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Orbital Magnetization in Correlated States of Twisted Bilayer Transition Metal Dichalcogenides

Xiaoyu Liu, Chong Wang, Xiao-Wei Zhang, Ting Cao, Di Xiao

Abstract

Recent observations of quantum anomalous Hall effects in moiré systems have revealed the emergence of interaction-driven ferromagnetism with significant orbital contributions. To capture this physics, we extend the modern theory of orbital magnetization to Hartree-Fock states and show that the standard expression remains valid with Hartree-Fock orbitals and Hamiltonians. We then benchmark our theory against the Kane-Mele-Hubbard model in a weak field, which yields excellent agreement with direct numerical calculations. Applying our theory to twisted MoTe$_2$ bilayers, we find orbital magnetization of order one Bohr magneton per moiré cell with a non-monotonic twist-angle dependence. Our work establishes a general theory of orbital magnetization in interacting moiré systems and provides quantitative guidance for interpreting recent experiments.

Orbital Magnetization in Correlated States of Twisted Bilayer Transition Metal Dichalcogenides

Abstract

Recent observations of quantum anomalous Hall effects in moiré systems have revealed the emergence of interaction-driven ferromagnetism with significant orbital contributions. To capture this physics, we extend the modern theory of orbital magnetization to Hartree-Fock states and show that the standard expression remains valid with Hartree-Fock orbitals and Hamiltonians. We then benchmark our theory against the Kane-Mele-Hubbard model in a weak field, which yields excellent agreement with direct numerical calculations. Applying our theory to twisted MoTe bilayers, we find orbital magnetization of order one Bohr magneton per moiré cell with a non-monotonic twist-angle dependence. Our work establishes a general theory of orbital magnetization in interacting moiré systems and provides quantitative guidance for interpreting recent experiments.

Paper Structure

This paper contains 8 equations, 2 figures.

Figures (2)

  • Figure 1: (a) Band structure of KMH model with different next-nearest-neighbor Coulomb interaction $V$. (b) Orbital magnetization calculated from Eq. \ref{['eq:orbmom_hf']} (black crosses) and from the finite-difference method (red open dots).
  • Figure 2: (a) Orbital magnetization (b) orbital moment per moiré unit cell for tMoTe$_2$. Open symbols and filled symbols represent non-interacting results and Hartree-Fock results, respectively. Upward and downward triangles represent CBM and VBM, respectively. (c) Energy gap between the first and second moiré valence bands at various twist angles from Wannier models. Open symbols represent results without interaction, while filled symbols include interaction. (d) Moiré unit cell area as a function of the twist angle.