852147
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 20 Vol. 103; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Chern insulators
Exact diagonalization
Graphene
Materials Science
Physics
Topological materials