Two-Step Excitation Triggered by One-Photon Absorption on Linear

May 12, 2016 - We report the decrease in absorption caused by a near-infrared laser pulse in the visible region in monolayer graphene. This absorption...
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Two-Step Excitation Triggered by One-Photon Absorption on Linear Dispersion in Monolayer Graphene Takeshi Koyama,*,† Kenta Mizutani,† Hiroki Ago,‡ and Hideo Kishida† †

Department of Applied Physics, Graduate School of Engineering, Nagoya University, Chikusa, Nagoya 464-8603, Japan Art, Science and Technology Center for Cooperative Research, Kyushu University, Kasuga, Fukuoka 816-8580, Japan

‡

ABSTRACT: We report the decrease in absorption caused by a near-infrared laser pulse in the visible region in monolayer graphene. This absorption decrease shows the existence of a two-step excitation process of carriers, in which one-photon absorption and Auger recombination sequentially occur. This process results from the linear dispersion nature of monolayer graphene. In addition, the monolayer graphene shows the ultrafast decay of carrier population. The observed properties are of importance for ultrafast optical switching utilizing the optical nonlinearity induced by carrier excitation.

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INTRODUCTION Monolayer graphene is a gapless semiconductor, which shows rapid decay of photoexcited carriers (photocarriers) in the conduction and valence bands as in metals.1 In addition, owing to its linear dispersion bands, an efficient intraband scattering between photocarriers (Auger recombination) has been theoretically proposed2,3 because the conservation of energy and momentum is easily satisfied for scattering on the linear dispersion. Experimental studies have shown this intraband scattering by observing optical responses at higher states above the original excitation energy.4,5 These studies have advanced understanding on the ultrafast photocarrier scattering in graphene and invoked the interest in the carrier dynamics in the high-energy region. Even thermal carrier population can extend to such higher states in graphene with a strong pulse excitation,6,7 and the thermal population is established very fast after the pulse excitation by the ultrafast carrier−carrier and carrier−phonon scattering.6−13 However, establishment of the thermal population requires a lot of carrier−carrier scattering. In contrast, as shown in Figure 1, the Auger recombination in graphene, that is, only a single scattering between photocarriers, potentially leads to nonthermal carrier population extending to higher states with the energy that is comparable to the original excitation energy. This photocarrier scattering to such higher

states is considered as a wide-range two-step excitation of carriers triggered by one-photon absorption, leading to future applications of graphene in ultrafast broadband optical switching devices that are operated at low-energy excitations. Nonthermal carrier population at higher states above the original excitation energy has been observed in conventional bulk semiconductors such as GaAs14,15 and InAs16 and quantum wells17 and understanding on the intraband scattering between photocarriers has been progressed. In the conventional bulk semiconductors, the wide-range two-step excitation called in this paper cannot occur because of the failure of conservation of energy and momentum in parabolic dispersion bands. Semiconductor quantum dots show the efficient Auger recombination of charges.18 Because the quantum dots are very small, which results in the emergence of discrete energy levels and the relaxation of the momentum conservation, the Auger recombination in the quantum dots is not considered as the two-step excitation by intraband scattering in a bulk system. The Auger recombination of excitons efficiently occurs in onedimensional materials such as quantum rods19 and carbon nanotubes.20 Because two particles, electron and hole, are excited in this recombination, the conservation of energy and momentum can be satisfied for any initial state.21,22 For this reason, the Auger recombination of excitons is inherently different from that of carriers, where a single particle is excited. Therefore, the wide-range two-step excitation of carriers even in a bulk system is a unique intrinsic phenomenon for graphene. The demonstration of this excitation is one of important issues for fundamental understanding of electron physics in graphene. In this paper, we demonstrate transient absorption spectra of monolayer graphene in the visible region excited by the near-

Figure 1. Schematic of a wide-range two-step excitation of carriers, in which one-photon absorption and Auger recombination sequentially occur. © XXXX American Chemical Society

Received: February 12, 2016 Revised: April 12, 2016

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DOI: 10.1021/acs.jpcc.6b01490 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C infrared pulses. Photoexcitation generates electrons and holes in the conduction and valence bands, respectively, both of which cause the state filling in the bands. Because this state filling results in the decrease in the oscillator strength of the relevant transition, carrier population can be detected through the decrease in absorption. The dependence of the decrease in absorption in the high-energy region on the photocarrier density is shown to investigate the possibility of the wide-range two-step excitation of carriers. From the decay behavior of the decrease in absorption and saturation density of carriers, the potential of graphene as ultrafast optical switching devices utilizing the optical nonlinearity induced by carrier excitation is discussed.

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EXPERIMENTAL METHODS

The graphene epitaxially grown on Cu(111)/sapphire by chemical vapor deposition, which was transferred onto an SiO2 substrate,23,24 was used in this study. The obtained graphene was confirmed to be p-doped monolayer graphene by Raman scattering measurements (the Fermi energy shift of −0.225 eV from the Dirac point).25 Femtosecond transient absorption measurements (pump−probe measurements) were carried out using a regenerative amplifier (100 Hz, 800 nm, 120 fs) seeded by a mode-locked Ti:sapphire laser.26 The output of the regenerative amplifier was divided into two beams. One beam was used as the pump pulse (pump photon energy 1.55 eV). The other beam was focused into the water cell to generate a white continuum pulse, which was used as the probe pulse. The polarizations of the pump and probe pulses were parallel to each other. Because the absorption changes observed in the pump−probe measurements were small, we calculated the differential absorption spectra (ΔA spectra) by subtracting the unpumped absorption spectrum from the pumped spectrum and plotted them in this study for clarity. Here, A = 1 − T, where T is transmittance. All measurements were carried out at room temperature.

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Figure 2. (a) Pump-fluence dependence of ΔA spectrum in monolayer graphene with a pump photon energy of 1.55 eV at the time origin. The inset indicates a scheme of the two-step excitation and the relationship between the pump and probe photon energies. The observed spectrum of pump pulse is plotted by the black curve. (b) ΔA spectra in monolayer graphene at the time origin (0 ps) and 0.2 ps with a pump fluence of 15 J m−2 at 1.55 eV. The dashed curves indicate the calculated results of the absorption changes induced by thermal carriers at temperatures Tc indicated in the figure.

ΔA =

⎧⎡ ⎛ E + 2μ ⎞ ⎛ E − 2μ ⎞⎤ πe 2 ⎪ ⎥ ⎢tanh⎜ ⎨ + tanh ⎟ ⎜ c c ⎟ 4ε0hc ⎪ ⎝ 4kBT ⎠ ⎝ 4kBT ⎠⎥⎦ ⎩⎢⎣ ⎫ ⎡ ⎛ E + 2μ ⎞ ⎛ E − 2μ ⎞⎤⎪ ⎥⎬ − ⎢tanh⎜ c ⎟ + tanh⎜ c ⎟ ⎪ ⎢⎣ ⎝ 4kBT0 ⎠ ⎝ 4kBT0 ⎠⎥⎦⎭

RESULTS AND DISCUSSION

where e is the elementary charge, ε0 is the permittivity of vacuum, h is the Planck constant, c is the speed of light in vacuum, E is the probe photon energy, μ is the chemical potential of −0.225 eV (the origin of the energy is set at the Dirac point), kB is the Boltzmann constant, Tc is the carrier temperature after the pump-pulse irradiation, and Tc0 is the room temperate of 300 K. As shown in Figure 2b, the observed ΔA spectrum at the time origin cannot be reproduced by the calculation for any Tc (dashed curves), indicating that the ΔA spectrum at the time origin is predominantly governed by the nonthermal carriers. In contrast, it is confirmed that the ΔA spectrum at 0.2 ps, comparable to10 or longer than the thermalization time of carriers in graphene,6−9,11−13 can be reproduced for Tc of 5000 K. Next, the dependence of ΔA on the density of the photocarriers generated is examined. By considering that the value of ΔA induced by the state filling in the vicinity of the pump photon energy is proportional to the photocarrier density, the photocarrier density is estimated by using the pump-fluence dependence of ΔA at 1.65 eV at the time origin, which is plotted in the inset of Figure 3a. Below 4.0 J m−2, the value of ΔA shows a linear dependence on the fluence, whereas

Figure 2a shows the pump-fluence dependence of ΔA spectrum at the time origin. In the spectrum with a pump fluence of 0.81 J m−2, the value of ΔA monotonously increases toward the higher energy, and above 2.2 eV, it is zero within the error. This decrease in absorption is caused by the state filling for the photocarrier population in the vicinity of the pump photon energy (1.55 eV). As the pump fluence increases, the value of ΔA decreases and the high-energy tail of the spectrum is stretched. Observing the spectra with pump fluences above 4.0 J m−2 indicates almost constant values from 2.6 to 2.9 eV, monotonous increases above ∼2.9 eV, and almost zero values near the measurement limit at 3.05 eV within the error, suggesting that another spectral component is superimposed above ∼2.6 eV. To reveal the origin of this component, (1) comparison with the calculation of ΔA spectra induced by thermal carriers and (2) dependence of ΔA on the density of the photocarriers generated are discussed in the following. First, the comparison with the calculation of ΔA spectra induced by thermal carriers is shown. The calculated spectrum is given by7,10 B

DOI: 10.1021/acs.jpcc.6b01490 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Auger-type scattering in graphene; especially, the experiments30 showed that the Auger recombination process is predominant compared to the competing process of impact excitation in the case of the pump fluence above 0.75 J m−2. In our experiments, the pump fluence is above 0.81 J m−2, and the results are in agreement with the previous study. Because the graphene used in this study is p-doped and the Fermi energy shift from the Dirac point is −0.225 eV, holes cannot be excited by scattering between the photoexcited holes to the states with the (hole) energy above 1.325 (= (1.55/2) + ((1.55/2) − 0.225)) eV, corresponding probe photon energy of 2.65 (= 1.325 × 2) eV. However, electrons can be excited to the states with the (electron) energy of about 1.55 eV, corresponding probe photon energy of 3.10 eV. The state filling of either electrons or holes causes absorption decrease. Thus, it is possible that the absorption decrease above 2.65 eV is observed. The ΔA spectra in Figure 2a show the intriguing feature from ∼2.6 to 2.9 eV that the ΔA signals are almost constant. This intriguing feature is presumably explained by the increase in the density of states28,31 and the decrease in the scattering rate between photocarriers,25 both of which are caused by the sublinear dispersion relationship in the high energy region. The increase of ΔA signal above ∼2.9 eV and almost zero value at 3.05 eV is qualitatively explained by the infinite small density of states around the Dirac point, whereas in the previous study by Obraztsov et al.,5 only the low rate of carrier scattering with large momentum change was pointed out. When one photocarrier is scattered to the state with the energy of twice the original excitation energy, the other is scattered to the Dirac point. In this case, the scattering rate is zero because the rate is proportional to the density of states of the relevant states. The quantitative analysis on the spectral shape might be possible from comparison with theoretical calculation, but such calculation is beyond the present study. It is noted that the time resolution in this study was 120 fs and probably longer than the thermalization time of carriers in graphene;6−9,11−13 however, the absorption change due to the nonthermal carriers can be observed at the time origin in the high energy region, when and where influence of the thermal population is relatively weak as indicated in Figure 3 of ref 10. Finally, to test the potential for graphene to function as ultrafast optical switching utilizing the optical nonlinearity induced by carrier excitation, response time of ΔA and saturation density of carriers are investigated. Figure 4a shows the time evolution of ΔA at 2.60 eV with a pump fluence of 15 J m−2. The ΔA signal shows an ultrafast decay to zero until ∼1 ps, and it is fitted by a biexponential function model, ∝ C exp(−t/τ1) + (1 − C)exp(−t/τ2), which is convoluted with the instrument response function of a Gaussian shape with a full width at half-maximum of 120 fs (in this study, the error of the convolution-fitting method is 20 fs). In the case that C = 0.61, τ1 = 0.07 ps, and τ2 = 0.23 ps, the decay curve is reproduced well. The effective decay time constant defined as Cτ1 + (1 − C)τ2 is 0.13 ps. Even at the lower photon energy of 1.65 eV, the ΔA signal decays to zero in several picoseconds (Figure 4b). The signal is fitted by the biexponential function model with the parameters, C = 0.88, τ1 = 0.27 ps, and τ2 = 2.03 ps. The effective decay time constant defined as Cτ1 + (1 − C)τ2 is 0.48 ps. These results indicate the ultrafast decay of carrier population in graphene. The saturation density of carriers Ns, which is a measure of the emergence of strong correlation between carriers caused by the phase-space filling and the exchange interaction,32 is

Figure 3. Dependences of (a) ΔA at 1.65 eV and (b) spectral weight of −ΔA in the range of 2.60−3.05 eV at the time origin on estimated photocarrier (electron or hole) density. The insets in (a) and (b) show dependences of (a) ΔA at 1.65 eV and (b) spectral weight of −ΔA in the range of 2.60−3.05 eV on pump fluence, respectively.

above this fluence, the saturation behavior is observed. In the linear-dependence regime, 2.29% of photons in the pump pulse are absorbed by graphene27,28 and electron−hole pairs are generated. In this regime, the photocarrier density (here, the density is defined as electron density or hole density) is proportional to the pump fluence. The obtained linear relationship between the photocarrier density below 3.7 × 1013 cm−2 and the value of ΔA is plotted as a line in Figure 3a. In the saturation regime, however, sufficient photocarriers are generated that lead to almost complete state filling and photons cannot be absorbed any more. Because the spectral weight in the vicinity of the pump photon energy (1.55 eV) is an order of magnitude larger than that above ∼2.6 eV, we assume that the decrease in photocarrier density in the vicinity of the pump photon energy caused by carrier−carrier interaction is negligibly small. Hence, the decrease in absorption at 1.65 eV is considered to be proportional to the photocarrier density generated by the pump pulse. The photocarrier density above 4.0 × 1013 cm−2 is estimated by extrapolation of the line obtained in the linear-dependence regime, as shown in Figure 3a. Now, the dependence of ΔA above 2.6 eV on the photocarrier density N estimated by the above calculation is discussed. The spectral weight of −ΔA in the range of 2.60− 3.05 eV is calculated and is plotted against the estimated photocarrier density in Figure 3b. The spectral weight is fitted to a function proportional to ∝ Na (solid curve), where a = 2.2. The power of ∼2 indicates that the origin of the spectral component above 2.6 eV is carrier population generated by two-body interaction between photocarriers. It is observed that this carrier population does not originate from the two-photon absorption because the spectral weight does not show a quadratic dependence on the pump fluence, as shown in the inset in Figure 3b. Therefore, these results provide an evidence of the carrier excitation by scattering between photocarriers as illustrated in Figure 1. The previous theoretical29 and experimental studies30 progressed understanding on the C

DOI: 10.1021/acs.jpcc.6b01490 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-52-7894450. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank T. Matsuno for support in performing pump−probe measurements. This work was supported by MEXT/JSPS KAKENHI (Grant No. 26107520, 15H03530, and 15K13304) and PRESTO-JST.

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REFERENCES

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Figure 4. Time evolutions of ΔA at (a) 2.60 eV and (b) 1.65 eV in monolayer graphene with a pump fluence of 15 J m−2 at 1.55 eV. The curves indicate the result of fitting analysis based on a biexponential function model.

discussed below. The theoretical treatment shows that the ratio of N to Ns is given by −ΔA/A.32 In the linear-dependence regime shown in Figure 3a, the slope is −1.8 × 10−16 cm2. Using this slope and the value of 0.0229 for A, Ns is calculated to be 1.3 × 1014 cm−2. Taking the nearest-neighbor distance between carbon atoms in graphene as 0.142 nm,33 the density of carbon atoms (π electrons) in graphene is 3.8 × 1015 cm−2. Thus, Ns is ∼3.3% of π electrons in graphene. In the high excitation regime, for example, the pump fluence is 15 J m−2, N (= 5.9 × 1013 cm−2) reaches about a half of Ns, and thus, the scattering between photocarriers effectively occurs, leading to the clear spectral observation of carrier population excited by the scattering as shown in Figure 2a. The obtained value of Ns is comparable to the previously reported value (5.84 × 1013 and 8.16 × 1014 cm−2 for 2−4 and 9−11 layers of graphene, respectively) and orders of magnitude larger than that in a 10nm-thick GaAs quantum well.34 The ultrafast decay of carrier population and the large saturation density are of importance for ultrafast optical switching utilizing the optical nonlinearity induced by carrier excitation. Therefore, graphene has potential application in ultrafast optical switching devices.

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CONCLUSIONS In summary, we observed transient absorption spectra of monolayer graphene excited by the near-infrared pulses. It was demonstrated that the carrier excitation by the intraband scattering between photocarriers, that is, wide-range two-step excitation triggered by one-photon absorption, effectively occurs in graphene. The high saturation density and ultrafast decay of carriers indicate that the potential of graphene to be used in ultrafast optical switching devices in the visible region operated even by the infrared-pulse irradiation using most available ultrafast laser systems such as Ti:sapphire lasers. D

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