Topological Phases in AB-Stacked MoTe$_2$/WSe$_2$: $\mathbb{Z}_2$ Topological Insulators, Chern Insulators, and Topological Charge Density Waves

Abstract

We present a theory on the quantum phase diagram of AB-stacked MoTe2/WSe2 using a selfconsistent Hartree-Fock calculation performed in the plane-wave basis, motivated by the observation of topological states in this system. At filling factor ν = 2 (two holes per moiré unit cell), Coulomb interaction can stabilize a Z2 topological insulator by opening a charge gap. At ν = 1, the interaction induces three classes of competing states, spin density wave states, an in-plane ferromagnetic state, and a valley polarized state, which undergo first-order phase transitions tuned by an out-of-plane displacement field. The valley polarized state becomes a Chern insulator for certain displacement fields. Moreover, we predict a topological charge density wave forming a honeycomb lattice with ferromagnetism at ν = 2/3. Future directions on this versatile system hosting a rich set of quantum phases are discussed.

Intrinsic spin Hall torque in a moire Chern magnet

“…1b). This is consistent with previous results on AB-stacked MoTe 2 /WSe 2 bilayers [3], where a magnetic Chern insulator arises due to the interplay of strong Coulomb repulsion and underlying Berry curvature of the moiré subbands [19][20][21][22][23].…”

Colloquium: Quantum anomalous Hall effect

“…So far, these strategies have not succeeded, presumably because the spatial distribution of adatoms is inevitably disordered and the hybridization between graphene and adjacent materials tends to be weak. Heavier elements that can also form honeycomb or buckled honeycomb lattice structure, such as silience (Ezawa, 2012(Ezawa, , 2013Kaloni et al, 2014;Pan et al, 2014;Qian et al, 2019;Zhang et al, 2013b,c), germanene (Hsu et al, 2017;Pham and Ganesh, 2020;Wu et al, 2014b;Zhang et al, 2019c;Zou et al, 2020), stanene (Li, 2019;Wu et al, 2014b;Xu et al, 2013;Zhang et al, 2016a,b) and bismuth systems (Ji et al, 2016;Jin and Jhi, 2015;Liu et al, 2015;Niu et al, 2015), have aslo been considered as possible QAH effect hosts. In addition to these 2D materials containing a single element, honeycomb lattices are also common in more complex materials, including organic triphenyl-transition-metal compounds (Wang et al, 2013b), half-fluorinated GaBi (Chen et al, 2016), co-decorated in-triangle adlayers on a Si(111) surface (Zhou et al, 2017), monolayer jacutingaite (Luo et al, 2021), monolayer PtCl 3 (You et al, 2019), monolayer EuO 2 (Meng et al, 2021) and ( 111) perovskite-type transition-metal oxides (Xiao et al, 2011).…”

Realization of the Haldane Chern insulator in a moiré lattice

“…The spins of the two bands are anti-aligned in AB-stacked bilayers. The system realizes a generalized Kane-Mele tight-binding Hamiltonian [11][12][13][14][15][16][17] (Methods). Particularly, the next-nearest-neighbor (or intralayer) hopping has a complex value because of time reversal symmetry breaking in each (K or K') valley of the monolayers.…”

“…Despite its profound impact on the field of topological physics 8,9 and recent implementation in cold-atom experiments 10 , the Haldane model has remained elusive in solid-state materials. Here, we report the experimental realization of a Haldane Chern insulator in AB-stacked MoTe2/WSe2 moiré bilayers, which form a honeycomb moiré lattice with two sublattices residing in different layers 7,[11][12][13][14][15] . We show that the moiré bilayer filled with two charge particles per unit cell is a quantum spin Hall (QSH) insulator with a tunable charge gap.…”

“…Under a small out-of-plane magnetic field, it becomes a Chern insulator with Chern number 𝒄 = 𝟏 from magnetotransport studies. The results are qualitatively captured by a generalized Kane-Mele tight-binding Hamiltonian [11][12][13][14][15][16][17] . The Zeeman field splits the QSH insulator into two halves of opposite valley--one with a positive and the other a negative moiré band gap.…”