We synthesized an atomically thin monolayer of 2H-MoSe2 using chemical vapor deposition (**Supplementary Fig. S1**). The characteristic optical properties of the MoSe2 monolayer were confirmed through steady-state absorption and photoluminescence (PL) spectroscopy. Notably, in the steady-state absorption spectrum, we observed the well-documented *A* and *B* excitons of MoSe219 in the steady-state absorption spectrum, manifesting as peaks at 1.58 eV and 1.79 eV, respectively, as depicted in **Supplementary Fig. S2a**. Additionally, the *C* exciton appeared as a broad peak at higher energies, indicative of band nesting resulting from a shift in the valence band by 1Eg20. We point out that this type of band nesting, related to the *C* exciton, differs from the 2*E**g* band nesting we discuss later, which involves a shift in the valence band by 2*E**g* and plays a critical role in facilitating CM channels. The distinct peak at 1.54 eV (805 nm) in the PL spectrum signifies the direct bandgap (*E**g*) of monolayer MoSe2 (*E*g), which is 1.54 eV. This observation is in good agreement with the bandgap estimated from the Tauc plot (**Supplementary Fig. S2b**) and corroborates prior results21, 22.

Employing ultrafast transient absorption (TA) spectroscopy, we have uncovered compelling evidence of ideal CM in monolayer MoSe2, marked by distinct spectral signatures and a quantitative relationship between absorption changes and photon density. A key observation emerged when monitoring the kinetics of differential absorption \(|\varDelta \text{A}\left(E,t\right)|\) at probe energies of *E*probe = 1.58 eV (A exciton), as illustrated in Fig. 1b: a sudden two-fold increase in the maximum differential absorption (\({|\varDelta \text{A}\left(E\right)|}_{\text{max}}\)) occurred when the pump energy exceeded 2*E*g with the absorbed photon density at 1.5 ×1012 photons cm− 2 (**Supplementary Fig. S3**). This significant finding, together with the detection of two additional CM indicators—a transient Stark shift and delayed build-up time (See **Supplementary Note 1** for detailed analysis)—highlights the exceptional CM efficiency in this system.

To elucidate the significance of these observations, we analyzed the QY as a metric for CM efficiency. As depicted in Fig. 1c, \({|\varDelta \text{A}\left(E\right)|}_{\text{max}}\) demonstrates a linearly increase with absorbed photon density across all pump energies. When the pump energy *E* is less than 2*E*g, the slope for QY is established at 1, denoting the generation of a single carrier per photon (for a comprehensive discussion, see **Supplementary Note 2**), Remarkably, for pump energies slightly above 2*E**g*, the QY doubles to two, indicative of the excitation of two carriers per photon. This behavior contrasts sharply with the gradual increases observed in bulk MoSe2 (**Supplementary Fig. S4**) and other materials11, 12, 15, highlighting a unique, quantized leap in CM efficiency at the threshold energy and establishing a new benchmark for CM performance across materials.

Building on these findings, Fig. 1d presents a comparative analysis of QYs for monolayer and bulk MoSe2, with the pump energy normalized to their respective bandgaps. This comparison vividly illustrates an ideal quantized jump at the CM threshold energy, where the monolayer achieves 100% CM efficiency (\({\eta }_{CM})\), starkly differing from the lower efficiencies seen in the bulk form. The CM threshold energy for the monolayer MoSe2 matches 2*E*g, closely paralleling the 2.05*E*g threshold of its bulk counterpart. A gray dashed line in Fig. 1d represents the simulated quantum-limit curve, based on CM conversion efficiency theories (**Supplementary Note 3**). This pronounced difference in CM efficiency not only marks a significant advancement in CM performance but also establishes a precedent unmatched by any other material previously studied.

Having demonstrated the occurrence of ideal CM in monolayer MoSe2 through ultrafast TA spectroscopy, we now turn our attention to the material properties that enable this exceptional efficiency: notably, the availability of numerous CM channels at the threshold energy *E* = 2*E*g and the effective suppression of heat dissipation via carrier–lattice scattering. Our first-principles calculations reveal that monolayer MoSe2 possesses a rich array of CM channels at *E* = 2*E*g, consistent with energy-momentum conservation laws. By adapting a method previously outlined in the literature 23, we quantitatively assess the density of feasible CM channels \(N\left({I}_{1}\right)\) for initial states \({I}_{1}\) in the conduction band, as shown in Fig. 2a (See **Supplementary Note 4** for the detailed methods and analysis). The calculated values, particularly around the \(K\) or \(K{\prime }\) points, substantiate the abrupt increase in quantum yield observed at 2*E*g (Fig. 1d), providing a theoretical foundation that not only corroborates our empirical observation but also underscores the immense potential of the monolayer for high-efficiency optoelectronic applications.

The unique presence of 2*E**g* CM channels is monolayer MoSe2, which requires precise band structure tuning not found in its bulk counterpart, underscores the exceptional optoelectronic properties of the monolayer. Unlike the monolayer, bulk MoSe2 definitively lacks 2*E**g* CM channels, a limitation imposed by energy-momentum conservation laws, as demonstrated in **Supplementary Fig. S14** (See **Supplemental Note 4** for the DFT calculations of CM channels in bulk MoSe2.). Notably, in bulk MoSe2, significant contributions to \({N(I}_{1})\) emerge only within the energy range 2*E*g < *E* < 2.2*E*g, explaining the gradual increase in QY beyond the threshold energy *E* = 2.05 *E**g*, observed in Fig. 1d. This gradual increase is governed by the stringent criteria of energy-momentum conservation. The stark contrast in the behavior of bulk and monolayer MoSe2 not only highlights the advanced properties of the monolayer structure but also points to its superior potential for high-efficiency photovoltaic applications, where efficient carrier multiplication can significantly enhance device performance.

The abundance of 2*E**g* channels in the monolayer MoSe2 is intimately linked to its unique electronic structure, epitomized by 2*E**g* band nesting and inherent valley symmetry. Specifically, near the *K* (or equivalently, *K'*) points, the highest occupied bands and the third lowest unoccupied bands come into close alignment when shifted by 2*E*g (See Fig. 2c). The alignment is a direct consequence of the crystal symmetry in monolayer MoSe2, which results in an approximate equal splitting of the hybridized \({d}_{{x}^{2}-{y}^{2}}\) and \({d}_{xy}\) orbitals. As detailed in **Supplementary Fig. S11**, these nested bands facilitate a multitude of intra-valley (See Fig. 2b, for example) and inter-valley CM channels near the *K* point. Moreover, the valley degeneracy of the monolayer effectively equals the number of intra-valley CM channels to that of inter-valley CM channels, bolstered by the local inversion and time-reversal symmetry—termed here as valley symmetries. These symmetries significantly boost the CM rate for 2*E*g excitation, where a singular intra-valley CM channel at *K* or *K'* catalyzes the creation of two additional inter-valley CM channels between *K* and *K'* (For an in-depth analysis, we invite the reader to consult **Supplementary Note 4**, which elaborates on the symmetry considerations underpinning these observations.).

After delving into the 2*E**g* CM channels, our focus shifts toward the transport properties of hot carriers, which are crucial for achieving ideal CM efficiency in MoSe2 monolayer. Employing femtosecond spatiotemporal transmission adsorption microscopy, (for detailed experimental methods, see **Supplementary Note 5)**, we unveil the capacity of monolayer MoSe2 for enhanced spatial separation and delayed thermalization of hot carriers. Figure 3b presents the spatiotemporal dynamics of excited carriers in monolayer, shedding light on hot-carrier diffusion processes (detailed analysis provided in **Supplementary Note 6**). Unlike their bulk counterparts, hot carriers in the monolayer demonstrate immediate spatial separation and exhibit significantly extended lifetimes, a comparison starkly evident in the juxtaposed top and bottom panels of Fig. 3b. This differential behavior is further highlighted in Fig. 3c, in which diffusion profiles are traced within a \(\pm\) 2 \(\mu \text{m}\)range. Remarkably, within a sub-picosecond duration, hot carriers in the monolayer are shown to spread across this range, showcasing rapid and efficient spatiotemporal separation.

Our examination of the excited carrier dynamics in the monolayer MoSe2 reveals a pronounced increase within the first two picoseconds. We obtain squared width broadening \({{\Delta }\sigma }^{2}\left(t\right) = {\sigma }^{2}\left(t\right) - {\sigma }^{2}\left(0\right)\), where \(\sigma \left(t\right)\) is the Gaussian full width at half maximum as a function of time, from the measured profiles in Fig. 3c, as illustrated in Fig. 3d. This dynamic behavior fits a power function \({{\Delta }\sigma }^{2}\left(t\right)=D{t}^{\alpha }\) with \(\alpha =1\), from which we calculate a diffusion coefficient (\({D}_{\text{m}\text{o}\text{n}\text{o}}{= \varDelta \sigma }^{2}/2t\)) showing a diffusion rate of 1.0 × 104 cm2 s−1 (Fig. 3d). Remarkably, this rate surpasses that for other CM materials24, 25 and even Au26 by one to two orders of magnitude, evidencing the exceptional hot-carrier expansion capability of the monolayer. The minimal influence of carrier–carrier scattering on this diffusivity, as opposed to the more pronounced effect of carrier–lattice scattering, indicates that the enhanced hot-carrier expansion characteristic of the monolayer is likely responsible for its reduced carrier–lattice scattering rates. Highlighting the distinct advantage of monolayer MoSe2 in hot-carrier transport dynamics, these findings point to its superior potential for efficient CM, markedly setting it apart from other materials.

In contrast to the monolayer, our measurements reveal a significantly higher carrier-lattice scattering rate in bulk MoSe2, as evidenced by the more gradual hot-carrier expansion depicted in Fig. 3d. For the bulk material, \({{\Delta }\sigma }^{2}\left(t\right)\) showed a steady increase only up to *t =* 5 ps, resulting in a hot-carrier diffusion coefficient of \({D}_{\text{b}\text{u}\text{l}\text{k}}\) = 2.6 × 103 cm2 s−1 in the initial phase—substantially lower by an order of magnitude compared to the monolayer. This discrepancy is attributed to the bulk carriers to occupy in-plane dimensions with less confinement out-of-plane, offering a broader array of states for thermal excitation than in the monolayer. Conversely, in 2D systems like the monolayer MoSe2, rapid hot carrier expansion within the sub-picosecond range effectively reduces the density of excited carriers in the spatial domain27, 28. Such dynamics are crucial for enhancing CM efficiency in monolayer structures by preventing spatial congestion of the excited electrons, thereby facilitating a more efficient CM process.

To shed light on the diffusion mechanism of hot carriers, we analyzed their initial spreading by fitting it to the power function \({{\Delta }\sigma }^{2}\left(t\right)=D{t}^{\beta }\), where the \(\beta\) represents transport exponent determining the nature of carrier spreading. A \(\beta\) value of 1 denotes classical diffusion, typified by the scattering motion of particles, whereas \(\beta =2\) suggests ballistic motion, characterized by scattering-free carrier transfer25, 29, 30. In Fig. 3e, we display the power fit as a function of delay time for the monolayer, revealing that carriers propagate with \(\beta =2\) up to 0.7 ps (indicated by a red dot), implying that hot carriers experience diffusion predominantly through ballistic transport initially25, 31. However, beyond this sub-picosecond regime, the fit deviates from \(\beta =2\) (marked by a green dot), transitioning to linear diffusion (\(\beta =1\)), as denoted by a blue dot in Fig. 3e.

To further elucidate ballistic transport, we drew a correlation between the excess energy of photons and energy conservation30. During photoexcitation, this excess energy is directly converted into kinetic energy, as described by the equation of \({E}_{ex}=\frac{1}{2}{m}^{*}{v}_{B}^{2}\), where \({v}_{B}\) is ballistic velocity, \({E}_{ex}\) is excess energy of photon, and \({m}^{*}\) is effective mass. For the monolayer, the ballistic velocity is computed to be \(6.6\times {10}^{5} m/s\), which is approximately equivalent to the maximum hot-carrier velocity (\({\left.\partial \sigma /\partial t\right|}_{max}\)) of \(7.2\times {10}^{5} m/s\). Moreover, the values for ballistic velocity and hot carrier in the bulk material are in good agreement: \(4.8\times {10}^{5} m/s\) and \(5.3\times {10}^{5} m/s\), respectively.

Building on the observed ballistic motion and subsequent hot-carrier expansion in MoSe2, we delve into the physical processes underpinning carrier multiplication (CM) and their spatial distribution over time, as depicted in Fig. 4. Following photoexcitation, carriers are instantaneously excited to match the beam size of the system. Within the first 0.5 ps, these carriers undergo scatter-free ballistic movement due to their excess energy, enabling rapid diffusion at rates surpassing 104 cm2/s. This swift expansion aids in spatially separating the accumulated carriers, significantly mitigating intra-band scattering.

It is critical to acknowledge the competitive dynamics between CM and Auger recombination4. With ballistic transport occurring concurrently with CM, the system can potentially augment CM efficiency by minimizing the rate of Auger recombination and annihilation27, 28. Given the elevated kinetic energy in the monolayer, we anticipate that the CM in monolayer MoSe2 surpasses that of its bulk counterpart.

Subsequent to ballistic transport, the excited carriers adopt a Fermi-Dirac distribution, transitioning into what are termed hot carriers. Despite being slower than their initial ballistic motion, these carriers retain substantial kinetic energy due to their heightened temperature, achieving rate on the order of 103 cm2/s in the monolayer24 (Fig. 3d). Ultimately, these hot carriers dissipate their energy via phonon emission, leading to a phonon-limited diffusion process, characterized by a remarkedly lower rate of 10 cm2/s, delineating a comprehensive picture of carrier dynamics from initial excitation to eventual exciton formation.

Lastly, the ideal CM that we have achieved signifies a substantial increase in hot carriers generation. By postulating a uniform initial energy distribution of carriers, we can assess CM efficiency using the ratio *R*CM, defined as *R*CM = (*N*CM – *N*0)/*N*0 × 100%, where *N*CM and *N*0 represent the number of carriers generated within the energy range from 2*E**g* to 3*E**g* with and without CM, respectively. This ratio quantifies the increase in carrier generation attributable to CM compared to the scenario without CM. As illustrated in Fig. 1a, van der Waals layered thin films currently reach an *R*CM of only 42%, falling short of the half of the enhancement goal. This shortfall underscores significant opportunities for further optimization of *R*CM toward the ideal CM (*R*CM = 100%). The strides made in realizing ideal CM in this study markedly influence hot carrier generation, opening new avenues for optimizing and harnessing CM efficiency.