Flat band properties of twisted transition metal dichalcogenide homo- and heterobilayers of MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$

Abstract

Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo-and heterobilayers that are obtained by combining MoS2, WS2, MoSe2 and WSe2 monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculate the electronic band structure using a tight-binding model parametrized from first-principles densityfunctional theory. For homobilayers, we find that the two highest valence bands exhibit a graphenelike dispersion and become flat as the twist angle is reduced. In contrast, not all heterobilayers have flat valence bands. Specifically, we find that those systems in which the highest valence band derives from K or K' states of the constituent monolayers do not exhibit flat bands, even at small twist angles. In all systems, qualitatively different band structures are obtained when atomic relaxations are neglected.

Magic in twisted transition metal dichalcogenide bilayers

“…With the fully relaxed structure, the lowenergy moiré valence bands of twisted bilayer WSe 2 are found to come from the ±K valley (shown in Fig. 1c), as opposed to the Γ valley in previous computational studies [30,31] and consistent with recent works [27,32].…”

Spin-orbit correlations and exchange-bias control in twisted Janus dichalcogenide multilayers

“…6c), we observe that the combination of spin-orbit coupling and exchange proximity effect breaks the original +k → −k degeneracy of the electronic structure, demonstrating the existence of the exchange proximity effect. It is worth to note that, although this calculation focuses on the interplay of spin-orbit effect and exchange proximity, corre-lated states could be studied purely from first-principles methods 28,51,[75][76][77][78] . These calculations would be nevertheless a remarkable challenge from the computational point of view due to the existence of non-collinear magnetism, spin-orbit coupling, and a large number of atoms in the moire unit cell.…”

“…[33][34][35][36][37] The emergence of flat bands and correlated states in dichalcogenide systems represent an illustrative example of the versatility of twist engineering in these systems. [38][39][40][41][42][43][44] Spin-orbit coupling effects in these flat band systems [45][46][47][48][49][50][51] have also been proposed to bring up unique possibilities for spin and valley control. However, the emergence of correlated states in Janus dichalcogenides has remained largely unexplored, and studies on spin-orbit effects have focused mainly on Ising spin-orbit coupling.…”

Light-matter coupling and quantum geometry in moiré materials

“…Although much research has focused on TBG, for which flat bands appear only for certain narrow ranges around specific twist angles (so-called magic angles, the largest of which is 1.1 ± 0.1 o [28,31,32]), the general concept of flat-band engineering is much more broadly applicable [40]. For example, recent advances into multilayered and/or electrostatically gated graphitic systems [76][77][78][79][80][81][82][83][84], twisted bilayer boron nitride [85], twisted homo-or heterobilayers of semiconducting transition metal dichalcogenides [86][87][88][89][90][91][92][93], monochalcogenides [94] or twisted bilayers of mag- From the band structure one might naïvely expect that the coupling to light in flat bands vanishes. However, a geometric contribution (present, e.g., in TBG), can contribute to light-matter coupling and dominates in flat band systems (bottom row).…”