Ultrafast Multi-Level Logic Gates with Spin-Valley Coupled Polarization Anisotropy in Monolayer MoS2

The inherent valley-contrasting optical selection rules for interband transitions at the K and K′ valleys in monolayer MoS2 have attracted extensive interest. Carriers in these two valleys can be selectively excited by circularly polarized optical fields. The comprehensive dynamics of spin valley coupled polarization and polarized exciton are completely resolved in this work. Here, we present a systematic study of the ultrafast dynamics of monolayer MoS2 including spin randomization, exciton dissociation, free carrier relaxation, and electron-hole recombination by helicity- and photon energy-resolved transient spectroscopy. The time constants for these processes are 60 fs, 1 ps, 25 ps, and ~300 ps, respectively. The ultrafast dynamics of spin polarization, valley population, and exciton dissociation provides the desired information about the mechanism of radiationless transitions in various applications of 2D transition metal dichalcogenides. For example, spin valley coupled polarization provides a promising way to build optically selective-driven ultrafast valleytronics at room temperature. Therefore, a full understanding of the ultrafast dynamics in MoS2 is expected to provide important fundamental and technological perspectives.

S tructural inversion symmetry together with time reversal symmetry allows monolayer MoS 2 to possess the same magnitude of magnetic moments but the opposite signs at the K and K9 valleys 1,2 . Furthermore, spinorbit coupling separates the spin-up and spin-down states of the valence band [3][4][5] , which plays a crucial role in spintronics 6 , valleytronics 7 , and semiconductor devices 8,9 . As shown in Figure 1(a), there is fascinating coupling between energy, spin, and valley. Utilizing these degrees of freedom of monolayer MoS 2 , optically driven logic gates can be realized. Figure 1(b) illustrates that a two-level logic gate can be operated by being sequentially excited with circularly polarized 2.01 eV (resonant with exciton B) and 1.98 eV (resonant with exciton A) pulses at room temperature. According to our time-resolved studies, the nonequilibrium population between the K and K9 valleys lasts for ,1 ps in monolayer MoS 2 , which is an excellent candidate material for the ultrafast optical control. For the application to a high-rate optical pulse control, the problem of the accumulation of the remnant coherence after the control pulse always exists. Thus, the following pulse to control the succeeding step must wait for the decoherence of the target. This limits the bandwidth of optical spin controlling devices.
Circularly polarized luminescence from monolayer MoS 2 has been demonstrated to have the same helicity as the circular polarization of an excitation laser [3][4][5]10,11 . This highly polarized luminescence has only been observed with resonant excitation. Furthermore, the valley-spin lifetime was previously predicted to be .1 ns 3 . However, a time-resolved study of polarized photoluminescence (PL) exhibited that the carrier spin flip time is in the time scale of several picoseconds, which is limited by the time resolution of the PL measurement system 12 . Mai et al. 13 further observed that the polarized exciton A decays only within several hundred femtoseconds, according to optical pump-probe measurements. Under the controversial situation, the full dynamics and physical insight of the polarized excitons in monolayer MoS 2 , including the spin-valley coupling, have not yet been conclusively studied.
In this work, we propose optically driven ultrafast two-level MoS 2 -logic gates through a systematic study of the ultrafast dynamics of monolayer MoS 2 with 30-fs time resolution. The identification of a single atomic layer of MoS 2 is confirmed by photoluminescence spectra, Raman spectra and AFM measurements, as shown in Figure 2. Through the resonant and off-resonant excitations in the direct bandgap, the valley polarization dynamics in monolayer MoS 2 was clearly observed. The pump pulse used in this study was generated by a wavelength-tunable optical parametric amplifier. Meanwhile, a probe pulse with a visible broadband spectrum was produced by self-phase modulation in a sapphire plate (see Supplementary Information, S4). As shown in Figure 3, the absorption spectrum of a monolayer MoS 2 clearly presents A (,1.89 eV) and B (,2.04 eV) excitonic transitions, which indicates the splitting of the valence band at the K valley due to spin-orbit coupling 14,15 . In order to distinguish the non-equivalent K and K9 valleys, polarizations of pump and probe pulses were adjusted to be circularly polarized by quarter wave plates. Figure 4 shows a 2D display of photon energy-and time-resolved transient difference absorbance DA(v, t) at 78 K. In the measurements, the polarizations of broadband probe pulses were adjusted to be s 1 and s 2 while the pump pulses were set as s 1 circular polarization and 1.89 eV to resonate with exciton A. For both s 1 and s 2 probes, the time-resolved spectra exhibited negative DA in the spectral band of exciton A and exciton B. The negative DA signal could be caused by stimulated emission from the excited state and/or photobleaching due to the depletion of the ground state and the population of the excited state. The lifetime of photobleaching is usually much longer than that of stimulated emission because a stimulated emis-  sion occurs only within the lifetime of the excited state, whereas photobleaching occurs until the ground state is fully repopulated. Obviously, DA is significantly probe polarization-dependent within 100 fs as shown in Figure 4(c) and Figure 4(d). The nonlinear optical response after 100 fs is independent of the angular momentum of the initially excited distribution, which indicates that the initial polarization distribution relaxes to some quasi-equilibrium states in 100 fs. Following the fast spin-polarization relaxation, the peaks in the DA spectrum show a blue-shift before 10 ps and a red-shift after 10 ps as shown in Figure 4(a) and Figure 4(b). We note that the pump induced response at the K9 valley is observed even when exciton A at the K valley is excited by the s 1 pump, in contrast to the cases of excitons coupled to pump and probe pulses, which do not share common states. This unexpected phenomenon could be explained through various possible mechanisms, e.g., the dark excitons generated by pump pulses 13 , the weakening of the excitonic binding energy 16 or the dielectric screening from the excited excitons 16 .
The measured time-resolved traces of DA(v, t) were fitted using the sum of three exponential functions and a constant term, as in equation (1).
The fitting results are shown in Figure 5. For the s 1 probe, the time constants, t spin , t exciton and t carrier are 55 6 7 fs, 1.0 6 0.2 ps and 26.3 6 5.4 ps, respectively. For the s 2 probe, they are 60 6 40 fs, 0.96 6 0.49 ps, and 25.7 6 8.6 ps, respectively. Due to the small signal amplitudes at the photon energies of ,1.93 eV and ,2.08 eV, the fitting error is large. Comparing the spectra of the s 1 and s 2 probes in Figure 5(a), DA exciton , DA carrier and DA e-h exhibit similar dependence on the probe photon energy with the exception of DA spin . Thus, these three relaxation processes take place independently of the initial polarization distribution within 100 fs. However, DA spin is completely different from the cases of s 1 and s 2 probes in that it is dependent on the relative polarization between the probe and pump beams. In the case of the s 1 pump and s 1 probe, DA spin is negative and possesses larger amplitude than in the case of the s 1 pump and s 2 probe. This implies that the polarized exciton A at the K valley excited by the s 1 pump pulses leads to intense photobleaching and stimulated emission only when the probe pulses have the common circular polarization to the pump pulses and the probe photon energy overlaps the band of exciton A. Moreover, the spectral shape of DA fits well with excitonic transition A, which indicates that the valley polarization is efficiently excited at the high-symmetry K point 17 . On the other hand, the s 2 probe pulses generate exciton A with opposite spin polarization at the K9 valley. Excitons with opposite polarization leads to the generation of biexcitons, which is the origin of induced absorption (DA . 0) at ,1.87 eV 13,18 , as shown in the right panel of Figure 5(a). The mean transition energy of excitonic band A is further calculated at every time delay (see Supplementary Information, S2), i.e., the time-dependent energy gap between excited electrons and holes, is plotted in the inset of Figure 5(a). Since the photobleaching (caused by the same polarizations s 1 for the pump and probe) and biexciton formation (caused by opposite polarizations s 1 for pump and s 2 for probe), the results of the s 1 and s 2 probes before 100 fs show distinct energy differences in transition A. After randomization of the polarized excitons generated by a pump pulse, the energy difference disappears. Blue shift and red shift take place when the polarizations of the pump and probe are the same and opposite, respectively. Similar energy difference (,13 meV at t , 0 ps in this study) is also observed on the CdSe nanocrystals with the splitting of bright-dark exciton states 19,20 . It is found that the flipping transition time scales with the energy split of bright-dark exciton states. Once the energy split increases to ,14 meV for the small size of nanocrystals, the flipping transition time is in the range of tens of femtoseconds. This implies that the energy difference between the K and K9 valleys caused by the inhomogeneity of initially excited population in the K and K9 valleys leads to the fast spin randomization time. Moreover, the exciton size (diameter , 1.86 nm 21 ) and spin randomization time (,60 fs) of monolayer MoS 2 also satisfy the size dependence of spin flip rate in semiconductor nanocrystals 19,20 . The behaviors can be rephrased as follows. The time constant t spin , 60 fs reflects the lifetime of spin polarized exciton A. It has relevant decay time but different behaviors between the co-circular polarizations and anticircular polarizations of the pump and probe beams. Since the hole spin states are non-degenerated at the K and K9 valleys, the relaxation of hole spin is blocked by spin-valley coupling. On the contrary, spin states of electrons can be easily destroyed because the spin states of the conduction band are degenerate. Thus, the relaxation of the electron spin of excitons causes the transition from optically active excitons to dark excitons.
The difference absorbance, DA exciton , probed by s 1 and s 2 circular polarizations have the same photobleaching phenomena, i.e., the blue shift of exciton A in the time range of ,10 ps. This implies that the excess population of excitons is created in both the K and K9 valleys through intervalley scattering, which further reveals the relaxation of hole spin polarization. Renormalization of the selfenergy of the exciton is induced by mutual exciton-exciton interaction leading to photobleaching together with a blue shift of the exciton band within the exciton lifetime 22 . Therefore, DA exciton with a time constant of t exciton , 1 ps represents the exciton intervalley transition and dissociation rate.
After the excitons are dissociated to become free carriers in highly excited states, the exciton peak exhibits a red shift. This shift is attributed to the intravalley scattering of free carriers, in which electrons relax to the bottom of the conduction band and holes relax to the top of the valence band. The DA carrier spectra show the sum of bleaching at transition energy peaks and the induced absorption of broad conduction band. Thus, the intermediate relaxation time t carrier , 25 ps was assigned to the intraband transition of free carriers. The decay time of DA e-h is found to be too long to be determined in the present work. The constant term DA e-h , exhibits only bleaching behavior which can be attributed to the electron-hole recombination in the direct band. The recombination time was estimated to be ,300 ps in a previous study 23 . Time-resolved measurements were also performed with the s 1 pump and s 1 probe at room temperature (293 K). The fitting results of the measured pump-probe data are shown in Figure 6. The amplitude of DA becomes lower and the peak positions shift to lower energy at 293 K compared with the result at 78 K. The red shift of DA implies the band gap is reduced with increasing temperatures 24 . The amplitude ratio of DA spin to DA exciton at different temperatures are more or less similar, i.e., 2.22 6 0.27 for 78 K and 1.81 6 0.49 for 293 K. This indicates that the spin-valley coupled polarizations are almost the same at various temperatures 12 .
The same experiment was also performed by changing the excitation energy from 1.89 eV to 2.01 eV to be resonant to the band of exciton B instead of exciton A (see Figure 3). Figure 5(c) shows the spectra of three relaxation components obtained from the fitting using equation (1). DA spin has finite size not only in the energy range of exciton B but also the energy range slightly higher than that of exciton A. This is because the excitation at 2.01 eV with a s 1 circular polarization simultaneously populates both exciton B at the K9 valley, resulting from the resonance excitation caused by the s 1 pump, and the higher energy side of exciton A at the K valley. Therefore, the calculated difference absorbance DA spin covers the band of transition B and the region of the high energy side of transition A. Additionally, DA exciton is comparable with DA spin in the energy range of exciton B and even larger than DA spin in the energy range of exciton A. Consequently, the signal of spin-valley coupled polarization can be sizable in the energy range of exciton B, which is the resonance excitation energy of the pump, as in the case shown in Figure 4(a), but its polarization anisotropy becomes much smaller. On the other hand, the spin-valley coupled polarization in the energy region of exciton A, which is off-resonant, is strongly diminished. This kind of reduction in spin-valley coupled polarization anisotropy, as observed in the PL experiments 11,12 , could be attributed to efficient intervalley scattering.
In conclusion, the present study completely elucidates the fairly comprehensive ultrafast dynamics of spin-polarized excitons in monolayer MoS 2 . Owing to the high temporal resolution and visible broadband detection, the time constants for the 60-fs spin-polarized exciton decay, 1-ps exciton dissociation (intervalley scattering), and 25-ps hot carrier relaxation (intravalley scattering) have been clearly identified. Temperature-dependent measurements further disclose the transition energy shifting and conservation of spin-valley coupled polarizations at various temperatures. Moreover, substantial intervalley scattering strongly diminished the spin-valley coupled polarizations under off-resonant excitation condition. These results provide