Topological insulators in twisted transition metal dichalcogenide homobilayers (1807.03311v2)

Abstract: We show that moir\'e bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe$_2$. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe$_2$ at $+K$ ($-K$) valley can be described using a two-band model with a layer-pseudospin magnetic field $\boldsymbol{\Delta}(\boldsymbol{r})$ that has the moir\'e period. We show that $\boldsymbol{\Delta}(\boldsymbol{r})$ has a topologically non-trivial skyrmion lattice texture in real space, and that the topmost moir\'e valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moir\'e cell.

• The paper demonstrates the emergence of quantum spin-Hall states in twisted TMD homobilayers using a two-band Kane-Mele model.
• It employs a layer-pseudospin magnetic field to show a skyrmion lattice texture that encodes the bands’ nontrivial topology.
• Numerical results identify critical twist angles where band gaps and overlaps suggest promising avenues for spintronic applications.

Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers

The paper "Topological insulators in twisted transition metal dichalcogenide homobilayers" authored by Fengcheng Wu et al. investigates the emergence of topological properties in moiré bands of twisted transition metal dichalcogenide (TMD) homobilayers, focusing specifically on bilayer MoTe$_2$. This paper is predicated on the realization that the moiré superlattices formed in such bilayers can exhibit significant modifications in electronic properties, leading to the manifestation of topologically nontrivial states.

Key Concepts and Framework

The central theme of the paper revolves around the characterization of valence band states in $\pm K$ valleys of twisted bilayer TMD structures. Due to the noted spin-orbit coupling and inversion symmetry breaking in monolayers, these valleys offer a fertile ground for studying topological effects. The researchers employ a two-band model that utilizes a layer-pseudospin magnetic field $\boldsymbol{\Delta}(\boldsymbol{r})$, which notably exhibits a topologically nontrivial skyrmion lattice texture in real space. This skyrmionic nature is pivotal as it encodes the topological characteristics of the resulting moiré bands.

The paper’s theoretical framework adapts the Kane-Mele quantum spin-Hall model to describe these valence bands, showcasing that the effectively narrow bands at small twist angles accommodate quantum spin-Hall states. This translation into a topological insulator framework is corroborated by non-zero valley-contrasting Chern numbers assigned to the moiré bands.

Numerical Results and Analysis

The paper presents substantial numerical results showcasing the behavior of moiré bands across various twist angles. For instance, it identifies critical angles at which bands overlap or form gaps, transferring the system from a topological insulator to other insulating phases under certain conditions. Of particular note are the calculated winding numbers of the skyrmion lattice textures that elucidate the nontrivial topological aspects, especially under inversion-symmetry breaking conditions such as externally applied electric fields that create sublattice asymmetry.

Practical and Theoretical Implications

The findings enrich our understanding of electronic interactions in low-dimensional systems, pointing toward potential practical applications in quantum computing and advanced materials design. The unconventional distribution of Berry curvature and stark density of states variations at smaller twist angles suggest the viability of using these bilayers in devices exploiting correlated electron phenomena. Furthermore, the realization of topological insulators in such TMD structures widens the scope for employing two-dimensional materials in developing robust edge states for spintronic applications.

Speculations on Future Directions

Looking forward, this paper opens several avenues for research, particularly in exploring heterobilayer systems or those with induced heterostructures that leverage different elemental dichalcogenides to fine-tune the topological characteristics and electronic correlations of these systems. The intersection of moiré superlattice physics with strong electron correlation effects offers exciting prospects for the realization of exotic quantum states, including fractional topological insulators. Moreover, the 'tear-and-stack' technique for creating these moiré systems promises increased experimental fidelity in probing theoretical predictions, potentially leading to advancements in the control and manipulation of quantum phases in condensed matter.

Overall, this paper is a significant contribution to condensed matter physics, particularly in understanding and controlling the topological properties in twisted bilayer systems of TMDs. It promises to influence both theoretical pursuits and material-based technologies in the quest for exploiting quantum properties in two-dimensional materials.