57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

Graphene, a single layer of carbon atoms, has superior charge transport, thermal transport, and mechanical properties. These make graphene a very attractive candidate for several applications in energy science and technology.  Among these properties, charge transport is the most extensively studied one since it is the foundation of most applications. In the first year of this project, we have used ultrafast laser techniques to study two of the key issues on hot carrier dynamics in graphene: the diffusion and the energy relaxation of hot carriers. In the first study, we measured diffusion coefficient of charge carriers in several types of graphene samples under different temperatures. In the second study, we directly measured optical phonon scattering time in graphene, and studied how the phonon scattering changes with the density of charge carriers. These studies provided important information for applying graphene in energy technologies.

In the second year of this project, we further studied nonlinear optical effects of graphene, and demonstrated that they can be used to effectively monitor charge carriers. This provides new tools to study charge carrier dynamics, and opened up new opportunities in using graphene in photonic devices. Furthermore, we have extended our studies to other graphene-like two-dimensional crystals, to further understand influence of changes in dimensionality on charge carrier dynamics.  As an example, we have studied charge carrier dynamics in atomically thin MoS₂.

1. Third harmonic generation in graphene

For many applications, nonlinear optical properties of graphene play important roles. However, these properties have been less explored, and a clear understanding is still yet to establish. On second-order nonlinear optical properties of graphene, theoretical studies have suggested rather large second-order nonlinear susceptibilities, especially in AB-stacking bilayer graphene. However, experiments have shown very weak second-harmonic generation from graphene and few-layer graphite, including AB-stacking bilayer graphene. Several third-order nonlinear optical effects, including two-photon absorption and four-wave mixing, have also been studied in recent experiments. However, the strength of the third order response has not been determined yet.

In this project, we performed the first study on third-harmonic generation in graphene. Third harmonic generation is the simplest third-order nonlinear optical effect. In this process, the electric field of incident light generates a third-order polarization at triple frequency, in addition to the linear and second-order (if nonzero) polarizations. Radiation of this polarization gives rise to light at triple frequency. From a quantum mechanical point of view, this process can be described as combining three photons of the incident light to one photon that is three times more energetic.

We have observed third-harmonic generation in graphene samples with different number of layers and on different substrates. We found that for monolayer graphene, the third order nonlinear susceptibility is on the order of 10^-17 m²/V². This is much larger than most semiconductors. We also found that the susceptibility is independence of light wavelength in the visible and near infrared ranges. For few-layer graphene flakes of less than 7 atomic layers, the susceptibility is proportional to the thickness. Finally, we found that the susceptibility can be significantly modified by carriers injected by a pump pulse. With an excited carrier density of 10¹²/cm², the third order nonlinear susceptibility is reduced by about 60%. Hence, third-harmonic generation can be used to measure the carrier density, and hence to study charge carrier dynamics. This is complementary to the conventional technique using the linear susceptibility.

2. Charge carrier dynamics in atomically thin MoS₂

There exist more than 100 types of layered materials in which atomic sheets are stacked together by weak van der Waals forces. Most of them can be used to fabricate two-dimensional systems. They represent a diverse and rich, but largely unexplored, source of materials. Graphene is the most well-known example. However, many other layered materials can also be explored. Very recently, significant progress has been made on one type of layered transition metal dichalcogenide, MoS₂. In 2010, two groups independently discovered an indirect-to-direct bandgap transition that occurs when varying the thickness from bulk to monolayer. In 2011, monolayer MoS₂ transistors with a 10⁸ on/off ratio and a room-temperature mobility of more than 200 cm²/Vs have been demonstrated. In 2012, several groups reported observation of valley selective optical excitation and luminescence in monolayer MoS². These studies paved ways to apply two-dimensional MoS²for photonics, electronics, and valleytronics.

We have fabricated atomically thin MoS₂ flakes on Si/SiO₂ substrates, and studied charge carrier dynamics in these flakes by using transient absorption microscopy. We injected carriers by direct interband absorption of a 390-nm pump pulse, and detected by measuring the differential reflection of a 660-nm probe pulse. We found that the excitonic absorption is reduced by the carriers, which is consistent with the phase-state filling effect. By spatially and temporally resolving the signal, we deduce a carrier lifetime of 100±10 ps and a carrier diffusion coefficient of 20±10 cm²/s, corresponding to a mobility of 800 cm²/Vs and a diffusion length of 450 nm. We also demonstrate that the charge carriers can be probed by free carrier absorption of a 780-nm probe, and deduce a free carrier absorption cross section of 3.6±0.6×10⁻²⁰ m². These parameters are important for electronic and photonic applications. Furthermore, the demonstrated technique can be used as a powerful tool to study charge carriers in various MoS₂-based structures. For comparison, we also study bulk crystals of MoS₂ using the same procedures.