Optical Pump-Terahertz Probe Spectroscopy

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Ultrafast Spectral Photoresponse of Bilayer Graphene: Optical Pump−Terahertz Probe Spectroscopy Srabani Kar,†,‡ Van Luan Nguyen,¶ Dipti R. Mohapatra,† Young Hee Lee,¶,§ and A. K. Sood*,†,‡ †

Department of Physics, Indian Institute of Science, Bangalore 560 012, India Center for Ultrafast Laser Applications, Indian Institute of Science, Bangalore 560 012, India ¶ Center for Intergrated Nanostructure Physics (CINAP), Institute for Basic Science, Sungkyunkwan University, Suwon 16419, Korea § Department of Energy Science and Department of Physics, Sungkyunkwan University, Suwon 16419, Korea ‡

S Supporting Information *

ABSTRACT: Photoinduced terahertz conductivity Δσ(ω) of Bernal stacked bilayer graphene (BLG) with different dopings is measured by time-resolved optical pump terahertz probe spectroscopy. The real part of photoconductivity Δσ(ω) (ΔσRe(ω)) is positive throughout the spectral range 0.5−2.5 THz in low-doped BLG. This is in sharp contrast to Δσ(ω) for high-doped bilayer graphene where ΔσRe(ω) is negative at low frequency and positive on the high frequency side. We use Boltzmann transport theory to understand quantitatively the frequency dependence of Δσ(ω), demanding the energy dependence of different scattering rates such as short-range impurity scattering, Coulomb scattering, carrier− acoustic phonon scattering, and substrate surface optical phonon scattering. We find that the short-range disorder scattering dominates over other processes. The calculated photoconductivity captures very well the experimental conductivity spectra as a function of lattice temperature varying from 300 to 4 K, without any empirical fitting procedures adopted so far in the literature. This helps us to understand the intraband conductivity of photoexcited hot carriers in 2D materials. KEYWORDS: bilayer graphene, photoinduced terahertz conductivity, optical pump−terahertz probe, doping, short-range scattering carrier dynamics of photoexcited bilayer graphene15,16 using optical probe. The intraband spectral response to terahertz radiation has not been explored so far. At this point, it is important to mention that though there are many experimental studies on the photogenerated carrier relaxation in single-layer graphene, the quantitative understanding of the spectral dependence of dynamic conductivity Δσ(ω) (Δσ(ω) = σ(ω)|pump on − σ(ω)|pump off) is still lacking. In most of these studies, a simple Drude model with an average momentum relaxation time is used to interpret the photoconductivity spectra. For example, Jnawali et al.10 semiqualitatively argued that the negative photoconductivity in SLG is due to an increase of scattering rate of the hot carriers which can explain the real part of Δσ(ω) (ΔσRe(ω)) but not the imaginary part. In comparison, Docherty et al.11 observed negative ΔσRe(ω) which was fitted by a Lorentzian function with negative amplitude. In our previous work, we also have

I

n single layer graphene (SLG), optical excitation with a linearly polarized ultrafast optical pulse gives rise to an initially anisotropic distribution of carriers at high energies.1−3 Thereafter, strong carrier−carrier and carrier− phonon interactions quickly (around 150 fs) relax the hot carriers from anisotropic to an isotropic thermal distribution1,3 with carrier temperature Te and a quasi Fermi level, followed by subsequent carrier cooling by transferring energy to the lattice, studied theoretically3−5 and experimentally6,7 in recent years. The primary cooling takes place through emission of optical phonons within a few hundreds of femtoseconds up to around 100 meV energy. In the next step of cooling, elastic acoustic− phonon emission lasting around tens of picoseconds or defectmediated inelastic high energy and high momentum acoustic phonon emission (supercollision process)8,9 occurs, lasting for a few picoseconds. During these many-body interaction processes, the intraband dynamics of hot carriers can be observed by transmission of ultrafast terahertz pulse, showing many interesting features such as decrease or increase of terahertz absorption due to Fermi energy renormalization,9,10 non-Drude response9−11 of hot carriers, and nonlinear THz conductivity.12−14 In contrast, there are limited studies on © XXXX American Chemical Society

Received: December 2, 2017 Accepted: January 8, 2018 Published: January 8, 2018 A

DOI: 10.1021/acsnano.7b08555 ACS Nano XXXX, XXX, XXX−XXX

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Cite This: ACS Nano XXXX, XXX, XXX−XXX

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Figure 1. (a, b) Raman spectra of (a) HFLD and (b) LFHD. (c, d) THz signals transmitted through bare quartz and BLG ((c) HFLD and (d) LFHD). (e, f) Conductivity spectra, σ(ω) of (e) HFLD and (f) LFHD before photoexcitation from 0.5 to 2.5 THz.

fitted our data of Δσ(ω) by the Drude model along with an empirical Lorentzian function, both having negative amplitudes.9 The origin of negative amplitude in the Lorentzian model is far from clear, although it was suggested to be due to stimulated THz emission by population inversion from the photoexcited graphene.11,17 This suggestion is questionable because angle-resolved photoemission measurements by Gierz et al.18 limit the time duration of population inversion to be within 130 fs after photoexcitation. Thus, the spectral dependence of Δσ(ω) is still an open question to be explored in photoexcited graphene. The goal of this study is to develop a theoretical understanding of our experimentally measured photoinduced conductivity of Bernal stacked bilayer graphene (BLG), both at low and high carrier densities with lattice temperature varying from 4 to 300 K. Different kinds of intraband scattering phenomena have been quantitatively evaluated, showing that short-range disorder and carrier−acoustic phonon interactions are dominant scattering channels to describe the effective scattering rate. We numerically derive energy dependence of all the scattering rates by employing Fermi golden rule, which in turn is used to calculate the frequency dependent conductivity spectra through semiclassical Boltzmann approach. Here we present results for two different kinds of BLG samples: one having low Fermi energy and high defect density (LFHD) and the other having comparatively higher Fermi energy and low defect density (HFLD). Our numerically derived photoconductivity spectra agree very well with the experimental

photoconductivity spectra. Without invoking any empirical function, we finally draw an outline of the importance of different scattering mechanisms on terahertz conductivity spectra, which may be applicable to other 2D materials.

RESULTS AND DISCUSSION Raman Spectra. We start by comparing the Raman spectra of HFLD and LFHD, recorded using an excitation wavelength 532 nm, as shown in Figure 1a,b. The bands centered at 1589 cm−1 (fwhm ∼12 cm−1) in HFLD and 1583 cm−1 (fwhm ∼24 cm−1) in LFHD are the G bands, corresponding to the E2g phonons at the Brillouin-zone center. However, the full width at half-maximum (fwhm) of the G bands suggests that the Fermi energy of LFHD is close to the Dirac point and that of HFLD is ∼60 meV.19 The bands at ∼2692.5 cm−1 in HFLD (Figure 1a) and ∼2677.8 cm−1 (Figure 1b) in LFHD are associated with the overtone of the disorder-activated D band associated with phonons near the K-point in the Brillouin zone (called 2D modes), which depends on the number of graphene layers. The fwhm of the 2D band is ∼53 cm−1 in HFLD and ∼46 cm−1 in LFHD, and the peak intensities of the G band and 2D band are comparable. These spectra are fitted with four Lorentzians, each with a fwhm of 24 cm−1, as expected for bilayers.20 Furthermore, disorder-activated D band, associated with the phonons near the K-point of the Brillouin zone, at ∼1343 cm−1 in LFHD is completely absent in HFLD, showing negligible defect density in the latter. B


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Figure 2. (a, b) ΔT/T(t2) for (a) HFLD and (b) LFHD at the peak of transmitted terahertz signal of unexcited BLG. (c, d) Change of terahertz transmission throughout the terahertz fields obtained at 3.8 and 2.7 ps after photoexcitation in (c) HFLD and (d) LFHD, respectively. (e, f) Corresponding photoinduced complex conductivity, Δσ(ω) for (e) HFLD and (f) LFHD. Open (closed) circles represent real (imaginary) part of Δσ(ω).

Photoinduced Conductivity Spectra. The main goal of this paper is to understand the spectral response of dynamic terahertz photoconductivity after photoexcitation with an 800 nm optical pump. In general, just after photoexcitation in graphene, strong carrier−carrier scattering occurs and the photoexcited carriers thermalize to a quasi-equilibrium state with a very high carrier temperature, Te, and a well-defined Fermi level, EF. Subsequent cooling of hot carriers occurs through optical phonon emission within hundreds of femtoseconds followed by defect-assisted acoustic phonon emission (called supercollision) occurs within a few picoseconds.9 Hence, in the following sections, we take the hot carriers to be distributed maintaining the Fermi−Dirac distribution with a higher electron temperature Te than the lattice temperature (Te > TL). The electron temperature Te decreases with time to equilibrate to the lattice temperature Tl. We also take into account the shift of the Fermi energy due to the rise of electron temperature to maintain the total charge carrier density. Figure 2a,b show the temporal change of terahertz transmission ΔT(t2)/T probed at the peak of terahertz fields TBLG(t1), obtained by varying the pump delay line t2. ΔT(t2)/T is positive in HFLD and negative in LFHD, i.e., after photoinjection of hot carriers THz transmission increases in HFLD and decreases in the other one. The solid black lines are fit to data by exponential function ∝ exp(−t2/τ2), where the relaxation time τ2 is 3 ± 0.1 ps for HFLD, and 1.4 ± 0.1 ps for LFHD, comparable to their values in single layer graphene. We now study the intraband spectral response in detail, for which

Time Domain Terahertz Spectroscopy of BLG Prior to Photoexcitation. Next, we simultaneously measure the terahertz electric fields, TBLG(t1) passing through BLG on quartz substrate and TQuartz(t1) through the same bare quartz substrate by varying the terahertz detection delay line t1, shown in Figure 1c,d. HFLD exhibits measurable absorption due to higher free carrier density while LFHD shows negligible absorption of terahertz fields as expected for low doping. The spectral dependence of transmission is obtained by S(ω) = | TBLG(ω)|/|TQuartz(ω)|, where TBLG(ω) and TQuartz(ω) are the Fourier transforms of TBLG(t1) and TQuartz(t1), respectively. The real part of conductivity, as shown in Figure 1e,f, is calculated by using9 σ(ω) =

ns + 1 Z0

(

1 S(ω)

)

− 1 , where ns = 2.2 is the

refractive index of quartz substrate, taken to be independent of frequency in the terahertz range and Z0 = 377 Ω is impedance of free space. In HFLD, at low frequency σ(ω) is large (∼10 2e 2

G0) (G0 = h = 77 μS is quantum of conductance) and decreases with frequency, indicating that the scattering rate is low so that the carriers can respond to the oscillatory THz fields. In comparison, conductivity σ(ω) for LFHD is ∼0.7 G0 and independent of frequency. This implies that the Fermi energy is close to the Dirac point and the scattering rate (1/τ) is high, i.e., ωτ ≪ 1, τ being the average momentum relaxation time. The solid blue lines in Figure 1e,f are fits with our proposed model with Fermi energy (60 ± 5) meV in HFLD and (10 ± 5) meV in LFHD and will be discussed later. C


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σ(Te , Tl , ω) =

0

e2 2

∞

1 τ −1(ϵ, Te , Tl) − iω ⎛ df (ϵ, Te) ⎞ vk2⎜ − ⎟d ϵ ⎝ dϵ ⎠

∫0

g (ϵ)

(2)

1 dϵ

Here, v k = ℏ dk is the group velocity of the charge carriers. f(EF, Te) = [1 + exp{β(ϵ − EF)}]−1 where β = 1/(kBTe) is Fermi Dirac distribution function. g(ϵ) = ∑k′δ(ϵ − ϵk′) is the density of states (DOS), and energy dispersion is taken to be

complex photoconductivity Δσ(ω) of LFHD shows a spectrally independent increase of conductivity, as in the unexcited state (Figure 2f). In comparison, HFLD shows interesting spectral dependence of Δσ(ω) (Figure 2e). The ΔσRe(ω) is negative at the low-frequency region and positive at the high-frequency region, while the imaginary part of Δσ(ω) (ΔσIm(ω)) is completely negative. To the best of our knowledge, this kind of intraband spectral response has not been observed in graphene so far. The solid lines in Figure 2e,f are the calculated values, which will be discussed later. To understand this unusual spectral features, we measured the photoinduced change by varying the lattice temperature. Figure 3 shows complex Δσ(ω)

|ϵ| = (ℏvFk)2 + (γ /2)2 ± (γ /2), “+” indicates the upper conduction band, “−” indicates the lower conduction band, and γ = 0.39 eV is the interlayer hopping energy between A and B sublattices of the bilayer. In all of the calculations, we have neglected the contribution from upper conduction band since in our samples Fermi energy lies far from the upper conduction band minima or lower valence band maxima. Please note that eq 2 has energy-dependent scattering rates which will be computed. The effective scattering rate includes short-range scattering from charge neutral defects, Coulomb scattering, acoustic phonon scattering, and substrate surface (quartz) polar optical phonon scattering (see eq 9). In the following sections, we will discuss different scattering mechanisms and their dependence on carrier energy. Short-Range Scattering from Charge-Neutral Defects. Short-range scattering of photoexcited carriers arises from neutral impurities such as structural defects, dislocation lines, or adatoms.22 The scattering rate due to short-range carrier-defect scattering in BLG is given by23 τsr−1(ϵk ) =

1 q dq dθniV02(1 − cos θ )δ(ϵk − ϵk ′) 2π ℏ (1 + cos 2θ ) (3) 2

∫∫

where wavevector q = |k − k′|, θ ≡ θkk′ is the angle between k and k′, ni is the density of short-range disorder per unit area, and V0 is the disorder potential. Here τ−1 sr is independent of Fermi energy position, and carrier temperature and is only dependent on ni and V0. The above expression can be solved analytically giving the relation τsr−1 =

Figure 3. Photoinduced conductivity spectra (Δσ(ω)) of HFLD at lattice temperatures of 300, 100 and 4 K at 2.8 ps after photoexcitation. The open (closed) circles represent the real (imaginary) part of Δσ(ω). Solid and dotted lines are the fits to real and imaginary parts of conductivity, respectively.

2π ℏ3vF2

(π + 83 )(ϵk ∓ 2γ ).

The scattering rate increases linearly with energy shown in Figure 4a. A finite density of states close to the Dirac point leads to nonzero finite value of τ−1 sr at ϵk → 0. In comparison, the scattering rate due to short-range impurity in SLG is given by τsr−1(ϵk ) =

niV02 ϵ 4ℏ3vF2 k

i.e., τ−1 sr is again a linear function of ϵk but

τ−1 sr → 0 as ϵk → 0. Long-Range Coulomb Scattering. For Coulomb impurity scattering of the photoexcited carriers, arising from the trapped charged impurities in the underlying substrate22 as well as oxygen functional group, the scattering rate can be obtained from eq 3 by replacing V0 by |V(q)/εq|, where V(q) = 2πe2 exp(−qd)/(κ q) is the Fourier transform of 2D Coulomb potential in an effective background lattice dielectric constant κ. Here εq ≡ εq(T) = 1 + V(q)Π(q, T) is the 2D finite temperature static RPA dielectric function. Π(q, T) is the irreducible finite temperature polarizability function taken from refs 24−26. The calculated Coulomb scattering rates τ−1 C for different scatterer densities are shown in Figure 4b for Fermi energy 60 meV and 300 K temperature. Please note that unlike

at 2.8 ps after photoexcitation, with open circles showing the real part and closed circle showing the imaginary part, at lattice temperatures 300, 100, and 4 K. We note that the spectral dependence is quite similar at all the temperatures, only difference being that the amplitude of ΔσRe(ω) on the low frequency side increases on cooling. Theoretical Modeling. We have employed semiclassical Boltzmann transport theory to explain the spectral dependence of the photoinduced conductivity Δσ(ω), given by21 Δσ(ω) = σ(Te ≠ TL , ω) − σ(Te = TL , ω)

niV02

(1)

where D


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10 −2 Figure 4. Energy dependence of scattering rates (a) short-range scattering rate τ−1 sr (ϵ) for scatterer density 1 to 4 × 10 cm , (b) Coulomb −1 −1 10 −2 scattering rate τC (ϵ) for scatterer density 1 to 4 × 10 cm , (c) acoustic phonon scattering rate τap at four different lattice temperatures 4 K (red), 100 K (blue), 200 K (green), and 300 K (gray), (d) surface polar phonon scattering rate τ−1 op at four different lattice temperatures 4 K (red), 100 K (blue), 200 K (green), and 300 K (gray).

−1 τ−1 sr , τC decreases with energy. In comparison to single layer graphene,23 where τ−1 C → ∞ as ϵ → 0, BLG shows finite value due to finite density of states at the Dirac point. Acoustic-Phonon Scattering. We now turn to the case of electron-acoustic phonon scattering which can be treated as a quasi-elastic process. The energy dependence of the scattering rate is27,28

1 q dq dθ(1 − cos θ ) 2π ℏ 1 − f (ϵk ′) |C(q)|2 Δkk ′ 1 − f (ϵ k )

τap−1(ϵk ) =

|C(q)|2 =

(6)

Here, D is the deformation-potential coupling constant, and ρm is the graphene mass density. For single-layer graphene, in a high-temperature regime where equi-partitioning of the acoustic phonons Nq = kBT/ℏωq applies, the scattering rate −1 τ−1 ap is simply proportional to ϵkT, i.e., τap vanishes in the limit of ϵk → 0. In comparison, as shown in Figure 4c, τ−1 ap has a nonzero finite value in the vicinity of Dirac point for bilayer graphene. This arises again from the finite density of states at the Dirac point. Other than that, the trend of nonmonotonic increase of τ−1 ap with ϵk is similar to that of SLG. At low temperature, T < TBG, where TBG = 2kFvphℏ/kB is the characteristic Bloch−Grüneisen temperature (here, TBG ∼ 77 K)27 and a dip in τ−1 ap at ϵk = EF (taken to be 60 meV in the calculations) originates from limited phase space for phonon scattering due to freezing out of short wavelength phonons and sharpening of Fermi surface,28 resulting in extremely long-lived quasi-particles below the Bloch−Grüneisen temperature. It is important to note that the carrier-acoustic phonon scattering rate is comparable to short-range scattering rate at low defect density and hence has non-negligible contribution in determining effective carrier-scattering rate. Surface-Optical Phonon Scattering. The BLG samples in our studies are placed on top of SiO2 substrate. For such a substrate, its bulk transverse optical (TO) phonons contribute

∫∫

(4)

where Δkk ′ = Nqδ(ϵk − ϵk ′ + ℏωq ) + (Nq + 1)δ (ϵk − ϵk ′ − ℏωq )

D2ℏq (1 + cos 2θ ) 2ρm vph 2

(5)

where ωq = vphq is the acoustic phonon energy, vph = 2 × 104 m/s is the acoustic phonon velocity,27 and Nq is the phonon 1 occupation number given by Nq = exp(βℏω ) − 1 The first term q

(second term) in eq 5 corresponds to the absorption (emission) of an acoustic phonon of wave vector q. C(q) is the matrix element for scattering of carriers by acoustic phonons, given by27,28 E


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12 −1 × 1012 s−1, and τ−1 at 300 K, and hence, the ap = 1.6 × 10 s effective scattering rate is dominated by the short-range scattering rate. In the same way, we have fitted Δσ(ω) in LFHD as shown in Figure 5, and the corresponding σ(ω) are shown in the

to the carrier scattering. We now consider the scattering of carriers by polar surface optical phonons of the substrate. We consider this interaction because surface-optical phonon scattering rate in SLG, as shown in ref 29, is comparable to short-range and acoustic phonon scattering rate. The scattering 30 rate τ−1 op is given by −1 (ϵ k ) = τop

1 2π ℏ

∫ ∫ q dq dθFν2(1 − cos θ) (1 + 1q /q)2 s

⎛ e−2qd ⎞ (1 + cos 2θ ) [Nνδ(ϵk − ϵk ′ + ℏων) ⎟ ⎜ 2 ⎝ q ⎠ + (Nν + 1)δ(ϵk − ϵk ′ − ℏων)]

(7)

where d = 3.14 Å is the distance of graphene layer above the substrate, ων = 59 meV is the frequency of substrate optical phonon, and Fν is the electron−phonon coupling parameter given by Fν2 =

⎞ ℏων ⎛ 1 1 ⎜⎜ ⎟ − εlow + ε0 ⎟⎠ 2 ⎝ εhigh + ε0

(8)

Here, εhigh (εlow) is high (low) frequency dielectric permittivity of the substrate, εavg = (εhigh + εlow)/2, and ε0 is free space permittivity. Nν = (exp(βℏων) − 1)−1 is the equilibrium phonon occupation number. q is scattered phonon wavevector, qs is Thomas−Fermi scattering wavenumber, given by24 qs = 2e2γ/εavgℏ2v2F for bilayer graphene. Figure 4d shows the energy dependence of the phonon scattering rate at different lattice temperatures. −1 It reveals that the τ−1 op is very low (in the range of ns ) as −1 −1 compared to τ−1 , τ , and τ due to a very high screening sr C ap effect. Hence, we neglect its contribution in effective scattering rate. Therefore, the effective scattering rate is obtained as 1 1 1 1 1 ≡ = + + τ(ϵ) τ (ϵ k ) τsr(ϵk ) τC(ϵk ) τap(ϵk )

Figure 5. Photoinduced conductivity spectra (Δσ(ω)) for LFHD at lattice temperatures of 300, 150 and 4 K at 1.3 ps after photoexcitation. The open (closed) circles represent the real (imaginary) part of Δσ(ω). Solid and dotted lines are the fits to real and imaginary parts of conductivity, respectively.

Supporting Information (Figure S2). The values of V0 and D are taken to be same as for HFLD. The fitted parameters are ni = (0.9 ± 0.2) × 1011 cm−2, one order larger than for HFLD and EF = 10 ± 5 meV. As measured Δσ(ω) is frequency independent, it is difficult to estimate value of Coulomb impurity scatterer density. To compare with short-range scattering we can introduce a similar number of long-range Coulomb scatterer density such as nd = 1 × 1011 cm−2 and find 13 −1 −1 12 −1 that for EF = 10 ± 5 meV τ−1 sr = 6 × 10 s , τC = 7 × 10 s , −1 12 −1 and τap = 1.3 × 10 s . This again shows that the effective scattering rate is dominated by the short-range scattering rate. The relative contributions of short-range scattering vis-à-vis acoustic phonon scattering in determining Δσ(ω) for different Fermi levels have been calculated and discussed in the Supporting Information (Figures S3−S5). We also calculated σ(ω) in the unexcited state as plotted in Figure 1e,f using the fitted parameters. It can be seen that calculated real σ(ω) in unexcited state (blue solid line) shows good agreement with the experimental data in both the BLG samples. At different delay time t2 after photoexcitation, complex Δσ(ω) are fitted as shown in Figure S6a for HFLD and Figure S6b for LFHD in the Supporting Information at a lattice temperature 300 K and a fluence of 340 μJ/cm2. In these calculations, the carrier temperature Te is varied as a function of delay time and all other parameters are kept fixed. The rise of carrier temperature (Te − Tl) thus obtained from the fitted Δσ(ω) at different delay times are plotted along with ΔT/T(t2)

(9)

Using eqs 1−9, the conductivity spectra σ(ω) of HFLD are calculated in photoexcited state(Te > Tl, orange lines in Supporting Information Figure S1) and unexcited state (Te = Tl, green lines in Supporting Information Figure S1), and then Δσ(ω) is obtained by using eq 1. The parameters are optimized to fit the calculated Δσ(ω) to our experimental data. Figure 3 shows the comparison of calculated and experimental Δσ(ω) at lattice temperatures 4, 100, and 300 K. It can be seen that the theoretical Δσ(ω) (both real and imaginary parts) agree well with the measured response of hot carriers to terahertz radiation. It is clear from Figure 3 that ΔσRe(ω) decreases (increases) at low (high) frequencies. The frequency at which real and imaginary parts of the conductivity cross each other (shown by stars in Supporting Information Figure S1), gives an estimate of the average scattering rate. Therefore, the rise of carrier temperature not only shifts the effective Fermi energy to lower value but also increases the scattering rate. Both effects lead to unusual photoconductivity spectra showing negative ΔσRe at low frequency and positive at high frequency region. In all of the calculations we have taken V0 = 10 eV nm2 (ref 23) and deformation potential D = 20 eV.31 All the photoconductivity spectra are fitted by taking short-range scatterer density ni = (1.0 ± 0.2) × 1010 cm−2, long-range scatterer density nd = 1.0 × 1010 cm−2, and EF = 60 ± 5 meV in HFLD. 13 −1 −1 Note that for EF = 60 ± 5 meV, τ−1 sr = 0.8 × 10 s , τC = 0.25 F


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Terahertz Measurements. To study the spectral dependent dynamic terahertz response of hot carriers in photoinjected graphene, we utilize time-resolved terahertz spectroscopy which has been proven to be a powerful probe of intraband transport phenomena.9,33,34 The graphene is excited by laser pump pulses of ∼50 fs centered at 800 nm. The spectral dependence of dynamic terahertz response is monitored by single cycle THz probe pulse at a fixed delay time after arrival of the optical pump. The transmitted THz probe is detected by using electrooptic sampling using 1 mm thick ZnTe crystal and the complete field is scanned by varying the probe delay line t1. To scan the transmitted terahertz fields either from unexcited or photoexcited sample, the probe delay line t1 was used. To measure the temporal decay of photoinduced change, the pump delay line t2 was scanned. The chopper was placed in the terahertz generation path to measure the unexcited spectra, whereas it was placed in the optical pump path to measure the photoinduced change of transmission.9,35 Temperature dependent experiments were performed by using continuous flow cryostat (Oxford model microstat He2), with temperature accuracy of 0.1 K.

in Figure 2a,b. This shows that the relaxation of Te(t) is also exponential with the same delay time as obtained for ΔT/T(t2).

CONCLUSIONS In summary, the response of the photoexcited hot carriers to terahertz fields in low and moderately doped bilayer graphene deposited on quartz substrate can be quantitatively understood by taking into account the energy dependence of different scattering rates to obtain the generalized frequency dependent conductivity spectrum. The relaxation dynamics is dominated by carrier−disorder interaction along with carrier−acoustic phonon interactions, as compared to charge-impurity Coulomb interaction or carrier−surface phonon interaction. Our semiclassical microscopic approach clearly shows that in the shift of the Fermi energy with transient electron temperature Te dominant scattering channels and their dependence on temperature are all essential to capture the spectral dependence of photoconductivity in bilayer graphene. This insight will be helpful in designing different ultrafast devices using bilayer graphene.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b08555. Calculated σ(Te, ω) before and after photoexcitation are shown in Figure S1 for HFLD and in Figure S2 for LFHD; individual contributions of short-range scattering and acoustic phonon scattering in Δσ(ω) for different Fermi levels are discussed and shown in Figures S3−S5; Δσ(ω) at different delay times after photoexcitation (Figure S6) (PDF)

METHODS Preparation of HFLD Bilayer Graphene Samples. Singlecrystalline monolayer graphene was synthesized on Cu (111) film via chemical vapor deposition method at atmospheric pressure. Cu substrate was annealed for 2 h with 1000 sccm Ar and 200 sccm H2 at 1060 °C. During graphene growth, H2 gas was reduced to 50 sccm and 25 sccm of CH4 (0.1% diluted in Ar) was injected for atmospheric CVD growth. After 25 min growth, CH4 gas was finally turned off, followed by cooling to room temperature. As a consequence, monolayer single-crystalline graphene was obtained on Cu film. PMMA was then spin-coated on graphene/Cu substrate (2500 rpm, 1 min). The PMMA/graphene film was detached away from Cu film by a bubbling transfer using 0.1 M NaOH electrolyte and then submerged into distilled water to clean the residuals. The PMMA/graphene film was then suspended on a holder, which was clamped onto the arm of a micromanipulator mounted on an optical microscope. Another graphene/Cu substrate was placed on movable and rotable stage such that both graphene layers face directly onto each other and no polymer residues remain at the interface. The top graphene was aligned with bottom graphene by optical microscope. The relative misorientation angle between both graphene layers was controlled by rotable stage and was close to 0° ± 0.1°. After finishing the alignment, PMMA/graphene film was moved down slowly to overlap with graphene/Cu substrate and the stage was heated up to 150 °C to dissolve PMMA which eventually enhance adhesion of two graphene layers. Cu substrate was etched away, and the overlapped bilayer graphene was transferred to both sides polished quartz substrate by conventional transfer method. Similarly prepared AB-stacked BLG samples have been extensively characterized using angle-resolved photoemission spectroscopy, quantum Hall effect, self-consistent effective mass characterization, and transmission electron microscopy and are described in our published work.32 Preparation of LFHD Bilayer Graphene Samples. LFHD was grown by chemical vapor deposition method on 25 μm thick properly cleaned copper foil using acetone, acetic acid, deionized water, isopropyl alcohol, and methanol successively. In order to remove the oxides and chemical residues, the copper substrates were heated at 1000 °C for 30 min in the presence of hydrogen at a pressure of 20 Torr. Subsequently, methane was flowed into the chamber and graphene growth was continued for 30 min keeping hydrogen and methane at a fixed ratio of 2:3, followed by cooling at a rate of 20 °C/ min for first 20 min without changing the hydrogen flow rate. Then, the system was cooled by a normal fan up to a temperature of 350 °C in 1 h, followed by natural cooling to room temperature. The graphene was transferred onto the 1 mm thick quartz substrate by means of the standard PMMA technique.9

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Young Hee Lee: 0000-0001-7403-8157 A. K. Sood: 0000-0002-8652-1389 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS A.K.S. thanks the Nano Mission Project under the Department of Science and Technology, India, for funding. Y.H.L. acknowledges the financial support by the Institute for Basic Science of Korea (IBS-R011-D1), Republic of Korea. We thank Mithun K. P. and Vikas Arora for their help in experiments. REFERENCES (1) Mittendorff, M.; Winzer, T.; Malic, E.; Knorr, A.; Berger, C.; de Heer, W. A.; Schneider, H.; Helm, M.; Winnerl, S. Anisotropy of Excitation and Relaxation of Photogenerated Charge Carriers in Graphene. Nano Lett. 2014, 14, 1504−1507. (2) George, P. A.; Strait, J.; Dawlaty, J.; Shivaraman, S.; Chandrashekhar, M.; Rana, F.; Spencer, M. G. Ultrafast OpticalPump Terahertz-Probe Spectroscopy of the Carrier Relaxation and Recombination Dynamics in Epitaxial Graphene. Nano Lett. 2008, 8, 4248−4251. (3) Sun, D.; Divin, C.; Mihnev, M.; Winzer, T.; Malic, E.; Knorr, A.; Sipe, J. E.; Berger, C.; de Heer, W. A.; First, P. N.; Norris, T. B. Current Relaxation Due to Hot Carrier Scattering in Graphene. New J. Phys. 2012, 14, 105012. (4) Winzer, T.; Malic, E. The Impact of Pump Fluence on Carrier Relaxation Dynamics in Optically Excited Graphene. J. Phys.: Condens. Matter 2013, 25, 054201. G


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Optical Pump-Terahertz Probe Spectroscopy

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