Dissecting Interlayer Hole and Electron Transfer in Transition Metal Dichalcogenide Heterostructures via Two-Dimensional Electronic Spectroscopy

Monolayer transition metal dichalcogenides (ML-TMDs) are two-dimensional semiconductors that stack to form heterostructures (HSs) with tailored electronic and optical properties. TMD/TMD-HSs like WS2/MoS2 have type II band alignment and form long-lived (nanosecond) interlayer excitons following sub-100 fs interlayer charge transfer (ICT) from the photoexcited intralayer exciton. While many studies have demonstrated the ultrafast nature of ICT processes, we still lack a clear physical understanding of ICT due to the trade-off between temporal and frequency resolution in conventional transient absorption spectroscopy. Here, we perform two-dimensional electronic spectroscopy (2DES), a method with both high frequency and temporal resolution, on a large-area WS2/MoS2 HS where we unambiguously time resolve both interlayer hole and electron transfer with 34 ± 14 and 69 ± 9 fs time constants, respectively. We simultaneously resolve additional optoelectronic processes including band gap renormalization and intralayer exciton coupling. This study demonstrates the advantages of 2DES in comprehensively resolving ultrafast processes in TMD-HS, including ICT.

(2DIR), which extends to optical frequencies techniques commonly used in nuclear magnetic resonance 3 . 2DES measures the third-order nonlinear material polarization ( (3) ( )) following perturbation by a sequence of three laser pulses: two pump pulses and a probe pulse (Figure 1a). This method measures the same type of signal as transient absorption (TA) spectroscopy.
However, whereas TA methods employ a two-pulse sequence, pump and probe, with a single waiting time t2 between the pulses, 2DES introduces a second pump pulse with an additional time delay t1 between the two pumps. By scanning t1 and performing a Fourier transform to ω1, 2DES resolves the excitation frequency. The detection frequency (ω3) is measured directly either by heterodyne or homodyne detection in a spectrometer. In this way, 2DES is not limited by the same pulse bandwidth/temporal resolution tradeoff as TA techniques as there is no ambiguity of the initial light absorption event when using transform-limited broadband pulses. 2DES signals can be related to TA by integration of the real absorptive signal over a portion of the ω1 axis.
2DES generates two types of signals referred to as the rephasing and non-rephasing signals, defined by their phase matching criteria, kR and kNR: where kn is the wave vector of the n th pulse (pump 1 = 1, pump 2 = 2, probe = 3). The rephasing signal is analogous to a stimulated photon echo signal. Collection of both the rephasing and nonrephasing signals is necessary to reconstruct the real absorptive signal ( = + ). In a 2DES instrument with a partially collinear pump-probe beam geometry, like the one used in this experiment 4 , k1 = k2 so that both the rephasing and non-rephasing signals propagate collinearly with the probe pulse ( = = 3 ), allowing for measurement of the absorptive signal directly along the probe path 5,6 .
The inter-pump coherence time, t1, is so named as the system evolves as an electronic coherence following the light-matter interaction of the first pump pulse. During this time, the signal oscillates with the electronic transition frequency and decays rapidly. The light-matter interaction of the second pump pulse can bring the system back into a population either of the ground or of the initially excited state or can interact with a different electronic transition, putting the system into a coherent superposition between the two excited states. The waiting time t2 between the second pump and the probe ( Figure 1a) is scanned to allow the populations and coherent oscillatory dynamics to evolve. A final interaction with the probe results in a four-wave-mixing signal which yields information about how the state has evolved during t2.
The best way to represent 2DES data is to generate 2D maps which plot the signal as a function of excitation energy (ℏω1) and detection energy (ℏω3). Electronic transitions with inhomogeneous broadening show elongation of the signal along the diagonal (ℏω1 = ℏω3) at early times, whereas the antidiagonal line shape corresponds to the homogeneous width. The signals resulting from stimulated emission and photobleaching are positive in sign (red in our maps) and photoinduced absorption signals are negative (blue in our maps). Analysis of the t2-dynamics is typically done by selecting a specific point (ℏω1, ℏω3) in the 2D map and plotting the corresponding signal amplitude as a function of t2.

2DES setup
The home-built 2DES instrument generates a pair of time delayed pump pulses with pairs of birefringent wedges which scan the inter-pump pulse delay, t1, with high phase stability 4  steps from -50<t2<50 fs followed by 10 fs steps up to 1 ps.

Figure S1
. Absorption spectrum of the HS (black) plotted against experimental pump (purple) and probe (blue) spectra. Both pulses are generated from the same NOPA.
The pair of phase-locked pump pulses are generated using pairs of birefringent wedges in a device termed Translating-Wedge-Based Identical Pulses eNcoding System (TWINS) 4 . The pump pulse pair is generated with a 45° linearly polarized beam split into orthogonally polarized components after traveling through a series of birefringent α-barium borate plates and wedges.
Two pairs of birefringent wedges are cut to selectively delay either the horizontally or the vertically polarized pump component. The t1 delay between the pump pulses is controlled with a translation stage where one wedge of each pair is mounted. The delayed pump pair is projected back onto the 45° polarization with a linear polarizer 4 . In this study, t1 is continuously scanned in the -30 fs < t1 < 220 fs range. A portion of the pump beam is sampled after traveling through a chopper; the sampled beam is sent to a photodiode which is used to calibrate the t1 delay and to monitor the laser stability during the course of the experiment.

Pulse characterization
The instrumental response function (IRF) was measured using cross-correlated Polarization Gated  Figure S2. The average full-width half maximum (FWHM) of the PG-FROG is 21.9 fs ± 3.4 fs ( Figure S2a). Figure S2b shows the spectrogram of the IRF showing a negligible amount of linear and quadratic chirp across the main region of interest (1.9-2.1 eV). The IRF offers an upper limit for the temporal resolution of the setup.

Large-Area Sample Preparation
MoS2 and WS2 monolayers are obtained by gold-assisted mechanical exfoliation from bulk MoS2 (SPI Supplies) and WS2 (HQ graphene) 7 . A gold layer is deposited on top of the bulk TMDs.

2DES map of isolated WS 2
2DES measurements were additionally performed on large-area WS2 monolayer samples at 80 K ( Figure S4) using the same pump and probe spectra as in the WS2/MoS2 HS and MoS2 ML samples. For this reason, only the AW exciton is resolved. At early t2 the 2D maps is dominated by the strong diagonal peak of the AW exciton which is significantly inhomogeneously broadened along the diagonal (ℏω1 = ℏω3) and shows somewhat narrow homogeneous broadening along the antidiagonal. At later times (t2 = 200 fs) the elongated lineshape of AW rounds out due to spectral diffusion and loss of correlation between excitation and detection events.

Fitting procedure and time constants
In order to characterize the kinetic behavior of interlayer charge transfer (ICT) we performed a simple fit to point-traces of the 2DES data. Point-traces were selected based on the exciton energies of each relevant sample for a specific frequency combination (ℏω1, ℏω3) and were then averaged over the surrounding 10 meV in the 2DES maps. The temporal dynamics of all the excitonic peaks of the 2DES maps measured on the HS and the isolated layers together with the corresponding fits are reported in Figure S5, S6 and S7. coefficients are presented with the 95% confidence intervals. The build-up times τrise of the cross peaks dynamics in Figure 3b represent a precise estimation of the IHT and IET processes.
The 2DES measurements were performed on a limited temporal window (i.e. 1 ps) in order to achieve a high signal to noise ratio of the signals that allow us to perform high-quality fit of the temporal traces and to extract with accuracy the timescales of the early stage relaxation processes in the HS. For this reason, our fits can correctly reproduce only the formation and the fast (i.e. fs to ps) relaxation processes in TMDs while they cannot capture the long lived (i.e. hundreds of ps or ns) decay components expected for the radiative recombination process of interlayer excitons 8 .    The same instantaneous dynamics is observed in ML-WS2 and attributed to photoinduced renormalization of the optical gap. The strong negative feature at negative delays is attributed to a pump-perturbed free induction decay signal.