Strong Coupling of Coherent Phonons to Excitons in Semiconducting Monolayer MoTe2

The coupling of the electron system to lattice vibrations and their time-dependent control and detection provide unique insight into the nonequilibrium physics of semiconductors. Here, we investigate the ultrafast transient response of semiconducting monolayer 2H-MoTe2 encapsulated with hBN using broadband optical pump–probe microscopy. The sub-40 fs pump pulse triggers extremely intense and long-lived coherent oscillations in the spectral region of the A′ and B′ exciton resonances, up to ∼20% of the maximum transient signal, due to the displacive excitation of the out-of-plane A1g phonon. Ab initio calculations reveal a dramatic rearrangement of the optical absorption of monolayer MoTe2 induced by an out-of-plane stretching and compression of the crystal lattice, consistent with an A1g -type oscillation. Our results highlight the extreme sensitivity of the optical properties of monolayer TMDs to small structural modifications and their manipulation with light.


Experimental
Ultrafast spectroscopy experiments were performed using a custom broadband transient absorption microscope setup based on a Ti:sapphire laser system (Coherent Libra) which outputs 100 fs pulses at 1.55 eV with 2 kHz repetition rate.The pump was generated using a non-collinear optical parametric amplifier (NOPA) tuned to a centre energy of ∼ 2.36 eV.
The probe was created by white light continuum generation in a 1 mm sapphire plate using the laser fundamental.Pump and probe beams were focused onto the sample with a diameter of ∼ 5 and 3 µm , respectively, using an achromatic objective lens.Cross polarization was used to avoid scattering artefacts.The pump was pre-compressed using chirp mirrors to account for all transmissive optical elements in the beam path that introduce dispersion.
The pulse compression was optimized by measuring a target metallic sample with a nearly instantaneous response, resulting in an overall temporal resolution of ≤ 40 fs, comparable to the build-up time of excitons in MoS 2 as measured previously. 1 A pump fluence of ∼ 500 µJ cm −2 was used.The sample was mounted inside an ultra low vibration closed-cycle cryostat, and the temperature maintained at T = 10 K.The setup operates in backscattering geometry, whereby the reflected probe is dispersed by a spectrometer onto a CCD camera.
The differential reflectance of the sample (∆R/R ) is then obtained by modulating the pump using an optical chopper, while the pump-probe delay is controlled by a mechanical delay line.

Computational
Theoretical investigation of the absorbance has been carried out by means of ab initio simulations.DFT 2,3 and DFPT 4 calculations were performed with QUANTUM ESPRESSO, [5][6][7] where the Perdew-Burke-Ernzerhof exchange-correlation functional 8 and a plane-wave cutoff at 50 Ha were used.To replace the effect of core electrons, fully relativistic pseudopoten-tials were used from PSEUDODOJO 9 since spin-orbit coupling is taken into account.A vacuum distance of 40 a.u. was imposed in order to avoid the fictitious interactions between periodic layers.To calculate the quasiparticle correction, the GW method 10,11 was used in single-shot mode G 0 W 0 , applying the plasmon-pole approximation.In order to compute the optical properties taking into account the excitonic effects, the Bethe-Salpeter equation (BSE) 12 was solved, where the Tamm-Dancoff approximation was applied.14 valence bands and 13 conduction bands were considered for the correct description of the optical absorption.The polarizability per unit area of the MoTe 2 monolayer was obtained from the BSE results, and used to calculate the effective dielectric function and the absorbance.In order to compute the coherent part of the differential absorbance, DFT and BSE simulations were first performed for equilibrium atomic positions and then with the atoms displaced along the Raman active A 1g phonon eigen-mode ξ, as explained in Ref. 13 Both GW and BSE simulations were performed using YAMBO code. 14All calculations were performed with a 42 × 42 × 1 Monkhorst-Pack grid 15 for the Brillouin zone.

Figure S1 :Figure S2 :Figure S3 :Figure S4 :
Figure S1: Exciton decay dynamics obtained by multi-exponential fit.(a) Transient ∆R/R spectrum at 1 ps.Vertical dashed lines indicate photon energies 1.85 and 2.05 eV selected for multi-exponential fitting which correspond to the approximate positions of the photobleaching (PB) signal of the A' and B' excitonic resonances.(b) -(c) Fit of the PB signal for each photon energy using a bi-exponential decay function A f e −t/τ f + A s e −t/τs + y 0 that consists of a fast (τ f ) and slow (τ s ) component and a offset value, y 0 .Data for t > 0.3 ps was used to fit only the decay dynamics.The results of the fitting, including associated errors, are reported in the figure panels.

Figure S5 :
Figure S5: Excitation energy dependence of the oscillation amplitude.(a) Calculated optical absorbance (left axis) for the equilibrium structure of 2H-MoTe 2 .Normalized broadband pump spectra (right axis) with centre energies indicated in the legend.(b) Fourier transform (FT) map of the oscillatory signal component for each excitation (pump) energy.The pump fluence was ∼ 500 µJ cm −2 in all cases.(c) FT amplitude at 5.15 THz extracted from panel b for each excitation energy, revealing a similar spectral profile in all cases, and a slightly enhanced amplitude for higher pump energies.

Figure S6 :
Figure S6: Orbital character of the projected band structure from ab initio calculations.(a) Electronic band structure for undistorted (equilibrium) monolayer 2H-MoTe 2 , where the colour represents the projected density of states (PDOS) contributions from Mo and Te atomic orbitals expressed as a percentage.(b) Selected region around the K-point.The vertical arrows illustrate regions of the band structure related to the A/B excitonic transitions at K, and the A'/B' transitions along the K − Γ direction.