Progress in Research on Intervalley Scattering and Rabi Oscillation Driven by Coherent Phonons

Two dimensional transition metal chalcogenides have multi valley structures in their energy bands, giving them electron valley degrees of freedom, making them an ideal platform for studying multi body interactions. As the main mechanism of valley depolarization, the valley scattering process of free electrons or bound excitons is crucial for exploring excited state electron phonon interactions and designing and implementing valley electronic devices.

At present, theoretical and experimental research on valley to valley scattering is mostly based on thermal equilibrium or quasi equilibrium states. However, the ultra short laser pulse can drive the lattice and electrons away from the equilibrium state, and the ultrafast dynamic process and basic mechanism of the system are still unclear.

Recently, under the guidance of associate researcher Wang Yaxian and researcher Meng Sheng, Wang Chenyu, Liu Xinbao, Chen Qing and other doctoral students from the SF10 group of the Institute of Physics of the Chinese Academy of Sciences/State Key Laboratory of Surface Physics of the National Research Center for Condensed Matter Physics, used the nonadiabatic time-dependent density functional molecular dynamics method and software (TDAP) independently developed by the group, Explored the valley to valley scattering process of excited state electrons K → Q induced by coherent phonons in single-layer WSe2 (Figure 1), revealing the law of non equilibrium electroacoustic coupling at the femtosecond time scale.

Research has shown that the coherent oscillation of longitudinal acoustic phonons [LA (M)] along the boundary of the Brillouin zone can induce the transfer of photoexcited electrons occupying the K valley to the lower energy level Q valley. The scattering process has a time scale of about 400fs, which is consistent with experimental results. What is significantly different from the exponential decay of electron occupancy observed in current experiments is that the inter valley scattering driven by coherent phonons exhibits a novel feature of "stepped" changes.

On the one hand, valley to valley scattering mainly occurs when the amplitude of coherent phonons is minimum and the lattice vibration velocity is maximum; On the other hand, after scattering electrons from the K valley to the Q valley, an inverse scattering from the Q valley to the K valley is observed, similar to the Rabi oscillation process driven by a periodic field (Figures 1 and 2). These two features are significantly different from the Fermi Golden Rule, which adheres to the thermal phonon condition, elucidating the key role of non adiabatic effects. This non adiabatic electron phonon interaction is directly confirmed in the two-level model, that is, when the atom approaches the equilibrium position, the non adiabatic coupling matrix element reaches its peak, promoting electron transfer between valleys and inducing a stepped scattering process (Figure 3).

In addition, this study explores a universal path for modulating valley to valley scattering using coherent phonons. The increase in LA (M) phonon amplitude is beneficial for improving the valley to valley scattering rate of electron K → Q; Furthermore, by combining ultrafast laser pulses with nonlinear coupling between phonons, effective manipulation of the amplitude of shortwave LA (M) phonons can be achieved (Figure 4).

The relevant research results are titled "Coherent phonon driven interval scattering and Rabi oscillation in multipalley 2D materials" and published in the Physical Review Letters. The research work was supported by the National Key R&D Program, the National Natural Science Foundation of China and the Chinese Academy of Sciences.

Figure 1. Schematic diagram of photo excited electron valley to valley scattering in WSe2, as well as the Rabi oscillation of the K/Q valley occupation number.

Figure 2. (a) Coherent vibrations of K/Q valley instantaneous energy levels (upper) and LA (M) phonons (middle). Evolution of electron occupancy numbers on K/Q valleys. (b) Image above: Optical emission signals on simulated K/Q valleys at 40, 300, and 500fs. Figure below: Evolution of the electron signal ratio between K valley and Q valley over time in experimental and theoretical simulations. The gray dashed line is calibrated as the critical time corresponding to the K valley and Q valley signals.

Figure 3. (a) Time evolution of K/Q valley instantaneous energy levels in the model (red line) and TDDFT calculation (black line); (b) The time evolution of the Q-valley occupancy and non adiabatic coupled matrix elements (NACME) (blue background) calculated by the model.

Figure 4. (a) The variation of scattering rate from K valley to Q valley with LA (M) phonon amplitude; (b) Schematic diagram of the coupling between long wave A1 phonon and short wave LA (M) phonon; (c) The temporal evolution of LA (M) phonons driven by A1 phonons.

Source: Institute of Physics, Chinese Academy of Sciences