Ultrafast Coherent Exciton Couplings and Many-Body Interactions in Monolayer WS2

Abstract

Transition metal dichalcogenides (TMDs) are quantum confined systems with interesting optoelectronic properties, governed by Coulomb interactions in the monolayer (1L) limit, where strongly bound excitons provide a sensitive probe for many-body interactions. Here, we use two-dimensional electronic spectroscopy (2DES) to investigate many-body interactions and their dynamics in 1L-WS₂ at room temperature and with sub-10 fs time resolution. Our data reveal coherent interactions between the strongly detuned A and B exciton states in 1L-WS₂. Pronounced ultrafast oscillations of the transient optical response of the B exciton are the signature of a coherent 50 meV coupling and coherent population oscillations between the two exciton states. Supported by microscopic semiconductor Bloch equation simulations, these coherent dynamics are rationalized in terms of Dexter-like interactions. Our work sheds light on the role of coherent exciton couplings and many-body interactions in the ultrafast temporal evolution of spin and valley states in TMDs.

Keywords: coherent couplings; many-body interactions; transition metal dichalcogenides; ultrafast spectroscopy.

Figure 1

(a) Schematic momentum-space representation of the hexagonal unit cell with K and K’ valleys. Direct excitons are depicted as Coulomb-bound e–h pairs with their spins indicated by arrows. When using linearly polarized light, all excitons can be excited. (b) A 1L-WS₂ flake is deposited on a Ag substrate coated with 5 nm Al₂O₃. (c) Reflectivity (red) showing the A and B excitons at ∼2.01 and ∼2.4 eV, respectively. The laser spectrum (black) is tuned to cover both resonances, while predominantly exciting the A exciton.

Figure 2

Ultrafast pump–probe spectroscopy of 1L-WS₂ on a Ag substrate. (a) Pump–probe map of ΔR/R showing positive nonlinearities (ΔR/R > 0) at the A and B exciton energies. (b) Spectral crosscuts at selected waiting times showing the characteristic line shape of an EID nonlinearity, most clearly for the A exciton. (c) Zoom-in at early waiting times. The B exciton resonance shows pronounced oscillations at positive and negative T. (d) Waiting time dynamics of the A exciton resonance. For T < 0, the PPFID of the A exciton can be seen. For T > 0, the dynamics show an initial spike and delayed rise of the A exciton signal. (e) Dynamics at selected energies for the B exciton resonance showing pronounced ΔR/R oscillations with a period ∼11.5 fs (dashed vertical lines). A Fourier transform of the oscillatory component confirms an energy of ∼360 meV, in good agreement with the A–B exciton splitting. These oscillations are the signature of coherent coupling between A and B excitons.

Figure 3

2DES of 1L-WS₂. (a–d) 2DES maps at selected T. In addition to diagonal features at the A and B exciton energy, (A,B) and (B,A) cross-peaks arise from a coherent coupling between the two types of excitons. Vertical stripes for excitation energies above the A exciton at both the A and B exciton detection energy are signatures of many-body effects, such as EID, by an additional broad background density of states. (e,f) Evolution of spectral crosscuts at the A (e) and B (f) exciton excitation energy. The A exciton resonance undergoes a reduction in amplitude and change in symmetry within ∼50 fs, reflecting an EIS of the resonance energy by ΔE (inset in f). (g) Dynamics of the diagonal (A,A) and cross (B,A) peak. Within the first ∼50 fs, the (A,A) exciton amplitude partially decays, while the (B,A) cross-peak amplitude builds up. (h) Spectrally integrated 2DES trace, detected at the A exciton (green dots), together with pump–probe dynamics (blue line) of the A exciton. Similar 2DES traces, now integrated over excitation energies larger than (red) or smaller than (black) 2.06 eV. A delayed rise in ΔR/R reflects the relaxation of B exciton populations into the A exciton on a sub-50 fs time scale.

Figure 4

Simulation of ΔR/R measurements considering a 50 meV coupling between A and B excitons. (a) Scheme of the employed many-body Hamiltonian. In addition to the 1-quantum (1Q) states |X_A⟩ and |X_B⟩, three two-quantum (2Q) states are considered to phenomenologically account for many-body interactions. Different types of system–bath interactions with a dephasing rate γ are indicated. EID is introduced by altering the dephasing rates associated with the 2Q states. (b) Simulated pump–probe map (left). The absorption (blue) and laser spectra (black) are shown in the right panel. The simulations reproduce the exciton nonlinearities observed experimentally. The inset highlights the rapid ΔR/R oscillations induced by the A–B coupling. (c) Comparison between experimental (black) and simulated (red) ΔR/R line shape showing the dominant EID nonlinearity. (d) Experimental (black) and simulated (red) ΔR/R dynamics at the A and B excitons. The rapid oscillations at early times are qualitatively reproduced. (e) Simulated 2DES map at T = 100 fs, showing the dominant resonant EID nonlinearity of the diagonal peaks and cross peaks arising from the coherent A–B coupling.

Figure 5

(a) Scheme of Dexter-like intervalley coupling between the A and B excitons in different valleys. (b) Calculated ΔR/R dynamics with (solid lines) and without (dashed lines) Dexter coupling. If the Dexter coupling is omitted, the A–B exciton polarization interference is strongly suppressed, as B excitons are no longer driven by the Coulomb interaction. A minimal oscillation remains due to weak residual direct optical pumping of the B excitons with the tail of the spectrally broad 5 fs pump pulse.