Experiments: Mott transition from interlayer exciton to charge-separated plasmas

We use transfer stacking to form WSe 2 /MoSe 2 heterobilayers encapsulated by hexagonal boron nitride (h-BN), with the two TMDC monolayers aligned within the light cone (15) for radiative interlayer exciton emission (twist angle θ = 4° ± 2° from K/K or K/K′ stacking), with a dark heterobilayer sample with θ = 13° ± 2° (from K/K or K/K′ stacking) as control (see fig. S1 for optical images and figs. S2 and S3 for monolayer alignment). The WSe 2 and MoSe 2 monolayers are exfoliated from flux-grown single crystals, each with defect density <1011 cm−2, two orders of magnitude lower than in commonly used commercial crystals (16). This is critical for suppressing defect-mediated nonradiative recombination previously seen to dominate TMDC heterobilayers (6) and for sustaining high excitation density in the charge-separated e/h plasmas. All measurements are carried out with the samples at 4 K in a liquid helium cryostat. The spectroscopic measurements include steady-state PL with CW excitation (hν = 2.33 eV), TRPL with pulsed excitation (hν = 2.33 eV; pulse width, 150 fs), and transient reflectance spectroscopies with pulsed excitation (hν = 1.82 eV; pulse duration, 150 fs) (see fig. S4 for the experimental setup). At both excitation photon energies, we calculate the absorptance (percentage of incident light absorbed; see fig. S6) to be 8% at the low excitation density limit based on the reported dielectric functions of WSe 2 and MoSe 2 monolayers (17). We carefully calibrate experimental electron/hole density, n eh , by including the saturation of absorptance from self-consistent Maxwell semiconductor Bloch equation calculations (see figs. S8 and S9 and table S1). Under the experimental conditions used here, we find the measurements completely reproducible, i.e., there is no sample damage due to laser excitation. However, damage to other heterobilayer samples has been observed for laser excitation exceeding the upper limit shown here.

Figure 1A shows the CW PL spectra from the WSe 2 /MoSe 2 heterobilayer with n eh spanning over four orders of magnitude (1.6 × 1010 to 3.2 × 1014 cm−2), achieved by varying excitation power density from ρ = 0.5 W/cm2 to 1.5 × 105 W/cm2. We quantitatively calibrate the equilibrium excitation density based on n eh = F ∙ σ ∙ τ 0 , where F is the incident photon flux, σ is the absorptance, and τ 0 is the population decay time constant determined in TRPL; both σ and τ 0 are numerical functions of n eh (see below) determined systematically through our computations and measurements, respectively. A complete set of spectra with normalized peak intensities is shown for the 1.31 to 1.41 eV region in Fig. 1B. Also shown in Fig. 1A are PL spectra of MoSe 2 (blue) and WSe 2 (green) monolayers. The former is characterized by the neutral exciton (X M ) and the trion, while the latter consists of a series of peaks assigned to exciton (X W ), trion, biexciton, etc., in agreement with previous reports (18–21). At n eh ≤1 × 1013 cm−2 in the heterobilayer, PL from intralayer excitons is completely quenched, while interlayer exciton (IX) emission with E IX = 1.3566 ± 0.0005 eV (at n eh = 1.6 × 1010 cm−2) dominates (7, 22). The IX peak grows with n eh and blue shifts only by ~8 meV in the entire excitation density range, as is known for coupled (23) and uncoupled (24) III–V quantum wells.

To experimentally detect the Mott transition, we plot in Fig. 1C the n eh dependences of the integrated intensities from interlayer PL (solid black circles) and its spectral full width at half maximum (FWHM; open red triangles), along with the intralayer PL (open black squares) integrated over the 1.50 to 1.75 eV energy rage. The interlayer emission peak broadens substantially when the theory-assigned n Mott = 3 × 1012 cm−2 (vertical dashed line; see below) is crossed. The corresponding FWHM increases by as much as a factor of four, verifying that excitons (and the narrow linewidth they sustain) are absent above n Mott . We also observe that intralayer PL, corresponding to broad emission from MoSe 2 and/or WSe 2 monolayer(s), reappears and grows for n eh >1 × 1013 cm−2. As the charge-separated e/h plasmas form at n eh > n Mott , the band offsets between the two TMDC monolayers are reduced due to both band renormalization and charge separation. The latter can be understood from a simple capacitive model (see “The capacitor model for charge separation across the WSe 2 /MoSe 2 heterobilayer” section in the Supplementary Materials), which predicts from the e/h charge separation a voltage buildup, ΔV C . This ΔV C can cancel out the initial ~300 meV band offset (14), leading to the repopulation of the conduction (valence) band of WSe 2 (MoSe 2 ) and to intralayer radiative recombination. This interpretation is supported theoretically (Fig. 1D), which shows the computed source for PL emission, i.e., the probability of simultaneously finding electrons and holes in the K valleys of WSe 2 (green), MoSe 2 (blue), and between the two monolayers (black). The experimental onset of intralayer PL matches perfectly with the rise in the computed spontaneous emission source for MoSe 2 , while PL from WSe 2 remains suppressed. Further support for this interpretation comes from PL measurement on the control sample of a WSe 2 /MoSe 2 heterobilayer with θ = 13° ± 2° alignment. The large momentum mismatch between the K (or K′) valleys across the interface means that the interlayer excitons are nonradiative (10). We observe no measurable IX emission, but only intralayer PL at n eh >> n Mott (solid gray squares in Fig. 1C; see fig. S10 for the PL spectra).

We determine the lifetimes of interlayer exciton emission using TRPL under pulsed excitation (hν = 2.33 eV; see fig. S5 for the instrument response function, which gives a time resolution of ~40 ps). Figure 2A shows TRPL data in the broad initial excitation density range of n 0 = 1.1 × 1010 to 6.0 × 1013 cm−2. The corresponding time-integrated PL spectra (Fig. 2B) are similar to the CW PL spectra in Fig. 1A (see fig. S11 for direct comparisons). The PL decays at low excitation densities (1010–11 cm−2) are close to single exponentials, with a decay time constant of τ 0 = 200 ± 40 ns. As n 0 increases, particularly above n Mott , the PL decay becomes faster and exhibits a major deviation from single exponential. This behavior is expected for plasma luminescence, as demonstrated in various III–V quantum well systems (25). Above the Mott transition, luminescence from the e/h plasmas scales approximately with n eh 2. In addition, carrier density may decay nonradiatively, e.g., via Auger recombination that scales approximately with n eh 3. As a result, PL decays faster at higher carrier densities, but this is difficult to analyze quantitatively due to the varying Auger scattering cross sections resulting from the expected density-dependent Coulomb screening. Figure 2C plots the initial PL decay time constant as a function of n 0 . Our PL lifetimes are one to two orders of magnitude longer than those of previous reports on WSe 2 /MoSe 2 heterobilayers (7, 22, 26), suggesting the suppression of nonradiative recombination in the less defective TMDC samples used here. These long PL lifetimes are essential to reaching excitation density well above the Mott threshold and to obtaining high steady-state n eh under CW excitation, as n eh is proportional to τ 0 .

Fig. 2 TRPL emission from interlayer excitons in the WSe 2 /MoSe 2 heterobilayer. The sample at 4 K is excited by pulsed laser (hν = 2.33 eV; pulse duration, 150 fs). The energy-integrated emission from the interlayer exciton [see spectra in (B)] is detected as a function of time (A) for initial excitation densities of (from bottom to top) n 0 = 1.1 × 1010, 3.0 × 1010, 9.4 × 1010, 3.0 × 1011, 9.4 × 1011, 3.0 × 1012, 8.7 × 1012, 2.5 × 1013, and 6.0 × 1013 cm−2. (C) Initial decay time constants (solid circles) as a function of n 0 . The solid line is the biexponential fit to the data.

To further explore the properties of charge-separated e/h plasmas in the WSe 2 /MoSe 2 heterobilayer, we apply transient reflectance spectroscopy (time resolution ~40 fs; see fig. S5), which has been used before to probe excitons and electron-hole (e-h) plasma in TMDC monolayers (13) and charge separation in heterobilayers (5, 6). We excite the samples with a 150-fs pulse at 1.82 eV and probe the change in reflectance using broadband white light (1.2 to 1.8 eV). We present transient reflectance, ΔR/R 0 , as a function of pump-probe delay (Δt), where ΔR = R – R 0 ; R is the reflectance at Δt, and R 0 is the reflectance without the pump. At the 2D limit and low excitation densities, ΔR/R 0 is proportional to transient absorption (27). Figure 3 (A to D) shows pseudocolor plots of transient reflectance spectra in a broad range of excitation densities. At n 0 ≤ n Mott (Figure 3, A or B), each spectrum is dominated by two prominent photobleaching peaks at ~1.62 and ~1.70 eV, attributed to the reduction in oscillator strength (6) of transitions in monolayers WSe 2 and MoSe 2 , respectively. The induced absorption signal (red) on the sides of the main bleaching peaks can be attributed to shifts in intralayer transition energies resulting from competing effects of screening/Pauli blocking of the Coulomb interaction and band renormalization. Note that, at n 0 < n Mott , ΔR/R 0 is negligible below 1.5 eV, including the IX region. This is expected as the oscillator strength of the interlayer exciton is two orders of magnitude lower than those of the intralayer excitons in each monolayer (28). The absence of ΔR/R 0 signal below 1.5 eV is evident in horizontal cuts at selected Δt values, shown for n 0 = 1.0 × 1011 cm−2 in (Fig. 3E).

Fig. 3 Density-dependent transient reflectance spectra from the WSe 2 /MoSe 2 heterobilayer. The WSe 2 /MoSe 2 heterobilayer was excited at hν = 1.82 eV with initial excitation densities of n 0 = (A) 1.0 × 1011, (B) 9.6 × 1011, (C) 5.6 × 1012, and (D) 3.4 × 1013 cm−2 at a sample temperature of 4 K. The excited sample is probed with a white light, and the pseudocolor scale is ΔR/R 0 (blue , bleaching; red, induced absorption). Transient reflectance spectra at selected pump-probe delays (Δt) at n 0 = (E) 1.0 × 1011 and (F) 3.4 × 1013 cm−2 are also shown. The probe regions around 1.55 eV are blocked out due to low intensity and noise from white light which was generated by 1.55-eV laser light. Kinetic profiles obtained from vertical cuts at (G) 1.351 and (H) 1.624 eV in the 2D pseudocolor plots at the four n 0 values.

In agreement with the CW results in Fig. 1A, transient reflectance spectra under pulsed excitation reveal plasma formation above the Mott density. At n 0 = 5.6 × 1012 or 3.4 × 1013 cm−2 (Fig. 3, C and D), the spectra show, in addition to bleaching of intralayer exciton transitions, broad induced absorption extending to the low energy end (~1.3 eV) of the probe window. These broad features are evident in horizontal cuts (spectra) at short pump-probe delays, as shown for n 0 = 3.4 × 1013 cm−2 in Fig. 3F. This broad absorption feature is the optical signature of a 2D plasma, which consists of broad induced absorption (positive) extending to the renormalized bandgap and gain (negative) just above the bandgap (13, 29).