Ultrafast Spectral Photoresponse of Bilayer Graphene: Optical Pump

Jan 8, 2018 - Photoinduced terahertz conductivity Δσ(ω) of Bernal stacked bilayer graphene (BLG) with different dopings is measured by time-resolve...
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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 ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b08555 • Publication Date (Web): 08 Jan 2018 Downloaded from http://pubs.acs.org on January 8, 2018

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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 E-mail: [email protected] Abstract Photoinduced terahertz conductivity ∆σ(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 ∆σ(ω) (∆σRe (ω)) is positive throughout the spectral range 0.5-2.5 THz in low doped BLG. This is in sharp contrast to ∆σ(ω) for high doped bilayer graphene where ∆σRe (ω) is negative on low frequency and positive on the high frequency side. We use Boltzmann transport theory to understand quantitatively the frequency dependence of ∆σ(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 ACS Paragon Plus Environment

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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 K to 4K, without any empirical fitting procedures adopted so far in the literature. This helps to understand intraband conductivity of photo-excited hot carriers in 2D materials.

Keywords bilayer graphene, photoinduced terahertz conductivity, optical pump-terahertz probe, doping, short-range scattering.

In 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 distribution 1,3 with carrier temperature Te and a quasi Fermi level, followed by subsequent carrier cooling by transferring energy to the lattice, studied theoretically 3–5 and experimentally 6,7 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 next step of cooling, elastic acousticphonon emission lasting around tens of ps or defect mediated inelastic high energy and high momentum acoustic phonon emission (supercollision process) 8,9 occurs lasting for a few ps. 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 response 9–11 of hot carriers and non-linear THz conductivity. 12–14 In contrast, there are limited studies on carrier dynamics of photoexcited bilayer graphene 15,16 using optical probe. The intraband spectral response to terahertz radiation is not explored so far. At this point, it is important to mention that though there are many experimental studies on the photo-generated carrier relaxation in single layer graphene, the quantitaACS Paragon Plus Environment

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tive understanding of the spectral dependence of dynamic conductivity ∆σ(ω) (∆σ(ω) = σ(ω)|pump on −σ(ω)|pump off ) is still lacking. In most of these studies, simple Drude model with an average momentum relaxation time is used to interpret the photo-conductivity spectra. For example, Jnawali et al. 10 semi-qualitatively argued that the negative photo-conductivity in SLG is due to increase of scattering rate of the hot carriers which can explain the real part of ∆σ(ω) (∆σRe (ω)) but not the imaginary part. In comparison, Docherty et al. 11 observed negative ∆σRe (ω) which was fitted by a Lorentzian function with negative amplitude. In our previous work, we also have fitted our data of ∆σ(ω) by Drude model along with an empirical Lorentzian function, both having negative amplitudes. 9 The origin of negative amplitude in 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 limits the time duration of population inversion to be within 130 fs after photoexcitation. Thus the spectral dependence of ∆σ(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 K to 300 K. Different kinds of intraband scattering phenomena have been quantitatively evaluated, showing that shortrange 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 semi-classical Boltzmann approach. Here we present results for two different kinds of BLG samples: one having low Fermi energy and high defect density (LFHD) and other having comparatively higher Fermi energy and low defect density (HFLD). Our numerically derived photoconductivity spectra agree very well with the experimental photo-conductivity 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. ACS Paragon Plus Environment

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Results and Discussions

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 0.5-2.5 THz.

Raman Spectra We start by comparing Raman spectra of HFLD and LFHD, recorded using excitation wavelength 532 nm, as shown in Figures 1(a-b).PlusThe bands centered at 1589 cm−1 (FWHM ACS Paragon Environment 4

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∼ 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 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 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 bi-layers. 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.

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 Figures 1(c-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 Figures 1(e-f), is calculated by using 9 σ(ω) =

1 ns +1 ( S(ω) Z0

− 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 G0 ) (G0 =

2e2 h

= 77 µS is quantum of conductance) and it 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 ACS Paragon Plus Environment

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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 Figures 1(e-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.

Figure 2: (a-b) ∆T /T (t2 ) for (a) HFLD and (b) LFHD at the peak of transmitted terahertz signal of unexcited BLG. (c-d) The change of terahertz transmission throughout the terahertz fields obtained at 3.8 ps and 2.7 ps after photoexcitation in (c) HFLD and (d) LFHD, respectively. (e-f) Corresponding photoinduced complex conductivity, ∆σ(ω) for (e) HFLD and (f) LFHD. Open (closed) circles represent real (imaginary) part of ∆σ(ω). ACS Paragon Plus Environment

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Photoinduced Conductivity Spectra The main goal of this paper is to understand the spectral response of dynamic terahertz photo-conductivity after photo-excitation with 800 nm optical pump. In general, just after photo-excitation 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 fs followed by defect assisted acoustic phonon emission (called supercollision) occurs within a few ps. 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 rise of electron temperature to maintain the total charge carrier density. Figures 2(a-b) show the temporal change of terahertz transmission ∆T (t2 )/T probed at the peak of terahertz fields TBLG (t1 ), obtained by varying the pump delay line t2 . ∆T (t2 )/T is positive in HFLD and negative in LFHD i.e., after photo injection of hot carriers THz transmission increases in HFLD and decreases in the other one.The solid black lines are fits 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 we record the photoinduced change of terahertz transmission ∆T (t1 ) throughout the terahertz pulse at a fixed time delay t2 after arrival of the pump pulse. This is shown in Figures 2(c-d) (t2 = 3.8 ps for HFLD and t2 = 2.7 ps for LFHD). The transmitted spectra are converted to photoinduced conductivity 9 ∆T (ω)/T (ω) (Figures 2(e-f)). The real part of complex photo-conductivity ∆σ(ω) = − nZs +1 0 ∆σ(ω) of LFHD shows spectrally independent increase of conductivity, as was in unexcited state (Figure 2f). In comparison, HFLD shows interesting spectral dependence of ∆σ(ω) (Figure 2e). The ∆σRe (ω) is negative at low frequency region and positive at high frequency region, while imaginary part of ∆σ(ω) (∆σIm (ω)) is completely negative. To the best of our ACS Paragon Plus Environment

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knowledge this kind of intraband spectral response has not been observed in graphene so far. The solid lines in Figures 2(e-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 ∆σ(ω) at 2.8 ps after photoexcitation, with open circles showing the real part and closed circle showing the imaginary part, at lattice temperatures 300K, 100K and 4K. We note that the spectral dependence is quite similar at all the temperatures, only difference being that the amplitude of ∆σRe (ω) on the low frequency side increases on cooling.

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

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Theoretical Modeling We have employed semi-classical Boltzmann transport theory to explain the spectral dependence of the photo-induced conductivity ∆σ(ω), given by 21

∆σ(ω) = σ(Te 6= TL , ω) − σ(Te = TL , ω),

e2 where σ(Te , Tl , ω) = 2

Z 0

∞

(1)

  df (, Te ) 1 2 v − d, g() −1 τ (, Te , Tl ) − iω k d

(2)

is the group velocity of the charge carriers. f (EF , Te ) = [1 + exp{β( − EF )}]−1 P with β = 1/(kB Te ) is Fermi Dirac distribution function. g() = k0 δ( − k0 ) is density of p states (DOS), and energy dispersion is taken to be || = (¯ hvF k)2 + (γ/2)2 ± (γ/2), ‘+’ sign

Here vk =

1 d ¯ dk h

is for the upper conduction band and ‘−’ sign is for the lower conduction band, γ = 0.39 eV is the interlayer hopping energy between A and B sublattices of the bilayer. In all 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 carrierdefect scattering in BLG is given by 23

−1 (k ) τsr

1 = 2π¯ h

Z Z

qdq dθ ni V02 (1 − cos θ)δ(k − k0 )

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(1 + cos 2θ) , 2

(3)

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where, wavevector q = |k − k0 |, θ ≡ θkk0 is angle between k and k0 , ni is the density of short −1 is independent of Fermi range disorder per unit area, V0 is the disorder potential. Here τsr

energy position and carrier temperature and is only dependent on ni and V0 . The above −1 = expression can be solved analytically giving the relation τsr

ni V02 2 2π¯ h3 vF

(π + 83 )(k ∓ γ2 ). The

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

ni V02 2 k 4¯ h3 vF

−1 i.e.,τsr is

−1 → 0 as k → 0. again a linear function of k but τsr

Long-Range Coulomb Scattering For Coulomb impurity scattering of the photoexcited carriers, arising from the trapped charged impurities in the underlying substrate 22 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)/(κq) 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 τC−1 for different scatterer densities are shown in Figure 4b for Fermi energy 60 meV and 300 −1 K temperature. Please note that unlike τsr , τC−1 decreases with energy. In comparison to

single layer graphene, 23 where τC−1 → ∞ as  → 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 is 27,28

−1 τap (k )

1 = 2π¯ h

Z Z

qdq dθ (1 − cos θ)|C(q)|2

1 − f (k0 ) ∆kk0 1 − f (k )

where ∆kk0 = Nq δ( k0 + Plus h ¯ ωqEnvironment ) + (Nq + 1)δ(k − k0 − h ¯ ωq ), k − ACS Paragon 10

(4)

(5)

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where ωq = vph q is the acoustic phonon energy, vph = 2 × 104 m/s being the acoustic phonon velocity, 27 and Nq is the phonon occupation number given by Nq =

1 . exp(β¯ hωq )−1

The first

term (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 by 27,28

|C(q)|2 =

D2h ¯ q (1 + cos 2θ) . 2ρm vph 2

(6)

Here D is the deformation-potential coupling constant, ρm is the graphene mass density. For single layer graphene, in high-temperature regime where equi-partitioning of the acoustic −1 is simply proportional to k T i.e., phonons Nq = kB T /¯ hωq applies, the scattering rate τap −1 −1 has a nonzero vanishes in the limit of k → 0. In comparison, as shown in Figure 4c, τap τap

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 non-monotonic increase −1 with k is similar to SLG. At low temperature T < TBG , TBG = 2kF vph h ¯ /kB being of τap −1 at k = EF characteristic Bloch-Gr¨ uneisen temperature (here TBG ∼77 K), 27 a dip in τap

(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 Bloch Gr¨ uneisen temperature. It is important to note that the carrier-acoustic phonon scattering rate is comparable to shortrange 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 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 −1 comparable to short-range and acoustic phonon scattering rate. The scattering rate τop is

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given by 30

−1 τop (k )

 −2qd  Z Z e (1 + cos 2θ) 1 1 2 = qdq dθ Fν (1 − cos θ) 2π¯h (1 + qs /q)2 q 2   × Nν δ(k − k0 + h ¯ ων ) + (Nν + 1)δ(k − k0 − h ¯ ων )

(7)

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

h ¯ ων = 2



 1 1 − . εhigh + ε0 εlow + 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(β¯ hων ) − 1)−1 is the equilibrium phonon occupation number. q is scattered phonon wavevector, qs is Thomas-Fermi scattering wavenumber, given by 24 qs = 2e2 γ/εavg h ¯ 2 vF2 for bilayer graphene. Figure 4d shows the energy dependence of the phonon scattering rate at different lattice temperatures. −1 −1 −1 , τC−1 and τap is very low (in the range of ns−1 ) as compared to τsr It reveals that the τop

due to very high screening effect. Hence, we neglect its contribution in effective scattering rate. Therefore, the effective scattering rate is obtained as 1 1 1 1 1 ≡ = + + τ () τ (k ) τsr (k ) τC (k ) τap (k )

(9)

Using Eqs. [1-9], the conductivity spectra σ(ω) of HFLD are calculated in photoexcited state(Te > Tl , the orange lines in supporting information Figure S1) and unexcited state (Te = Tl , the green lines in supporting information Figure S1), and then ∆σ(ω) is obtained by using Eq. 1. The parameters are optimized to fit the calculated ∆σ(ω) to our experimental data. Figure 3 shows the comparison of calculated and experimental ∆σ(ω) at lattice temperatures 4K, 100K and 300K. It can be seen that the theoretical ∆σ(ω) (both real and imaginary parts) agree well with the measured response of hot carriers to terahertz radiation. ACS Paragon Plus Environment

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−1 Figure 4: Energy dependence of Scattering rates (a) short-range scattering rate τsr () for −1 10 −2 scatterer density 1 to 4 × 10 cm , (b) Coulomb scattering rate τC () for scatterer density −1 1 to 4 × 1010 cm−2 , (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 −1 scattering rate τop at four different lattice temperatures 4 K (red), 100 K (blue), 200 K (green), and 300 K (gray).

It is clear from Figure 3 that ∆σRe (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 ACS Paragon Plus Environment

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Figure 5: Photoinduced conductivity spectra (∆σ(ω)) for LFHD at lattice temperatures 300 K, 150 K and 4 K at 1.3 ps after photoexcitation. The open (closed) circles represent the real (imaginary) part of ∆σ(ω). Solid and dotted lines are the fits to real and imaginary parts of conductivity, respectively. rate. Therefore, the rise of carrier temperature not only shifts effective Fermi energy to lower value, but also increases the scattering rate. Both effects lead to unusual photo-conductivity spectra showing negative ∆σRe at low frequency and positive at high frequency region. In all the calculations we have taken V0 = 10 eV nm2 [Ref. 23] and deformation potential D = 20 eV. 31 All the photo-conductivity 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 , −1 and EF = 60 ± 5 meV in HFLD. Note that for EF = 60 ± 5 meV, τsr = 0.8 × 1013 s−1 , −1 τC−1 = 0.25 × 1012 s−1 , and τap = 1.6 × 1012 s−1 at 300 K, and hence the effective scattering

rate is dominated by the short-range scattering rate. In the same way, we have fitted ∆σ(ω) in LFHD as shown in Figure 5 and the corresponding σ(ω) are shown in 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 ∆σ(ω) is frequency independent, ACS Paragon Plus Environment

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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 −1 = 6 × 1013 s−1 , density such as nd = 1 × 1011 cm−2 and find that for EF = 10 ± 5 meV τsr −1 τC−1 = 7 × 1012 s−1 , and τap = 1.3 × 1012 s−1 . This again shows that the effective scattering

rate is dominated by the short-range scattering rate. The relative contributions of shortrange scattering vis-a-vis acoustic phonon scattering in determining ∆σ(ω) for different Fermi levels have been calculated and discussed in supporting information (S -II, Figures S3-S5). We also calculated σ(ω) in the unexcited state as plotted in Figures 1(e-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 ∆σ(ω) are fitted as shown in Figure S6a for HFLD and Figure S6b for LFHD in the supporting information at 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 ∆σ(ω) at different delay times are plotted along with ∆T /T (t2 ) in Figures 2(a-b). This shows that the relaxation of Te (t) is also exponential with the same delay time as obtained for ∆T /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 semi-classical microscopic approach clearly shows that 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 photo-conductivity in ACS Paragon Plus Environment

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bilayer graphene. This insight will be helpful in designing different ultrafast devices using bilayer graphene.

Methods Preparation of HFLD Bilayer Graphene Samples Single-crystalline monolayer graphene was synthesized on Cu (111) film via chemical vapor deposition method at atmospheric pressure. Cu substrate was annealed for 2h 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 0.1M 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 ACS Paragon Plus Environment

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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

Terahertz Measurements To study the spectral dependent dynamic terahertz response of hot carriers in photo-injected 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 electro-optic 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), ACS Paragon Plus Environment

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with temperature accuracy of 0.1 K.

Acknowledgement AKS thanks Nano Mission Project under Department of Science and Technology, India for funding. YHL 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.

Supporting Information Available • S-I: Calculated σ(Te , ω) before and after photoexcitation are shown in Figure S1 for HFLD and in Figure S2 for LFHD. • S-II: The individual contributions of short-range scattering and acoustic phonon scattering in ∆σ(ω) for different Fermi levels are discussed and shown in Figures S3-S5. • S-III: Figure S6 shows ∆σ(ω) at different delay times after photoexcitation.

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