Magnetic moir\'e surface states and flat chern band in topological insulators

TL;DR

This paper theoretically explores how magnetic moiré superlattices influence topological surface states, revealing the formation of flat Chern minibands and potential for time-reversal symmetry-breaking topological phases.

Contribution

It introduces a continuum model showing magnetic moiré potentials can gap Dirac cones and produce flat Chern bands, offering a new platform for topological phases.

Findings

Magnetic moiré potentials gap Dirac cones and create flat Chern minibands.

Special potential conditions realize various orbital models on honeycomb and kagome lattices.

Differences in potential strengths act as spin-orbit coupling, opening topological gaps.

Abstract

We theoretically study the effect of magnetic moir\'e superlattice on the topological surface states by introducing a continuum model of Dirac electrons with a single Dirac cone moving in the time-reversal symmetry breaking periodic pontential. The Zeeman-type moir\'e potentials generically gap out the moir\'e surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\pm1$. This result provides a promising platform for realizing the time-reversal breaking correlated topological phases. In a $C_6$ periodic potential, when the scalar $U_0$ and Zeeman $\Delta_1$ moir\'e potential strengths are equal to each other, we find that energetically the first three bands of $\Gamma$-valley moir\'e surface electrons are non-degenerate and realize i) an $s$-orbital model on a honeycomb lattice, ii) a degenerate $p_x,p_y$-orbitals model on a honeycomb lattice, and iii) a hybridized $sd^2$-orbital model on a kagome lattice, where moir\'e surface Dirac cones in these bands emerge. When $U_0\neq\Delta_1$, the difference between the two moir\'e potential serves as an effective spin-orbit coupling and opens a topological gap in the emergent moir\'e surface Dirac cones.