Topological Exciton Bands in Moiré Heterojunctions

Abstract

Moiré patterns are common in van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valley Zeeman field.Stacking two-dimensional (2D) materials into van der Waals heterostructures opens up new strategies for materials property engineering. One increasingly important example is the possibility of using the relative orientation (twist) angle between two 2D crystals to tune electronic properties. For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].In this Letter, we study the influence of moiré patterns on collective excitations, focusing on the important case of excitons in the transition metal dichalcogenide (TMD) 2D semiconductors [7,8] like MoS 2 and WS 2 . Exciton features dominate the optical response of these materials because electron-hole pairs are strongly bound by the Coulomb interaction [9][10][11][12]. An exciton inherits a pseudospin-1/2 valley degree of freedom from its constituent electron and hole, and the exciton valley pseudospin can be optically addressed [13][14][15][16], providing access to the valley Hall effect [17] and the valley selective optical Stark effect [18,19].As in the case of graphene/hexagonal-boron-nitride and graphene/graphene bilayers, a moiré pattern can be established in TMD bilayers by using two different materials with a small lattice mismatch, by applying a small twist, or by combining both effects. TMD heterostructures have been realized [20][21][22] experimentally and can host interesting effects, for example the observation of valley polarized interlayer excitons with long lifetimes [23], the theoretical prediction of multiple degenerate interlayer excitons [24], and the possibility of achieving spatially indirect exciton condensation [25,26]. Our focus here is instead on the intralayer excitons that are more strongly coupled to light. As we explain below, the moiré pattern produces a periodic potential, mixing momentum states separated by moiré reciprocal lattice vectors and producing satellite optical absorption peaks that are revealing. The exciton energy-momentum dispersion can be measured by tracking the dependence of satellite peak energies on twist angle.The valley pseudospin...

Topological Quantum Optics in Two-Dimensional Atomic Arrays

“…Large splitting of the σ þ , σ − valley polarizations due to interaction-induced paramagnetic responses was recently demonstrated in TMDCs [67]. Moiré patterns [68] could provide deep subwavelength (a < 36 nm) periodic potentials for TMDC excitons and give rise to topological bands and chiral excitonic edge states [23]. In such Moiré heterojunctions the band gaps-and thus the group velocities of edge states-are predicted to be small (Δ < 1Γ 0 ).…”

Interlayer coupling in commensurate and incommensurate bilayer structures of transition-metal dichalcogenides

“…However, these structures can locally exist in an incommensurate bilayer with large scale moiré superlattice pattern. 39,40,46 In a local region with a size much larger than the monolayer lattice constant but much smaller than the moiré supercell, the atomic registry between the two layers is locally indistinguishable from an R-or H-type commensurate bilayer, which is characterized by a continuously varying r 0 . The local band structure of this region is then given by that of the commensurate bilayer with the corresponding r 0 value.…”

“…The local band structure of this region is then given by that of the commensurate bilayer with the corresponding r 0 value. 39,40,46 As r 0 varies from position to position in a moiré supercell, the r 0 -dependent conduction/valence band energy shifts δE c/v (r 0 ) can be responsible for the observed position-dependent local band gap modulation.…”

“…Moreover, recent theoretical studies have shown that the interlayer coupling together with the formation of a large scale moiré superlattice pattern can lead to the emergence of topological orders in a TMD heterobilayer. 39,40 To gain further insights into these interesting phenomena, it is essential to understand the strength and the form of the interlayer coupling in TMD bilayers.…”

Large Excitonic Reflectivity of MonolayerMoSe2Encapsulated in Hexagonal Boron Nitride

“…A two-dimensional (2D) layer of emitters, such as atomic lattices or excitons (9)(10)(11), has also been predicted to act as an efficient mirror when the incident light is resonant with the resonance frequency of the system. Such atomically thin mirrors represent the ultimate miniaturization limit of a reflective surface, and could enable unique applications ranging from quantum nonlinear optics (9-11) to topological photonics (12,13).…”