Excitons in mesoscopically reconstructed moiré heterostructures

Abstract

Moiré effects in vertical stacks of two-dimensional crystals give rise to new quantum materials with rich transport and optical phenomena that originate from modulations of atomic registries within moiré supercells. Due to finite elasticity, however, the superlattices can transform from moiré-type to periodically reconstructed patterns. Here we expand the notion of such nanoscale lattice reconstruction to the mesoscopic scale of laterally extended samples and demonstrate rich consequences in optical studies of excitons in MoSe₂-WSe₂ heterostructures with parallel and antiparallel alignments. Our results provide a unified perspective on moiré excitons in near-commensurate semiconductor heterostructures with small twist angles by identifying domains with exciton properties of distinct effective dimensionality, and establish mesoscopic reconstruction as a compelling feature of real samples and devices with inherent finite size effects and disorder. Generalized to stacks of other two-dimensional materials, this notion of mesoscale domain formation with emergent topological defects and percolation networks will instructively expand the understanding of fundamental electronic, optical and magnetic properties of van der Waals heterostructures.

Fig. 1. Characteristics of MoSe₂–WSe₂ HBLs in H- and R-type stacking.

a, Schematics of H- and R-type heterostacks with ideal moiré (left) and periodically reconstructed (right) patterns. The coloured regions represent high-symmetry atomic registries, as illustrated in the respective circles. b, Optical micrograph of sample 1 with H- and R-stacks (delimited by dashed lines) of CVD-grown MoSe₂ monolayers (small triangles) on a large WSe₂ monolayer (large triangle). c, Interlayer exciton PL map (left) with selected bright (H1, R1) and dark (H2, R2) spots indicated by diamonds and circles, respectively, as well as P_c (middle) and P_l (right) maps for the H and R-stacks in b. d,e, Photoluminescence spectra at the bright and dark spots marked in c. At an excitation power of 2 μW, the H1 and R1 spectra are representative for regions with a single bright peak, whereas the H2 and R2 spectra (scaled by 50 and 5, respectively) are characteristics of dark regions with broad and structured PL, which evolves into narrow peaks at a low excitation power of 0.01 μW (scaled by 250 and 25, respectively). All spectroscopy data were recorded on sample 1. f,g, Scanning electron micrographs of H- (f) and R- (g) heterostacks recorded with secondary electron imaging. Source data

Fig. 2. Mesoscopic reconstruction in finite size simulations.

a,d, Maps of reconstructed domains in triangular tips of R-type (a) and H-type (d) heterostacks with a twist angle θ = 0.4° (only triangle halves are shown in the projections; the scale bars are 200 nm). The top maps show moiré patterns without reconstruction (delimited by dashed lines from the moiré core of the HBL), whereas the maps below show periodic reconstruction and mesoscopically reconstructed domain patterns obtained for different zero-twist deformations around the points marked by black dots at dimensionless positions α (note that the orange $R_h^X$ and green $R_h^M$ domains can interconvert due to similar adhesion energies). b,e, Total areal energy for R (b) and H (e) at θ = 0.4°, and different untwisting points α (the energy of the respective periodic patterns is shown by solid lines). c,f, Total areal energy of periodic and optimally reconstructed (for α = 0) patterns for different twist angles θ in R (c) and H (f) (the energy of the respective moiré patterns is indicated by the dashed lines). Source data

Fig. 3. Spectral characteristics of excitons in reconstructed R-type MoSe₂–WSe₂ HBLs.

a, Evolution of differential reflection (DR) spectra of intralayer excitons following gradual displacement from a bright to dark region (shown from top to bottom for positions indicated by the black dots in Supplementary Fig. 9a). The peak multiplicity is a hallmark of nanoscale reconstructed domains. b–d, Interlayer exciton PL (b), P_c (c) and dispersion in a perpendicular magnetic field B (d), characteristic of extended 2D domains. The magneto-luminescence data were recorded under linearly polarized excitation with σ⁺ detection to determine the g-factor values from linear slopes. e–g, Same as b–d but for regions of 1D stripes with a large degree of linear polarization (as shown in the inset). h–j, Same as b–d but in a dark sample region of 0D domains (PL spectra shown with offsets and different scaling for excitation powers of 100, 2 and 0.01 μW). All data were recorded on sample 2 (Supplementary Fig. 9) ; g-factor values with least-square error bars were obtained from linear fits to the data shown in Supplementary Fig. 16. Source data

Fig. 4. Spectral characteristics of excitons in reconstructed H-type MoSe₂–WSe₂ HBL.

a, Evolution of differential reflection spectra of intralayer excitons following displacement from a bright to dark region (shown from top to bottom curves for positions indicated by red dots in Supplementary Fig. 10a) with peak multiplicity stemming from reconstructed nanoscale domains. b–j, Interlayer exciton PL (b, e, h), P_c (c, f, i) and B-field dispersion (d, g, j) for three representative positions. The magneto-luminescence data were recorded under linearly polarized excitation with σ⁺ detection to determine the g-factor values from linear slopes. Spots with bright PL (as in b) feature triplet and singlet peaks with opposite P_c signs and characteristic g-factors of about −16 and 12. Sample positions with low PL intensity exhibit structured spectra (as in e and h) with reduced P_c. Their characteristics differ both in spectral profiles and g-factors. Data in e–g are from sample 2, whereas all other data are from sample 3 (see Supplementary Fig. 10). The g-factor values with least-square error bars were obtained from linear fits to the data in Supplementary Fig. 17. Source data