Archive | 2021
Luminescence Anomaly of Dipolar Valley Excitons in Homobilayer Semiconductor Moiré Superlattices
Abstract
In twisted homobilayer transition metal dichalcogenides, intraand inter-layer valley excitons hybridize with the layer configurations spatially varying in the moiré. The ground state valley excitons are trapped at two highsymmetry points with opposite electric dipoles in a moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. We find that the spatial texture of layer configuration results in a luminescence anomaly of the moiré trapped excitons, where a tiny displacement by interactions dramatically increases the brightness and changes polarization from circular to linear. At full filling, radiative recombination predominantly occurs at edges and vacancies of the exciton superlattice. The anomaly also manifests in the cascaded emission of small clusters, producing chains of polarization entangled photons. An interlayer bias can switch the superlattice into a single-orbital triangular lattice with repulsive interactions only, where the luminescence anomaly can be exploited to distinguish ordered states and domain boundaries at fractional filling. Long-wavelength moiré patterns by van der Waals stacking of two-dimensional crystals has made possible the exploration into a new realm of physics. The local-tolocal variation of the interlayer registry leads to the spatial modulation of the local band structure, creating an artificial superlattice with a period in the range from a few to a few tens nanometers. In twisted graphene moiré, interlayer coupling at magic angles turns the massless Dirac cones into flat mini-bands, where a plethora of correlation phenomena are observed [1-9]. Another exciting moiré platform is the semiconducting transition metal dichalcogenides (TMDs) which host massive Dirac fermions at a timereversal pair of valleys located at the K and −K corners of the hexagonal Brillouin zone [10]. Moiré pattern in TMDs heterostructures introduces a triangular superlattice landscape for valley electrons [11], in which a variety of correlated insulating states have been observed at various filling factors [12-17]. Excitons formed by the Coulomb binding of valley electron and hole make possible a distinct many-body system in the TMD moiré superlattices with optical addressability and the bosonic statistics. The intralayer exciton (Xintra) has a large optical dipole with a fixed valley polarization selection rule, which underlies the versatile optical controls of valley dynamics [18-21]. In type-II heterobilayers, excitons also form in an interlayer configuration (Xinter), where the separation of constituent electron and hole into adjacent layers leads to a permanent electric dipole that turns on strong dipolar interactions and coupling to electric field [22-27]. The layer separation of the electron and hole leads to long recombination lifetime and valley lifetime of Xinter, favorable for valleytronic applications [28], as well as for the exploration of quantum many-body phenomena such as exciton Bose-Einstein condensation [29] and self-assembled crystal phase of the two-dimensional dipolar excitons [30]. In the moiré pattern, Xinter experiences a strong superlattice potential with spatial variation in the order of ~100 meV, and features an optical dipole that spatially varies on the scale of the moiré period, determined by the local stacking registry [31-41]. The lowest energy Xinter are then trapped at the potential minima, which can form an ordered array of quantum emitters. The radiative recombination of these Xinter ground states results in sharp emission lines with spectral width of ~ 0.1 meV, as observed in MoSe2/WSe2 heterostructures under low excitation power and temperature [34-36]. Photon antibunching experiment indicates that these trapped Xinter can serve as highly tunable single-photon emitters [36]. The repulsive dipolar interaction between the trapped Xinter manifests as blue shifts of their resonances observed in the photoluminescence spectrum [25-27]. At the potential minima, the 2 /3-rotational symmetry ( ) of the local atomic registries dictates circularly polarized optical selection rules of Xinter, with the emission polarization jointly determined by the valley, spin and stacking registry [31,42]. The polarization properties of the exciton emission (coor cross-polarized with respect to the excitation at Xintra resonance) can be used to identify the trapping location within a moiré supercell, which is switchable by an outof-plane electric field [31]. While these properties of Xinter in the heterostructure moiré are highly intriguing for novel optoelectronic applications, the very weak optical dipole has however placed an intrinsic limitation on their exploitation [39]. Here we present an exotic exciton system in twisted TMDs homobilayers. We show that because of the registry dependent interlayer coupling, the energies of intraand inter-layer valley excitons cross each other as functions of position in the moiré, giving rise to a texture of spatially varying exciton hybridization. In a moiré supercell, the ground state valley exciton is trapped at two degenerate high-symmetry points with opposite out-of-plane electric dipole moments, forming a honeycomb superlattice with repulsive on-site and attractive nearest-neighbor interactions. The spatial texture of the Xintra-Xinter hybridization leads to a luminescence anomaly of excitons in the traps. At equilibrium positions, they are as dark as Xinter, while a tiny lateral displacement in the order of Å dramatically increases the brightness, and the emission polarization is changed from circular to linear, with polarization angle reflecting the displacement direction. At full exciton filling of the honeycomb superlattice, radiative recombination predominantly occurs at edges and vacancies where excitons are displaced by the unbalanced dipolar interactions from neighboring sites. An interlayer bias can switch the excitonic superlattice to a single-orbital triangular one with repulsive interactions only. We show that the luminescence anomaly can serve as signatures for different correlated states and domain boundaries at fractional exciton filling. The anomaly also manifests in the cascaded emission of small clusters, producing chains of polarization entangled photons. Consider the near 0◦ twisted homobilayers with moiré period b much larger than the monolayer lattice constant, such that local regions can be approximated by commensurate bilayers with various R-stacking registries (Fig. 1a). For the conduction and valence band edge electrons at K valley, interlayer coupling has a sensitive dependence on the stacking registry and therefore becomes a periodic function of position in the moiré [43,44]: ( ) = ( ) h ( ) h∗ ( ) ( ) , ( ) = ( ) h ( ) h∗ ( ) ( ) . Here / ( ) is the energy shift of the conduction/valence band edge in the upper layer due to the interlayer coupling, while / ( ) is the one in the lower layer. h / ( ) is the interlayer hopping of the electron/hole. Their -dependences underlie the spatially-varying layer hybridizations of the valley electrons and holes in the moiré of TMDs homobilayers [43,44]. The phenomena to be explored are more pronounced for smaller b (≲ 10 nm), where the lattice reconstruction effect is insignificant [45], not considered here. We focus on the valley excitons formed by a pair of electron and hole at these band edges. The strong electron-hole Coulomb interaction leads to a binding energy of a few hundred meV, which is one order larger than the interlayer hopping (|h| ~ 20 meV). This allows one to start from the exciton basis obtained in the limit of vanishing interlayer hopping. The basis states in a given valley include the two Xinter, denoted as | ⟩ and | ⟩ which have opposite electric dipoles (Fig. 1b), and the two Xintra confined in the two layers respectively, denoted as | ⟩ and | ⟩ (Fig. 1b). In this basis, the exciton Hamiltonian reads, ( ) = − ħ ∇ 2 + ( ), (1)