External field regulation strategies for exciton dynamics in 2D TMDs

Wenwei Chen; Canghai Zheng; Jiajie Pei; Jiajie Pei; Hongbing Zhan; Hongbing Zhan; Hongbing Zhan

doi:10.1364/OME.483284

1. Introduction

The abundant excitonic species [1,2] due to enhanced Coulomb interaction [3,4] and valley spin locking effect due to reversal symmetry breaking [5] make 2D transition metal chalcogenides (TMDs) appealing in the application of innovative logic [5,6] and optoelectronic devices [7–9]. However, various many-body interactions affect the exciton dynamics during the exciton formation and relaxation, which limits the functionality of TMDs-based devices. For example, the exciton-exciton annihilation (EEA) leads to the decrease of photoluminescence quantum yield (PLQY) [10–12], the defect-trap shortens the exciton lifetime [13,14], and the intervalley scattering reduces the valley polarization [15–17]. Thanks to the stable physical and chemical properties of 2D TMDs, the external fields provide avenues to regulate the exciton dynamics and optimize device performance.

Notably, calculations show that tungsten-based TMDs and molybdenum-based TMDs have opposite spin-orbit splitting [18,19], which is further demonstrated experimentally to lead to different multi-particle exciton complexes [20,21] and dark excitonic states [22–24]. This implies that the response of exciton dynamics to external field regulation for different TMDs may exist discrepancy. In addition, from the perspective of device design, different TMDs-based devices have varied requirements for the regulation of exciton dynamics. For example, ultrafast optical switches require short exciton lifetimes [25], while high QY light-emitting devices require long exciton lifetimes [26]. Hence, understanding the specific effects and mechanisms of different external field regulation strategies on exciton dynamics is of great guiding significance for the design of high-performance TMDs-based devices. Although there have been several reviews of exciton regulation [27,28], they are mainly based on steady-state spectroscopy. Reviews focusing on recent advances in the external field regulation of exciton dynamics in different 2D TMDs are rare. In this review, based on the transient absorption spectrum (TA) and time-resolved photoluminescence (TRPL) spectrum, one can provide an accurate and comprehensive description of the ultrafast non-equilibrium process due to the high time resolution.

In this review, we first give a brief introduction to the crystal structure and energy band structures of 2D TMDs. Then, we discuss the underlying many-body interaction processes that are closely related to the regulation of exciton dynamics. Following this, we focus on summarizing different regulation strategies for the exciton dynamics in 2D TMDs. These strategies include defects engineering [13,29,30], strain engineering [12,31–33], electric field [34], magnetic field [35,23,36], optical field [10,37,38], thermal field [17,39]. We discuss the influence of these regulation strategies on different many-body interactions in exciton dynamics at ultrafast time scales, starting with photoexcitation, from intravalley electrons spin flip [40] on the femtosecond scale to radiative recombination of free excitons [41] on the picosecond scale. In addition, we also comprehensively discuss the fundamental mechanism of each regulation strategy for different many-body interactions. This is extremely important for understanding how to manipulate exciton dynamics to achieve target optical properties. Finally, we present the challenges and future research directions of external field-regulated exciton dynamics in 2D TMDs.

2. Introduction of TMDs

2.1 Crystal structure of TMDs

The family of TMDs with the formula MX₂ (where M is a transition metal atom of group IV-VIII and X is the chalcogen atom concluding S, Se, or Te) shares a similar layered crystal structure. According to electronic band structures determined by composition and phase, 2D TMDs are classified into four types: metallic TMDs, semimetallic TMDs, semiconducting TMDs, and insulating TMDs [42,43]. Among them, the 2 H phase MX₂ (M = W, Mo; X = S, Se, Te) has novel semiconducting properties and has been widely used to study exciton dynamics, which is the focus of this review [44]. As shown in Fig. 1(a), the monolayer 2 H MX₂ has a prismatic cell as a minimum repetition unit, in which the metal atom sits in the center of the triangular prismatic coordination and is bound to six chalcogen atoms located at the vertex of the triangular prismatic coordination through strong covalent bonds. For the comprehensive material characterization details please refer to reviews [45–48]. Monolayer 2 H MX₂ presents an A-B-A structure: a single layer of Molybdenum atoms sandwiched between two layers of Sulphur atoms. Therefore, the monolayer 2 H MX₂ exhibits hexagonal symmetry and lacks anisotropy. In some other types of TMDs [49] (MTe₂ and ReX₂) and emerging 2D materials [50] (β-InSe), excellent anisotropic optical properties were found due to their anisotropic lattice structures. Under the weak Van der Waal force, these monolayers will stack to form stable few layers of MX₂. In even layers structure, the inversion symmetry of monolayer MX₂ is inevitably broken because Sulphur atoms will be mapped to a vacancy when a metal atom is the inversion center, The inversion symmetry restore in bilayer MX₂ will lead to changes in optical properties, such as the disappearance of the second harmonic [5].

Fig. 1. (a) Schematic representation of the atomic structure of MX₂. Figure adapted and reprinted with permission from [18]. (b) Band structures of MoS₂, MoSe₂, MoTe₂, WS₂ and WSe₂ from 1 L to 2 L without SOC. Figure adapted and reprinted with permission from [57]. (c) Band structures of 1 L MoS₂, MoSe₂, WS₂ and WSe₂ with SOC. Figure adapted and reprinted with permission from [18]. (d) Valley spin splitting due to spin-orbit interaction in monolayer MoS₂, and in bilayer MoS₂, valley spin degeneracy due to the recovery of inversion symmetry breaking. Figure adapted and reprinted with permission from [5].

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2.2 Energy band structure of TMDs

Compared to zero-gap graphene [42,51] and relatively narrow gap black phosphorus [52], few-layer Mxene [53], and other emerging 2D materials [54], 2D TMDs exhibit relatively wide bandgaps ranging from 0.9-2.4 eV, which extends the application range of 2D photodetectors [42,50,55]. Moreover, 2D TMDs exhibit unique thickness-dependent energy band structures [18,56–58]. Taking MoS₂ as an example, the band gap of MoS₂ increases from 1.2 eV to 1.9 eV as the layer number decreases, and changes from an indirect band gap to a direct band gap when reduced to a monolayer, leading to a significant enhancement of PL [59]. As shown in Fig. 1(b), the band structure of each bulk TMDs displays the valence band maximum (VBM) at the K point and the conduction band minimum (CBM) at the midpoint along Γ-K. As the number of layers decreases, the weakened interlayer coupling will cause both the VBM and CBM to move to the K point, eventually resulting in a transition from indirect to direct bandgap [57]. Thus, the thickness-tunable bandgap in the visible and near-infrared regions and the direct excitonic transition emission under monolayers make 2D TMDs powerful candidates for high-quantum yield optoelectronic devices. Monolayer TMDs are generally used for fluorescent devices, while fewer layers could be used in sensitive photodetectors [60].

It should be pointed out that early theoretical calculations on TMDs’ band structure did not include the spin-orbit coupling (SOC) effect (Fig. 1(b)), while the recent calculations demonstrate that strong SOC will induce considerable band splitting in 2D TMDs (Fig. 1(c)). Due to the different effective atomic masses of metal atoms in MX₂, the band splitting of different TMDs exist discrepancy [18,61]. As shown in Fig. 1(c), the main difference between Mo-based TMDs and W-based TMDs in the spin splitting of the valence band lies at the K point in the Brillouin Zone (BZ). DFT calculations show the splitting of the valence band at K point is of the order of ∼150 meV for Mo-based TMDs, which increases to ∼400 meV for W-based TMDs because the heavier W compounds lead to stronger SOC. SOC also induces a spin splitting of the conduction band at the K point and the secondary minimum Q point which lies between the Γ and K point of the BZ. Compared with the valence band, the spin splitting of the conduction band at K point is relatively small: ∼ 3 meV for MoS₂, ∼ 21 meV for MoSe₂ and ∼ 27 meV for WS₂, and ∼ 38 meV for WSe₂. However, it should be noted that the spin splitting sign in conduction band at K point of Mo-based TMDs and W-based TMDs are opposite: in Mo-based TMDs, the VBM and CBM have the same spin, while that of W-based TMDs is the opposite. As for the Q point in the BZ of different TMDs, the main difference between W-based TMDs and Mo-based TMDs lies in the splitting energy of Q valleys and the energy difference between Q-K valleys. The spin splitting at the bottom of Q valley is 83 meV (MoS₂) and 0 meV (MoSe₂) for Mo-based TMDs, and 340 meV (WS₂) and 275 meV (WSe₂) for W-based TMDs. On the other hand, the CBM of Q valley is much higher than that of K valley in Mo-based TMDs, while the CBM of Q valley and K valley are close in W-based TMDs. This leads to the favorable formation of Q-K indirect dark excitons in Mo-based TMDs [19,24]. The layer index provides an additional degree of freedom to tune the spin degeneracy of TMDs by changing the inversion symmetry of the layers. Due to the broken inversion symmetry of monolayer TMDs, the spin splitting in inequivalent valleys must be opposite by time reversal symmetry (Fig. 1(d)), leading to valley-spin coupling [62], which can achieve valley polarization by circularly polarized light. As a comparison, the band structure remains spin degenerate because of inversion symmetry for bilayers [5,63]. Different excitonic state species may form and relax in different ways as a result of band degeneracy.

3. Fundamental processes of exciton dynamics in 2D TMDs

The abundant exciton species in 2D TMDs is the basis of constructing TMDs-based optoelectronic devices. Therefore, developing a comprehensive understanding of exciton dynamics in 2D TMDs is the prerequisite for regulating the quantum efficiency and performance of TMDs-based optoelectronic devices. There have been many reviews summarizing the internal processes of exciton dynamics from the perspective of time scale [64–66]. Here, we will provide a brief overview of the many-body interactions in exciton dynamics based on their respective principal mechanisms. The relaxation dynamics of excitons can be divided into radiative recombination and nonradiative recombination. The radiative recombination of free excitons is that the excited electrons form excitons with holes under Coulomb interaction and finally return to the ground state by emitting photons. This process determines the quantum efficiency of TMDs-based optoelectronic devices. In contrast, nonradiative recombination can reduce quantum efficiency through a variety of many-body interactions, such as species conversion, EEA, scattering, and defects trapping. There are numerous many-body interactions, each with a unique physical process. Hence, a deep understanding of the underlying mechanisms of different many-body interactions is a prerequisite for regulating exciton dynamics through various external field strategies.

Excitonic species conversion: The photoexcited carriers in 2D TMDs first form neutral exciton within hundreds of femtoseconds. Then, the neutral exciton can form a trion by trapping an extra electron or hole, or combine another exciton to form a biexciton [67,70] (Fig. 2(a)). This conversion of the neutral exciton to other exciton species can be regarded as the nonradiative relaxation of neutral excitons, resulting in a significant decrease in the emission intensity of neutral exciton [34,70]. This means that the conversion of neutral exciton to other exciton species needs to be inhibited for TMDs devices based on neutral exciton emission. In addition, not all species can be converted from neutral exciton under the same conditions. For example, the formation of trion depends on the nonequilibrium resident electrons or holes in the system [34], while the formation of biexciton depends on the population of electron-hole pairs. On the other hand, neutral exciton can be converted into different kinds of spin- or momentum-forbidden dark exciton [24,71], such as K-K dark exciton, K-Q indirect dark exciton, and K-K` indirect dark exciton (Fig. 2(b)), which will reduce the PL emission intensity of bright exciton. For example, Madéo et al. directly observed the K-K direct bright exciton converting to the K-Q indirect dark exciton on a ∼400 fs time scale [24]. This process depends on the strength of intervalley scattering, which will be discussed in detail in later sections.

Fig. 2. (a) The electron and hole configurations of exciton, trion and biexciton respectively. Figure adapted and reprinted with permission from [67]. (b) The schematic of the bright A exciton, intravalley dark K-K exciton, intervalley dark K-K′, and K-Λ exciton. Figure adapted and reprinted with permission from [68] (c) The schematic of K-K, K-Λ, K-K′ intervalley exciton scattering. Figure adapted and reprinted with permission from [17]. (d) Exciton scattering channels in 1 L and 2 L WS₂, the bright exciton at K-K can recombine radiatively as shown by the solid purple line or scatter nonradiatively via phonon emission toward dark exciton states (Q ≠ 0) as indicated by the dashed lines. Figure adapted and reprinted with permission from [69].

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Intra-/Inter-valley Scattering: The mechanism of phonon-assisted scattering in 2D TMDs is that photoexcited carriers transfer energy to lattice vibrations by interacting with optical phonons on ultrafast time scales from femtoseconds to picoseconds, leading to changes in energy or momentum of photoexcited species. For exciton dynamics in 2D TMDs, the activated phonon can assist carries or excitons scattering, including the intravalley electrons spin-flip and intervalley scattering [17,69] (Fig. 2(c)). This process will obviously affect the performance of TMDs-based devices, for example, valley depolarization caused by phonon-assisted scattering will limit the performance of valleytronics devices [15,72]. The scattering of electrons can be affected by many factors. Previous work has reported temperature-dependent phonon-assisted scattering, which is significantly suppressed at low temperatures [15,72]. Recent work points out that the strength of phonon-assisted scattering also depends on the band structure of 2D TMDs. As shown in Fig. 2(d), Raja et al. found that the overall exciton scattering efficiency in bilayer WS₂ was significantly enhanced compared with that in monolayer WS₂ [69]. This is because in bilayer WS₂, the Γ valley shift to much lower energies and the Λ′ valley becomes the lowest conduction band point compared to the monolayer. Hence, in addition to the more obvious Γ−K scattering channel, where the K−Λ′ scattering also becomes energetically favorable. The explanation above suggests that monolayer W-based TMDs will exhibit more effective K-Q intervalley scattering than Mo-based TMDs. Because the K and Q valleys in monolayer W-based TMD have similar energies, whereas the Q valleys in Mo-based TMDs have higher energy than the K valleys.

Auger recombination and EEA: Radiative recombination is the dominating relaxation channel for exciton at low carrier concentration. On the other hand, nonradiative recombination provided by Auger recombination and EEA is recognized to be the main relaxation channel for exciton at high carrier concentrations. In the Auger recombination, when an electron recombines with a hole, it transfers the excess energy to a second electron instead of emitting light, and the second electron then relaxes to its original energy level by emitting a phonon. As for EEA, this annihilation channel is an excitonic analog of the Auger recombination in 2D TMDs with tightly bound excitons. The mechanism of EEA is that at high excitation densities, two excitons collide, and then energy is transferred from one to the other, and the exciton that receives energy can be excited to a higher energy state [73–76] (Fig. 3(a)). Taking monolayer MoS₂ as an example, the EEA rate can reach $({4.3 \pm 1.1} )\times {10^{ - 2}}\; c{m^2}/s$ under high power excitation at room temperature, which is higher than that in conventional layered materials [11]. This significantly limits the luminescence efficiency of TMDs-based optoelectronic devices. However, Yuan et al. found that the EEA rates of indirect excitons in 2 L and 3 L WS₂ are two orders of magnitude smaller than those of direct excitons in monolayer WS₂, which is attributed to the additional requirement for phonon assistance for the EEA of indirect excitons in 2 L and 3 L WS₂ [77] (Fig. 3(a)). This implies that little differences in the microscopic processes of distinct excitons will result in varied EEA responses.

Fig. 3. (a) The schematic of direct exciton–exciton annihilation in 1 L WS₂ and indirect exciton–exciton annihilation in 2 L WS₂. Figure adapted and reprinted with permission from [77]. (b) The schematic of defect trap free exciton. Figure adapted and reprinted with permission from [78].

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Defects trapping: Defect-carrier interactions in 2D TMDs play an important role in the exciton relaxation dynamics, which determine the performance of electronic devices. Defects such as sulfur vacancies have been shown to be effective traps for photoexcited species, including carriers, excitons, and trions. As schematically shown in Fig. 3(b), defects in 2D TMDs can trap free excitons to form defect-bound excitons as nonradiative recombination channels for excitons [13,14]. In addition, although different types of defects all accelerate exciton nonradiative recombination, there are subtle differences in their mechanisms. Li et al. found that sulfur adatoms accelerated the nonradiative recombination of excitons by a factor of 7.9, compared with 1.7 times for vacancies, since the hole and electron traps generated by vacancies are much less localized than those generated by the adatom [79]. On the other hand, Liu et al. found that vacancy defects and compensatory doping defects in TMDs lead to 1 and 2 orders of magnitude decrease in carrier lifetime, respectively, compared to pristine WS₂, which was attributed to the difference in the phonon modes involved in electron−phonon coupling caused by defect types [29].

4. Regulation strategy of dynamics

4.1 Defects engineering

Due to the high surface-to-volume ratio for atomically thin TMDs, inevitable defects can obviously affect intrinsic carries dynamics, which will significantly affect the performance of TMDs-based optoelectronic devices. Therefore, understanding the role of defects in the above-mentioned processes is crucial for tuning TMD-based optoelectronic devices. In few-layer TMDs, sulfur vacancies and compensatory doping are generally considered the two most common types of defects [29], and the main manufacturing methods of these defects can be divided into physical and chemical strategies. The physical strategies include plasma treatment [29,78], laser irradiation [82,83], electron-beam irradiation [84], and ion irradiation [85]. The main principle is to bombard the sample with high-energy substances to break the in-plane chemical bonds. The density of defects can be adjusted by treatment time, and the types of defects can be controlled by using specific high-energy substances [29]. Chemical strategies include chemical-assisted annealing [86], passivation of chemical solution [81,87], and photochemical doping [88]. And these above chemical strategies are mainly to suppress the effect of defects. It is worth noting that the sample synthesis method affects the original defect density [30,89], with mechanical exfoliation generally being the lowest and CVD being the highest.

Sulfur vacancies or compensatory doping in 2D TMDs will introduce defect energy levels. As the schematic diagram illustrated in Fig. 4(a), these defect levels can efficiently trap pristine excitons to form bound defect excitons [29]. This process act as a non-radiative recombination channel for excitons of the pristine system, shortening the pristine exciton lifetime [13,14,89] and reducing the PLQY [29]. These strongly bound defect excitons also reduce the valley polarization by hybridizing the pristine excitons [90]. Recently, there have been plentiful works in improving the carrier lifetime and PLQY through physical or chemical strategies [29,80,82,87]. In the process of CVD synthesis of 2D TMDs, Cui et al. introduced oxygen atoms into sulfur vacancies to obtain oxygen-doping monolayer WS₂ [80]. The PLQY of oxygen-doped monolayer WS₂ has been enhanced by two orders of magnitude (Fig. 4(b)), even higher than that of the ME counterpart. They also found that oxygen doping inhibited the formation of trions (Fig. 4(c), d). Moreover, the TRPL spectra of oxygen-doped monolayer WS₂ found the average exciton lifetime (109.3 ps) has five times increase compared to undoped monolayer WS₂ (21.6 ps), meaning oxygen dopants can suppress the nonradiative recombination of excitons caused by defects (Fig. 4(c)). On the other hand, Bretscher et al. used the organic superacid bis(trifluoromethane) sulfonimide (H-TFSI) to passivate defects in monolayer MoS₂, resulting in up to 275-fold increase in neutral exciton PL (Fig. 4(f)) [81], more than twice that of other chemical passivation. This superacid treatment increases PL by improving the high n-doping of monolayer MoS₂ to suppress exciton-trion exchange. Excessive charges in high n-doping 2D TMDs caused by the defect will lead to the rapidly formation of trions, resulting in the decrease of neutral-exciton PLQY [85,91]. However, the effect of chemical treatment by-products on optoelectronic devices requires further investigation. In, addition, Ji et al. found that the functional groups of -OH on SiO can make the monolayer MoS₂ highly-p doped, thus inhibiting trion formation and enhancing PLQY [92].

Fig. 4. (a) Schematic of possible recombination mechanisms in pristine and defective TMDs monolayers. Figure adapted and reprinted with permission from [29]. (b) PL spectra of O-doped and undoped WS₂ monolayer at 293 K. Inset show normalized spectra. Figure adapted and reprinted with permission from [80]. (c) PL spectra of undoped and (d) O-doped WS₂ monolayer at 83 K, respectively. Figure adapted and reprinted with permission from [80]. (e) TRPL spectra collected from O-doped, undoped, and mechanical exfoliated WS₂ monolayer. Figure adapted and reprinted with permission from [80]. (f) Top: PL enhancement of MoS₂ using the different passivating agents. Bottom: PL enhancement of various chemical treatments on WS₂. Figure adapted and reprinted with permission from [81].

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In addition to shortening exciton lifetimes, defects in 2D TMDs also influence the diffusion dynamics of excitons (Fig. 5(a)). Liu et al. introduced sulfur vacancies into few-layer WS₂ by argon plasma [78]. The exciton diffusion coefficient decreased from 2.98 to 0.75 cm²/s with increasing plasma treatment time (Fig. 5(b)), which was caused by a large number of excitons being trapped by defects during the diffusion process. Moreover, there have been studies showing that the EEA rate constant is proportional to the exciton diffusion constant [93,94]. Therefore, the EEA rate can be suppressed by introducing defects to hinder excitons diffusion (Fig. 5(e)). Lee et al. increased the defect density of monolayer TMDs by laser irradiation [82]. In their work, the laser-irradiated region exhibited 3X higher PL intensity and QY compared to the region without treatment (Fig. 5(c)), and TRPL showed that the EEA rate constant reduced from 0.66 $\pm$ 0.15 cm²/s to 0.20$\; \pm \; $0.05 cm²/s (Fig. 5(d)). It is worth noting that the laser-irradiated region displayed lower PL compared to the region without treatment at low excitation levels, which is consistent with the defect-assisted nonradiative recombination mentioned above. This means that increasing exciton lifetime and PLQY by introducing defects to suppress EEA in 2D TMDs is feasible only under high excitation levels. This result can be applied to various applications of 2D TMDs, such as high-power optoelectronic conversion devices. While the opposite view is that these defects can act as new EEA centers for freely diffusing to promote EEA depending on the excitation power [95,96]. This will be discussed in detail in the subsequent excitation power section.

Fig. 5. (a) The 3D spatial distribution of the exciton population of 2D TAM images of pristine and defective few-layer WS₂ at different delay times. Figure adapted and reprinted with permission from [78]. (b) The time evolution of the variances of Gaussian profiles for the different plasma treatment times (0, 10, 30, and 40 s), diffusion coefficients obtained from fitting. Figure adapted and reprinted with permission from [78]. (c) PL spectra of the laser-irradiated region (red) and non-irradiated regions (black). Figure adapted and reprinted with permission from [82]. (d) TRPL curves of the laser-irradiated region (red) and non-irradiated region (navy) obtained with varying excitation levels. Figure adapted and reprinted with permission from [82]. (e) Schematic depicting laser-induced sulfur vacancies that hinder the diffusion of excitons to reduce the EEA rate. Figure adapted and reprinted with permission from [82].

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4.2 Strain engineering

Due to the atomic thickness and mechanical flexibility of 2D TMDs, strain engineering provides an ideal platform for tuning their intrinsic electronic and optical properties. There are many ways to achieve strain engineering for 2D TMDs or related heterojunctions. Depending on the strain transfer medium, we divide strain engineering into in-plane and out-of-plane modes. The in-plane mode applies strain to the sample through the deformation of the substrate or special structure of the substrate: transfer 2D material onto a flexible substrate and then directly stretching, compression, or bending of the substrate [32,97–99], or temperature leading to thermal expansion mismatch between 2D material and its substrate to achieve compressive or tensile strain [100]. In addition, wrinkles [31,97,101,102], bubbles [103], and periodic patterns [104,105] acquire strain by constructing specific substrate structures. In out- of-plane mode, strain is applied directly to the 2D materials through a medium outside the substrate: for example, applying compressive strain to the sample by AFM tip [106].

The regulation of carrier dynamics in 2D TMDs by strain engineering is based on regulating the band structure of 2D TMDs by changing the lattice constant [31,32,98,99,108,109]. Previous work found that strain engineering can shift the band gap to tune the exciton emission energy [98–100]. When the applied strain is large enough, the transition between the direct band gap and the indirect band gap can be realized. As shown in Fig. 6(a), monolayer MoS₂ transforms from a direct to an indirect band gap when the tensile strain reached 1.8% [31]. But for bilayer TMDs, the result is completely reversed. Take the bilayer WSe₂ as an example, a transition from indirect to direct bandgap was observed in bilayer WSe₂ when tensile strains from 0 to 1.51% were applied [32] (Fig. 6(b), c). This is because the strain response of the band gap of few layers TMDs is quite different from that of monolayer [98,104]. Under tensile or compress strain, the energy drops at the Q or Γ point in the Brillouin zone of monolayer TMDs is faster, while in few layers TMDs it is usually the K point [32,98,103,104]. In addition, it is worth noting that the band gap shift caused by strain in different TMDs is not uniform [100,101], and the shifts follow the order MoSe₂ < MoS₂ < WSe₂ < WS₂ [100].

Fig. 6. (a) PL spectra of monolayer MoS₂ as it is strained from 0 to 1.8%. Figure adapted and reprinted with permission from [31]. (b) Bilayer WSe₂ PL spectra at different strains. Figure adapted and reprinted with permission from [32]. (c) Schematic band structure, qualitatively showing occupancy of K_C and Σ_C CB minima at strain and zero-strain conditions and under illumination. Figure adapted and reprinted with permission from [32]. (d) Calculated JDOS for monolayer WS₂. Dashed lines denote values of 2E_X at the corresponding strain. Figure adapted and reprinted with permission from [12]. (e) PLQY approaching unity with the application of strain at a high G of 6.5 × 10¹⁹cm⁻²s⁻¹. Figure adapted and reprinted with permission from [12]. (f) Strain-induced formation of KΛ excitons of monolayer WS₂. Figure adapted and reprinted with permission from [107]. (g) Emission spectrum of monolayer WS₂ at T = 77 K in the unstrained and compressive strain. Figure adapted and reprinted with permission from [107].

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Recent studies have also found strain engineering can regulate other fundamental processes of exciton dynamics in 2D TMDs. Taking EEA as an example, the efficiency of EEA in 2D TMDs depends not only on the exciton density but also on the density of states (DOS) of high energy state $E = {E_C} - {E_V} = 2{E_X}$ (${E_X} $ is exciton transition energy) [12]. The monolayer TMDs exhibited enhanced EEA because the 2${E_X}$ coincided with inherent van-Hove singularity (VHS, high DOS on the band structure). Therefore, Kim et al. drove the 2${E_X}$ away from the VHS resonance to reduce EEA by strain engineering [12] (Fig. 6(d)), and achieved near-unity PLQY at all exciton densities (Fig. 6(e)). And for the scattering process, Chand et al. found that the minimum conduction band of K valley and Λ valley in monolayer WS₂ both shift at different rates under compression strain (Fig. 6(f)), which eventually enables phonon scattering of photoexcited electrons between momentum valleys, enhancing the formation of dark intervalley excitons [107] (Fig. 6(g)). Moreover, Liu et al. found that spin-orbit interaction can be manipulated by mechanical strain, and the spin-orbit splitting is obtained as 37.5 ${\pm} $ 1.4 meV by applying an inhomogeneous strain field to bilayer MoS₂, which is an order of magnitude larger than the theoretical prediction for monolayer MoS₂ [111]. This means that strain is expected to control the valley spin degrees of freedom of TMDs-based optoelectronic devices.

Notably, the non-uniform strain can locally change the valence and conduction bands of 2D TMDs, thus regulating carrier drift and exciton diffusion. As shown in Fig. 7(a), the point of maximum strain underneath the AFM tip will attract free carriers and be termed funneling. Hartas et al. found that the redistribution of free carriers under non-uniform strain leads to highly efficient conversion of excitons to trions, which can even reach 100% under 2.8% local strain without electrical gating [106] (Fig. 7(b)). On the other hand, non-uniform strain engineering has been reported to regulate dark exciton [107,112,113]. Gelly et al. used a nanosculpted tapered optical fiber to generate non-uniform strain and probe the near-field optical response of monolayer WSe₂ [110]. As shown in Fig. 7(c) and (d), the lowest energy states of strained monolayer WSe₂ shifted by as much as 390 meV. These red-shifting peaks originate from dark excitons because only dark excitons have a lifetime long enough to diffuse to high-strain regions, where the energetic minimum is (Fig. 7(e)).

Fig. 7. (a) The schematic profile of strain ε (top red curve) and band structure of monolayer WS₂ versus distance from the membrane center under non-uniform strain. Figure adapted and reprinted with permission from [106]. (b) Strain-dependent PL spectra for monolayer WS₂. Figure adapted and reprinted with permission from [106]. (c) The fiber-collected PL has a feature X₀ that matches in energy with X_A:1s at V_P = 0. At V_P = 10 V, peaks as low as 1.38 eV appear. Figure adapted and reprinted with permission from [110]. (d) PL spectra as a function of piezo-positioner voltage. Figure adapted and reprinted with permission from [110]. (e) Schematic of the strain-induced energy potential due to the fiber facet. Figure adapted and reprinted with permission from [110].

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4.3 Electric field

As schematically shown in Fig. 8(a), neutral excitons (${X^0}$) can bind excess electrons (e) or holes (h) in 2D TMDs to form positive or negative trions (${X^ + },\; \; {X^ - }$). Based on the electron or hole doping in 2D TMDs induced by an electric field, electrical control of various exciton-trion conversions in 2D TMDs has been demonstrated [34,114]. In Fig. 8(b), as ${V_g}$ increases from 0 to 40 V, more electrons are injected into monolayer WS₂, resulting in the complete conversion of neutral excitons to negative trions [1]. When ${V_g}$ is set to negative, the increase of hole injection can balance the excessive electrons in the system, due to the n-doping caused by defects in monolayer WS₂, and finally achieve the complete emission of neutral excitons. Further studies have also revealed electrically tunable excitonic fine structures in 2D TMDs, such as biexcitons [1,115] and dark trions [71] (Fig. 8(c)). These experimental results all reveal the feasibility of electrically controlled excitonic species in 2D semiconductor devices.

Fig. 8. (a) Illustration of the gate-dependent trion and exciton transitions $- 4.0,\; \; - 1.28,\; \; 0.24,\; \; 4.0\; V$. Figure adapted and reprinted with permission from [34]. (b) Photoluminescence spectra of 1 L WS₂ at the back-gate voltages between -40 and +40 V. Figure adapted and reprinted with permission from [1]. (c) PL spectra of 1 L WSe₂ at the gate voltages of , respectively. Figure adapted and reprinted with permission from [71]. (d) photoluminescence of the MoSe₂ monolayer as a function of the gate voltage. Figure adapted and reprinted with permission from [71]. (e) Exciton and (f) trion photoluminescence dynamics for three gate voltages at T = 7 K. Figure adapted and reprinted with permission from [71]. (g) TRPL spectra of the positive dark trion as a function of the gate voltage. Figure adapted and reprinted with permission from [71].

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However, quite different experimental results were observed in the study of electric field controlling the exciton recombination lifetime. Robert et al. distinguished the intrinsic radiative recombination time of neutral exciton and trion to be 1.8 p and 15 ps, respectively in monolayer MoSe₂ at 7 K. After determining that the electrical field tunable neutral exciton and trion PL emission (Fig. 8(d)), no significant change in the exciton and trion relaxation dynamics was observed as the applied voltage varies from -8 to 8 V [116] (Fig. 8(e), f). A similar result was observed in monolayer WS₂, the exciton and trion relaxation dynamics have no obvious change with the back-gate voltage varying from $- $50 V to $+ $50 V [114]. All the above studies only discuss the radiative recombination part of the exciton relaxation dynamics. In terms of the non-radiative part, Li et al. found that the lifetime of positive dark trion decreases from 215 ps to 50 ps as the gate voltage increases from $- $0.5 V to $+ $4 V, which was attributed to the increased hole doping that facilitated the non-radiative channels [71] (Fig. 8(g)).

In addition, the effect of the electric field on the valley polarization lifetime of 2D TMDs also has different results. As shown in Fig. 9(a), Rivera et al. investigated the valley polarization dynamics of interlayer exciton in MoSe₂/WSe₂ heterostructure and found that the valley polarization lifetime of intervalley exciton is 10 ns at 0 V. After applying a gate voltage of 60 V, the valley polarization lifetime increases to as long as 39 ns [117] (Fig. 9(b)), which is attributed to the suppression of intervalley exciton scattering [119]. The opposite view is that n-doping or p-doping leads to the increase of resident electrons (holes) in the system, reducing the scattering carriers required for interlayer exciton depolarization, and finally resulting in the decrease of valley polarization lifetime [118] (Fig. 9(c), d). Furthermore, Li et al. found the ferroelectric gating can promote electron-phonon interaction, introduce a strong surface polarization field, and controls the interfacial charge trapping/detrapping, enhancing room-temperature valley polarization [120]. Therefore, further experimental and theoretical studies are needed to fully understand the microscopic mechanism of electric field regulation of exciton dynamics.

Fig. 9. (a) Schematic of the interlayer exciton in the + K valley. Figure adapted and reprinted with permission from [117]. (b) Time-resolved interlayer exciton PL at selected gate voltages. The blue curve (right axis) shows the decay of valley polarization. Solid lines are single exponential fits to valley polarization decay. Figure adapted and reprinted with permission from [117]. (c) Depolarization mechanisms in natural and twisted WSe₂/WSe₂ bilayers. Figure adapted and reprinted with permission from [118]. (d) Exciton and valley dynamics in twisted WSe₂ at V_G = −8 V, 0 and 8 V. The extracted exciton and valley lifetimes are τ₁ = 0.1 ns and τ_v = 30 ps at V_G = −8 V and τ₁ = 40 ps and τ_v = 2.2 ns at V_G = 8 V. Figure adapted and reprinted with permission from [118].

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4.4 Magnetic field

The highly symmetric but not equivalent + K and -K valleys in monolayer TMDs can be selectively excited by circularly polarized light, known as valley polarization [5,6,121], which can achieve the manipulation of the valley pseudospin degree of freedom [6,62,122]. This makes TMDs a promising material for applications in quantum information devices. However, experiments [123,124] and theoretical calculations [125,126] have shown that it is difficlut to achieve high valley polarization and long valley lifetime due to the strong electron-hole exchange in monolayer TMDs. Therefore, it is necessary to improve the valley polarization and prolong the valley polarization lifetime by means of external regulation.

Recently, a series of works have demonstrated the possibility of controlling valley pseudospin via the valley Zeeman effect in an external magnetic field in monolayer [35,127,128], bilayer [129], and TMDs heterostructure [130,131]. The effect of the Valley Zeeman on the band structure is shown in Fig. 10(a), the external magnetic field will cause different Zeeman shifts in valence and conduction bands in the + K and -K valleys [62], while the circular polarization selectivity of the valleys is not affected because optical transition still conserves spin. As a result, an external magnetic field can break the valley degeneracy, enabling control of the valley polarization. Aivazian et al. investigated the valley Zeeman splitting and magnetic tuning of polarization and excitonic valley pseudospin in monolayer WSe₂ by polarization-resolved magneto-PL. As illustrated in Fig. 10(b), (c), the monolayer WSe₂ was excited by ${\mathrm{\sigma }^ - }$ (${\mathrm{\sigma }^ + }$) light and detected by ${\mathrm{\sigma }^ + }$ (${\mathrm{\sigma }^ - }$) light. The polarizations of ${\mathrm{\sigma }^ - }$ and ${\mathrm{\sigma }^ + }$ reach their maximum values at +7 T and -7 T, respectively (Fig. 10(d)) because the magnitude of the valley polarization depends on the relationship between the helicity and the direction of the magnetic field. And the polarization of ${\mathrm{\sigma }^ - }$ and ${\mathrm{\sigma }^ + }$ increases (decreases) as the magnetic field changes from -7 T to 7 T, which is due to the asymmetric intervalley scattering induced by the asymmetric response of -K and + K valleys to the magnetic field [35]. In addition, it also has been proved that a magnetic field can tune the polarization of trions. The magnetic field-dependent valley polarization response of the trion is quite different from that of the neutral exciton [35,132], which has been discussed in detail in related studies [132–134].

Fig. 10. (a) Valley Zeeman splitting in 1 L WSe₂. Energy level diagram of 1 L WSe₂ showing the three contributions to the valley Zeeman shifts (black for spin, green for valley, purple for atomic orbital). Figure adapted and reprinted with permission from [35]. (b) Polarization-resolved photoluminescence of 1 L WSe₂ for σ⁺ and (c) σ⁻ excitation, detected by σ⁺ (blue) and σ⁻ (light blue) polarization at magnetic fields of −7 T. Figure adapted and reprinted with permission from [35]. (d) Degree of photoluminescence polarization for exciton peak. Blue (red) represents σ⁺ (σ⁻) excitation. Figure adapted and reprinted with permission from [35] (e) The optical selection rules between the conduction and valence bands in the K⁻ and K⁺ valleys of MoX₂ (X = S, Se, Te) monolayers for circularly polarized σ⁺ (blue) and σ⁻ (orange) light in the absence of a magnetic field (B = 0) and with a magnetic field (B > 0). Figure adapted and reprinted with permission from [135]. (f) Helicity-resolved PL spectra of the neutral $X_A^0$ and the charged X^± excitons (dots) in monolayer MoTe₂ as a function of the magnetic field. Figure adapted and reprinted with permission from [135].

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It is worth noting that the regulating effect of the magnetic field on valley polarization is not consistent for all 2D TMDs materials due to the difference in the band spin-splitting structure. For example, for monolayer MoTe₂ under positive magnetic fields, both the spin-up valley at the bottom of the conduction band and the top of the valence band at the + K valley shift towards higher energies (Fig.10e), leading to significantly suppressed scattering of electrons and holes from the -K valley to + K valley. As a result, the circular polarization of neutral excitons can reach as high as 78% at 29 T [135] (Fig. 10(f)), which is difficult to achieve with magnetic field-tuned valley polarization in other TMDs materials [35,136–138]. However, the current research is based on tens of T magnetic fields to manipulate the valley polarization, which is not conducive to the application of devices. Further research is needed to enhance the magnetic field response of 2D TMDs to achieve low magnetic field-tunable valley polarization.

4.5 Optical field

The optical field can control the initial carrier density in 2D TMDs, and increased carrier density will lead to more complex many-body interactions such as enhanced trion emission [37,139], band renormalization [140], and EEA [10,77]. Incident laser with increased power, in addition to creating more electron-hole pairs, is expected to photo-ionize carriers trapped on the donors, resulting in a non-equilibrium excess electron density in the conduction band [37]. Previous studies have found a significantly enhanced trion emission in monolayer WS₂ under high excitation power [37,139] (Fig. 11(a)). Further accumulation of electrons on the conduction band with increasing excitation power will cause band renormalization. As shown in Fig. 11(b), Fan et al. observed a continuous red-shift in peak positions and a nonlinear increase in emission intensity in the PL of monolayer WS₂ with the increasing excitation power [140]. This is because the position of the Λ valley in the conduction band is lowered faster than that of the K valley by multi-particle renormalizations as carrier density increases, resulting in the decline of exciton emission energy. Moreover, in WSe₂/WS₂ heterostructures, Ye et al. enhanced interlayer exciton emission by increasing exciton power to improve interlayer electron transport [141] (Fig. 11(d)). This means that the ratio of interlayer exciton emission to intralayer exciton emission in heterostructures can be adjusted by excitation power.

Fig. 11. (a) Photoluminescence of 1 L WS₂ as function of excitation power. Figure adapted and reprinted with permission from [139]. (b) The PL spectra of the 1 L WS₂ at different excitation powers obtained at 80 K. Figure adapted and reprinted with permission from [140]. (c) Schematic of the band structure renormalization of the 1 L WS₂ as the carrier density increases. Figure adapted and reprinted with permission from [140]. (d) PL spectra of the WSe₂/WS₂ under a 473 nm excitation with different powers. Figure adapted and reprinted with permission from [141]. (e) Exciton dynamics at different pump fluences with a time scale of 45 ps. Figure adapted and reprinted with permission from [11]. (f) The trion decay dynamics for different pump fluences. Figure adapted and reprinted with permission from [142]. (g) Comparison of the transient absorption spectra at low (0.05 V nm⁻¹) and high (0.25 V nm⁻¹) mid-infrared field strengths. Figure adapted and reprinted with permission from [142,143]. (h) An effective two-dimensional potential for excitons and the associated energy levels. An external laser field can excite internal resonances of excitons, such as the 1s–2p transition, and drive the exciton wavepacket into the quasifree region of the potential. Figure adapted and reprinted with permission from [143].

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The high initial carrier density will eventually form high exciton density. Therefore, the EEA is non-negligible. [10,11,77]. For example, in monolayer WS₂, the EEA rate was determined to be 4.3 ${\pm} $ 1.1 ${\times} $ 10⁻² cm²/s [11] (Fig. 11(e)), which is two orders of magnitude larger than that of traditional semiconductors [10,144]. The high EEA rate in 2D TMDs materials limits the performance of TMDs-based optoelectronic devices. Interestingly, the trion has no EEA due to charge-like repulsion [142,145] (Fig. 11(h)). In contrast to neutral exciton, both time constants increase with the pump fluence, indicating that the trion decay is slower at higher excitation densities [142]. Therefore, the design of optoelectronic devices based on trion in 2D TMDs may be one of the ways to avoid EEA. On the other hand, the excitation intensities also determine the role of defects on EEA in 2D TMDs [30,146]. Zhang et al. found that the main role of the defect is defect-assisted exciton nonradiative recombination under weak excitation intensities. With increasing to medium exciton density, the EEA caused by the many-body interaction of free excitons dominates the exciton recombination process, while defects can inhibit EEA by hindering exciton diffusion. When further increased to high exciton density, the defects become new centers of many-body interactions for localized excitons and accelerate EEA [146].

Optical-field manipulation of electronic band structures is another frontier for exciton regulation of 2D TMDs, known as Floquet engineering. The mechanism is to drive excitons with a strong optical field, thus directly transferring the momentum of the oscillating laser to the electron-hole. As shown in Fig. 11(g), Kobayashi et al. observed that strong-field light induces a blueshift of exciton in excess of a hundred millielectronvolts in monolayer WS₂, and attributed to external laser field can excite internal resonances of excitons, such as the 1s-2p transition (Fig. 11(h)) [143]. And Aeschlimann et al. also observed similar strong-field light dressing of excitons in monolayer WSe₂ [147]. On the other hand, Pattanayak et al. achieved the regulation of intra-valley spin-flip scattering by using optical vortex (OV) beams to transfer the momentum of light into the center of exciton [148]. Thus, Strong optical field driving has the potential to achieve enhanced control of the electronic band structure.

4.6 Thermal field

Based on the temperature-dependent exciton thermalization and phonon-assisted intervalley and intravalley scattering on exciton dynamics in TMDs, regulating the operating temperature has become one of the ways to optimize the performance of 2D TMDs photoelectric devices. The first discussion is the influence of temperature on the radiative lifetime of exciton in 2D TMDs. It has been demonstrated experimentally [41,140,149] and theoretically [150,151] that the non-equilibrium population of thermal excitons leads to a linear increase in the radiation lifetime of excitons with temperature. The exciton radiative lifetime in 2D TMDs can be increased from a few picoseconds at liquid helium temperature to more than a nanosecond near room temperature.

When it comes to the valley polarization dynamic, the enhanced phonon-assisted scattering will lead to a decrease in valley polarization [152,153] and valley polarization lifetime [15,16,72,154] with increasing temperature. Previous works have reported that the degree of circular polarization of monolayer WS₂ decreases with increasing temperature, for example down to 10% [152] or even completely depolarized [153] at room temperature. This is attributed to the enhancement of phonon-mediated intravalley spin-flip [40] and intervalley carrier scattering [16,17,69] by increasing temperature. As schematically shown in Fig. 12(a), after using ${\boldsymbol{\mathrm{\sigma}}^ + }$ light selectively excited the + K valley, carries in the + K valley can be scattered to the -K valley with phonon-assistance and then recombine in the -K valley, leading to the reduction of valley polarization. And the valley polarization lifetime also decreases sharply with the strengthened intervalley scattering [16,155] (Fig. 12(b)). In addition, Wang et al. found that the phonon-assisted intravalley spin-flip provides an effective decay channel for valley polarization by TA measurements. In Fig. 12(c), the circularly polarized pump beam with central energy of 2.09 eV selectively excited the A-exciton instead of the B-exciton in the K valley. However, the signal of B-exciton formed within a few hundred femtoseconds, indicating the presence of intravalley spin-flip (Fig. 12(d), e). The rise time of the B-exciton decreases at higher temperatures, suggesting that the intravalley spin-flip is phonon-assisted [40] (Fig. 12(f), (g)).

Fig. 12. (a) Schematic of the valley-dependent exciton dynamics. The steady-state exciton population N₊ (N_-) in the + K(-K) valley under σ⁺ excitation is determined by the valley lifetime τ_V and the exciton lifetime τ. Figure adapted and reprinted with permission from [16]. (b) The valley dynamics of a monolayer MoS₂ at different temperatures. Figure adapted and reprinted with permission from [155]. (c) A-excitons are injected in the K valley by a circularly polarized pump (red arrow). due to intravalley scattering, causing a delayed formation of the bleaching signal around the B exciton. Figure adapted and reprinted with permission from [40]. (d) Red and blue curves are ΔT/T at 77 K around the A and B transitions. Figure adapted and reprinted with permission from [40]. (e) Close up at a shorter delay time of the transient optical response. Figure adapted and reprinted with permission from [40]. (f) ΔT/T at different temperatures. The dashed line through the maximum of each trace highlights the increasing rate of intravalley scattering at higher temperatures. The solid black lines are obtained by fitting the rising edge of the ΔT/T traces with an exponential convoluted with the IRF. Figure adapted and reprinted with permission from [40]. (g) Temperature dependence of ${\tau _{rise}}$, as obtained from the fits in (f). Figure adapted and reprinted with permission from [40].

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5. Conclusions and outlook

In this review, we summarized the external-field regulation strategies of exciton dynamics in 2D TMDs and discussed their underlying mechanisms. In addition to the radiative recombination process, complex many-body interactions induce diverse fundamental process, such as EEA, exciton species conversion, throughout the whole process of exciton formation to relaxation. External field-regulation strategies can modulate one or more fundamental processes based on their own specific mechanisms. For example, the electric field can regulate the conversion of exciton species based on the modulation of the concentration of resident carriers in the system. Hence, based on a deep understanding of the relationship between field regulation and exciton dynamics in 2D TMDs, the design and optimization of TMDs-based devices are expected to be guided.

From our perspective, it is indispensable to obtain desired performance by field regulation for TMDs-based devices. However, the following issues still remain to be tackled. First, as the basis of TMDs optoelectronic devices, the exciton dynamics may exist discrepancies in different TMDs systems. Note that the favorable formation of Q-K indirect dark excitons in monolayers W-based TMDs has been observed experimentally due to the close CBM of K and Q valleys. It implies that subtle differences in band structure can lead to varied exciton dynamics, which may influence the response to external field regulation. Hence, based on the opposite conduction band spin splitting of W-based TMDs and Mo-based TMDs, as well as the band degeneracy of TMDs at different layers, the related exciton dynamics including exciton formation to relaxation need further investigation. Second, although the underlying mechanisms of different external field regulations have been well discussed, there may be a slight discrepancy in the mechanism due to different modes of action. For example, in defect engineering, although different types of defects all provide nonradiative recombination channels, their effects are influenced by different localization strengths and different phonon modes caused by defect types. Therefore, when a certain regulation strategy has multiple modes of action, their regulatory effects on the performance of 2D TMDs deserves further exploration. Third, it should be pointed out that a definite regulation strategy may influence multiple processes of exciton dynamics simultaneously. It is important to distinguish the main process of regulation under different parameters for a field regulation strategy or the coupling effect between different regulation strategies. At last, the emerging classes of 2D noble-metal transition-metal dichalcogenides (NTMDs, such as PtSe₂, and PdSe₂) have recently exhibited novel physical properties and promising applications. Research on external field regulation of such NTMDs is rare and urgently needed.

Funding

National Natural Science Foundation of China (51872048, 52073061, 61905156); Natural Science Foundation of Fujian Province (2022J01555); Fuzhou University Testing Fund of precious apparatus (2022T002).

Disclosures

The authors declare that they have no competing financial interests.

Data availability

No data were generated or analyzed in the presented review paper.

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External field regulation strategies for exciton dynamics in 2D TMDs

Abstract

1. Introduction

2. Introduction of TMDs

2.1 Crystal structure of TMDs

2.2 Energy band structure of TMDs

3. Fundamental processes of exciton dynamics in 2D TMDs

4. Regulation strategy of dynamics

4.1 Defects engineering

4.2 Strain engineering

4.3 Electric field

4.4 Magnetic field

4.5 Optical field

4.6 Thermal field

5. Conclusions and outlook

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (12)

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