Localisation-to-delocalisation transition of moiré excitons in WSe2/MoSe2 heterostructures

Abstract

Moiré excitons (MXs) are electron-hole pairs localised by the periodic (moiré) potential forming in two-dimensional heterostructures (HSs). MXs can be exploited, e.g., for creating nanoscale-ordered quantum emitters and achieving or probing strongly correlated electronic phases at relatively high temperatures. Here, we studied the exciton properties of WSe₂/MoSe₂ HSs from T = 6 K to room temperature using time-resolved and continuous-wave micro-photoluminescence also under a magnetic field. The exciton dynamics and emission lineshape evolution with temperature show clear signatures that MXs de-trap from the moiré potential and turn into free interlayer excitons (IXs) for temperatures above 100 K. The MX-to-IX transition is also apparent from the exciton magnetic moment reversing its sign when the moiré potential is not capable of localising excitons at elevated temperatures. Concomitantly, the exciton formation and decay times reduce drastically. Thus, our findings establish the conditions for a truly confined nature of the exciton states in a moiré superlattice with increasing temperature and photo-generated carrier density.

Fig. 1. Optical properties of the WSe₂/MoSe₂ R-type HS1.

a Optical micro-graph (left) and sketch (right) of HS1. b Low-T μ-PL and μ-PLE spectra of the HS, left and right axis, respectively. In the μ-PL spectrum (P_exc = 2 μW), X indicates the intralayer exciton recombination from localised states of the MoSe₂ and WSe₂ monolayers (lower- and higher-energy side, respectively). MX is the moiré exciton band. In the μ-PLE spectrum, four exciton resonances are observed. These resonances can be attributed to the A and B excitons (where the hole sits in the upper, A, and lower, B, spin-split valence band maximum at K, and the electron sits in the spin-split conduction band minimum at K with same spin) of the MoSe₂ and WSe₂ layers. c μ-PL spectrum of the MX band acquired with very low laser power excitation (5 nW). The spectrum can be reproduced by five Gaussian functions (azure: single components; red line: total fit) that are spaced by (12.8 ± 1.3) meV. The very narrow lines that make up the broader Gaussian peaks correspond to single MXs recombining in moiré minima. d μ-PL spectra recorded at different temperatures (and P_exc = 20 μW). The moiré/interlayer (MX/IX) exciton band is visible up to room temperature. X indicates the exciton band related to the single layer MoSe₂ and WSe₂ constituents of the HS.

Fig. 2. Decay and rise of the moiré exciton band.

a T = 10 K and P_exc = 1 μW μ-PL spectrum of HS1. MX indicates the moiré-trapped interlayer exciton, and X indicates the intralayer exciton recombination. Three different spectral regions are highlighted on the MX band. On each of these regions, the μ-PL time evolution was recorded. b Time-evolution of the μ-PL signal recorded in the Δt = 0-800 ns interval from the laser pulse on the three spectral regions highlighted in panel a (note also the colour code). The decay time τ_d,n values obtained by fitting the data via Eq. (1) (see solid lines) are displayed. c The same as b for Δt = 0–1.0 ns. The rise time τ_r values displayed in the panels are those used to reproduce the data with Eq. (2) (see solid lines). The data in the right-most panel could not be fitted reliably.

Fig. 3. Photo-generated carrier density and temperature dependence of the exciton bands.

a T = 6 K μ-PL spectra of HS1 recorded for different laser excitation power values. MX indicates the moiré exciton band and X the intralayer exciton recombination in the MoSe₂ and WSe₂ layers (lower- and higher-energy side, respectively). b PL integrated intensity dependence on the laser power P_exc for the MX or MX-IX bands (azure symbols) and for the X band (light orange symbols) at T = 6 K (full symbols) and T = 90 K (open symbols), respectively. Solid and dashed lines are fits to the data with Eq. (3) for T = 6 K and 90 K, respectively. At T=6 K, the α coefficient values are 0.55 ± 0.02 and 0.89 ± 0.02 for MX and X, respectively. At T = 90 K, the α coefficient values are 0.99 ± 0.02 and 0.97 ± 0.03 for MX-IX and X, respectively. c Temperature variation of the α coefficient for the MX-IX and X bands. In the former case, a clear transition from a sublinear to a linear behaviour is found and ascribed to the transition from a moiré localisation regime to a free interlayer exciton one (hence the mixed label MX-IX). d T = 90 K μ-PL spectra for different laser excitation powers in the energy region where the MX and IX recombinations can be simultaneously observed. IX takes over MX upon increase of the photo-generated carrier density. e Same as d for T = 296 K, where only the IX transition is observable.

Fig. 4. Exciton magnetic moment sign reversal.

a μ-PL spectra of HS1 recorded for different temperatures and fixed P_exc = 10 μW focused via a 20 × objective (NA=0.4). MX indicates the moiré exciton band and IX the free interlayer exciton recombination. Note the major spectral transfer from MXs to IXs for T > 120 K. b Magneto-μ-PL spectra from 0 to 12 T (in steps of 1 T) of the MX band at T = 10 K and P_exc = 10 nW (focused via a 100× objective with NA = 0.82). The upper and lower panels correspond to the σ⁺ (red) and σ⁻ (blue) circular polarisations, respectively. The data are stacked by y-offset. The positive and negative slopes of the σ⁺ and σ⁻ polarisations with the field indicate a positive gyromagnetic factor. The arrows denote some specific MX lines. c Magneto- μ-PL spectra at T = 160 K and P_exc = 75 μW of the free IX band for the σ ⁺ and σ ⁻ polarisations. A negative Zeeman splitting (ZS) can be observed, with the σ ⁺ and σ ⁻ spectra being at lower and higher energy, respectively. d ZS of the five moiré-localised excitons M1 to M5 highlighted by the arrows in panel b (M1 is the lowest energy one, M5 the highest) and of the free IX exciton vs magnetic field measured in panel c, resulting in the gyromagnetic factors displayed in the figure. The ZS data of the M2 to M5 lines were shifted by y-offset for ease of visualisation. Error bars are within the symbol size.

Fig. 5. Unveling the moiré atomic registry through g-factor measurements.

a, b Helicity-resolved normalised μ-PL spectra of HS1 under magnetic field at T = 6 K for two different laser excitation powers P_exc (focused via a 100 × objective with NA = 0.82). The two sets of data were acquired in the same point of the HS. For P_exc = 0.2 μW (a), many narrow lines can be seen. M1, M2 and M3 indicate three such narrow lines. At high powers P_exc = 75 μW (b) a continuous band can be seen. c ZS of the lines M1-M3 of panel a and of the MX band of panel b, showing an opposite sign of the g-factor. The data of lines M2 and M3 are up-shifted by 1 and 2 meV, respectively (as indicated by the double-sided arrows on the left) for sake of clarity. d Top: Theoretical g-factors (cyan stars) estimated for MXs confined in the ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{X}}$, ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{h}}$, and ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{M}}$ atomic registries. The experimental g-factors calculated for the MX lines at low power (as an average of the g-factors estimated for the M1, M2 and M3 lines of panel c), and for the MX band measured at high power (pink data in panel c) are displayed as orange pentagons, and —based on their value— are associated to the ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{X}}$ and ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{h}}$ registries, respectively. The cyan solid line and the orange dashed line provide the g-factor calculated based on Eq. (5) and that measured experimentally (Fig. 4c, d) for the free IX, respectively. The insets show the atomic alignment corresponding to the three atomic registries. Error bars are within the symbol/line size. Bottom: Variation of the interlayer exciton potential landscape with respect to its minimum at the ${\mathrm{R}}_{\mathrm{h}}^{\mathrm{X}}$ point (ΔE) in R-type MoSe₂/WSe₂ HSs. Adapted from the calculations of ref. .

Fig. 6. Rise and decay times with increasing temperature.

a Time-evolution of the μ-PL signal of the investigated WSe₂/MoSe₂ heterostructure (HS1) recorded at different temperatures (and fixed laser excitation power P_exc = 44 nW) in the Δt = 0 − 1.0 ns interval from the laser pulse. The detection energy was set at the MX-IX band (see Fig. 3). The solid lines are fits to the data by Eq. (2). b Rise time τ_r values obtained by fitting the experimental data for different temperatures and two P_exc values. The setup time resolution is shown by the grey area. Notice that once the data get close to the resolution limit, the estimated rise time is affected by the system response and thus only qualitatively indicative. c Time-evolution of the μ-PL signal of the MX-IX band (see Fig. 3) recorded in the Δt = 0-800 ns interval from the laser pulse. The data were recorded at different temperatures, as indicated in the figure, and fixed P_exc. The grey area indicates the instrumental response. d Decay times τ_d,n values used to reproduce the data of panel c via Eq. (1). The same for the spectral weights w_d,n of the different time components, see Eq. (1).