Article www.acsnano.org Electrically Tunable Nonequilibrium Optical Response of Graphene Eva A. A. Pogna, Andrea Tomadin, Osman Balci, Giancarlo Soavi, Ioannis Paradisanos, Michele Guizzardi, Paolo Pedrinazzi, Sandro Mignuzzi, Klaas-Jan Tielrooij, Marco Polini, Andrea C. Ferrari,* and Giulio Cerullo* Cite This: ACS Nano 2022, 16, 3613−3624 Read Online ACCESS Metrics & More Article Recommendations ABSTRACT: The ability to tune the optical response of a material via electrostatic gating is crucial for optoelectronic applications, such as electro-optic modulators, saturable absorbers, optical limiters, photodetectors, and transparent electrodes. The band structure of single layer graphene (SLG), with zero-gap, linearly dispersive conduction and valence bands, enables an easy control of the Fermi energy, EF, and of the threshold for interband optical absorption. Here, we report the tunability of the SLG nonequilibrium optical response in the near-infrared (1000−1700 nm/0.729−1.240 eV), exploring a range of EF from −650 to 250 meV by ionic liquid gating. As EF increases from the Dirac point to the threshold for Pauli blocking of interband absorption, we observe a slow-down of the photobleaching relaxation dynamics, which we attribute to the quenching of optical phonon emission from photoexcited charge carriers. For EF exceeding the Pauli blocking threshold, photobleaching eventually turns into photoinduced absorption, because the hot electrons’ excitation increases the SLG absorption. The ability to control both recovery time and sign of the nonequilibrium optical response by electrostatic gating makes SLG ideal for tunable saturable absorbers with controlled dynamics. KEYWORDS: graphene, cooling dynamics, hot electrons, tunable dynamics, optical phonons, phonon bottleneck INTRODUCTION LiNbO335 and Si36 because of the superior mobility of SLG Single-layer graphene (SLG) has unique optoelectronic charge carriers, with high modulation depths both in amplitude properties,1−3 which stem from the physics of its massless (up to ∼60%)3,19,21,24,26 and phase (∼65°).3,31 Dirac fermions. These include high electron mobility SLG also exhibits large nonlinear optical response37−41 (>100 000 cm2 V−1 s−1 at room temperature (RT)4−7), because of a strong coupling to light. The third-order nonlinear broadband optical absorption,8 tunability of Fermi energy, optical susceptibility of SLG in the NIR at 0.7 eV is37 χ3 ∼ 5 × EF, via electrostatic gating,9 resulting from the linear dispersion 10−18 m2V−2, several orders of magnitude higher than in of conduction (CB) and valence bands (VB), and a vanishing dielectrics (e.g., ∼ 10−22m2V−2 for SiO242) and atomically thin density of states at the Dirac point.10 semiconductors (e.g., ∼ 6 × 10−20 m2 V−2 for single-layer Light absorption in SLG is due to the interplay of WSe243). Nonlinearities of higher order have been exploited intraband11−13 and interband14,15 transitions. In undoped for high-harmonics generation in SLG.38,39 The strong SLG, the first ones dominate in THz16 and microwaves,17 nonlinear response results also in saturable absorption,44 the second14 in near-infrared (NIR)15 and visible (VIS).14 optical Kerr effect,45 and optical bistability,46,47 i.e., the ability Electrical control of EF, by exploiting the band-filling effect,18 allows one to vary the density of electronic states available for Received: June 10, 2021 both intraband15 and interband transitions,3,18 thus affecting Accepted: January 6, 2022 the linear absorption of SLG over a broad range from Published: February 21, 2022 THz19−23 to NIR24−27 and VIS.28 This led to the development of SLG-based electro-optic modulators,3,24,25,27,29−33 which can reach higher modulation speed (up to 200 GHz34) than © 2022 American Chemical Society https://doi.org/10.1021/acsnano.1c04937 3613 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article to provide two stable optical outputs for a specific light input.48 opposite effect on SLG, activating additional absorption EF control via external gating allows one to tune the nonlinear channels, as shown by the appearance of photoinduced optical response of SLG, resulting in gate-tunable third- absorption (PA) (ΔT/T < 0). The ΔT/T changes are assigned harmonic generation37,40,41 and four-wave-mixing.49 to the EF dependence of the hot carriers cooling dynamics, The EF dependence of the transient absorption properties of simulated considering relaxation through emission of optical SLG when brought out of equilibrium remains still largely phonons. The gate tunability of the nonequilibrium optical unexplored, with studies limited to the THz range,50−53 response is key for optoelectronic applications, such as discussing the tuning of intraband photoconductivity with saturable absorbers (SA) with gate-tunable response. EF.50−52 The modulation of interband absorption in NIR and VIS is more challenging to study because EF needs to be ∼0.5 RESULTS AND DISCUSSION eV in order to cross the Pauli blocking threshold, above which We modulate EF by means of the electrostatic field effect71 the nonequilibrium optical properties have been only using an ionic-liquid top-gated field effect transistor (FET) theoretically explored.54 sketched in Figure 1a. The top-gate geometry, with The nonequilibrium optical response of SLG is crucial for optoelectronic applications, such as photodetectors,55 relying on the relaxation dynamics of photoexcited charge carriers. Numerous ultrafast optical spectroscopy experiments were performed on SLG56−60 to investigate the charge-carriers relaxation dynamics by looking at the modifications it induces on SLG absorption. In a pump−probe experiment, the system is photoexcited by an optical pulse, the pump, whose duration is to be shorter than the time scale of the relaxation processes under investigation. The relaxation of the photoexcited system is then monitored by detecting the absorption of a second optical pulse, the probe, as a function of the time delay with respect to the pump pulse.61 In SLG, interband absorption of the pump pulse induces out-of-equilibrium distributions of holes (h) and electrons (e) in VB and CB, respectively, peaked at ± ℏωpump/2, where ℏωpump is the pump photon energy. Carrier-carrier scattering drives the ultrafast e−h thermalization on a time-scale τth < 20 fs60 from out of equilibrium, to hot Fermi−Dirac distributions (HFD) with defined electronic temperature, Te. The HFD can be detected in a pump−probe experiment as a photobleaching (PB) signal,56−58 i.e., decreased probe absorption compared with equilibrium, because of Pauli blocking of interband transitions caused by the photogenerated e/h. The excess energy of the hot charge-carriers is released to the lattice via electron−phonon scattering with optical phonons,62−64 anharmonically coupled to acoustic phonons.62−65 Hot carriers’ cooling occurs on a few-ps time-scale56−58,60,65 and is influenced, through the activation of additional relaxation channels, by the dielectric environment (e.g., via near-field coupling to hyperbolic optical phonons of substrate or encapsulant material66). Defects can also accelerate the cooling via electron−phonon interaction, by acting as scattering centers mediating the direct coupling of the hot charge carriers with finite momentum acoustic phonons.67−69 This process, referred to as supercollision,67−69 accelerates the cooling for increasing defect density.70 Figure 1. (a) Schematic of device with source (s), drain (d) and Here we investigate the EF dependence of the non- gate (g) contacts used to tune the SLG EF while measuring its equilibrium optical response of SLG in the NIR range between transmission properties. (b) Photo of representative device. Scale 0.729 and 1.240 eV (1000−1700 nm), exploiting ionic liquid bar 5 mm. (c) Image of transferred SLG in a region near the drain gating to tune EF from −650 to 250 meV, thus exceeding the contact (dark area on the top). Scale bar: 100 μm. (d) 514.5 nm Pauli blocking threshold for interband absorption, achieved Raman spectrum of SLG as-grown and transferred on glass. when |EF| = ℏωprobe/2, where ℏωprobe is the energy of the probe beam. Applying ultrafast pump−probe spectroscopy with 100 fs time resolution, we detect the changes with EF of amplitude diethylmethyl (2-methoxyethyl) ammoniumbis(trifluoro- and sign of the differential transmission (ΔT/T), as well as of methylsulfonyl)imide (C6H20F6N2O5S2) as ionic liquid, is its relaxation dynamics. Starting from not intentionally doped chosen to allow light measurements in transmission through a SLG and increasing EF, we first observe a rise in PB amplitude ∼1 cm2 optical window. Large area (8 mm × 8 mm) SLG is (ΔT/T > 0) with a slow-down of its relaxation dynamics. prepared by chemical vapor deposition (CVD) as for ref 72. Above the Pauli blocking threshold, photoexcitation has an The device fabrication follows ref 73. Figure 1b is a photo of 3614 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article the device, and Figure 1c an optical image of the transferred SLG, showing no macroscopic tearing nor folding. Both as-grown and transferred SLG are characterized with a Renishaw InVia Raman spectrometer using a 50× objective, a CW laser at 514.5 nm, with power on the sample <0.5 mW to exclude heating effects. The Raman peaks are fitted with Lorentzians, with error bars derived from the standard deviation across 6 measurements and the spectrometer resolution ∼1 cm−1. The Raman spectrum of as-grown SLG on Cu is in Figure 1d, after Cu photoluminescence removal.74 The 2D peak is a single Lorentzian with full-width half- maximum FWHM(2D) ∼31 ± 3 cm−1, a signature of SLG.75 The G peak position Pos(G) is ∼1586 ± 2 cm−1, with FWHM(G) ∼ 16 ± 3 cm−1. The 2D peak position, Pos(2D), is ∼2704 ± 4 cm−1, while the 2D to G peak intensity and area ratios, I(2D)/I(G) and A(2D)/A(G), are 3.1 ± 0.4 and 6.2 ± 0.7. No D peak is observed, indicating negligible Raman active defects.76,77 The Raman spectrum of SLG transferred on glass is in Figure 1d. The 2D peak retains its single-Lorentzian line shape with FWHM(2D) ∼ 36 ± 1 cm−1. Pos(G) ∼ 1597 ± 1 cm−1, FWHM(G) ∼ 15 ± 1 cm−1, Pos(2D) ∼ 2696 ± 1 cm−1, I(2D)/I(G) ∼ 2 ± 0.2 and A(2D)/A(G) ∼ 4.9 ± 0.3, indicating p-doping with EF ∼ −230 ± 80 meV.71,78 I(D)/I(G) ∼ 0.06 ± 0.05 corresponds79 to a defect density ∼2.6 ± 1.9 × 1010 cm−2 for excitation energy 2.41 eV and EF = −230 ± 80 meV. Pos(G) and Pos(2D) are affected by the presence of strain.80 For uniaxial(biaxial) strain, Pos(G) shifts by ΔPos- (G)/Δε ∼ 23(60)cm−1%−1.80,81 Pos(G) also depends on EF.9,71 The average doping as derived from A(2D)/A(G), FWHM(G) and I(2D)/I(G), should correspond to Pos(G) ∼ 1588 ± 1 cm−1 for unstrained graphene.9,71 However, we have Pos(G) ∼ 1597 ± 1 cm−1, which implies a contribution from uniaxial (biaxial) strain ∼0.16 ± 0.02% (0.4 ± 0.04%).80,81 The gate voltage, Vg, polarizes the ionic liquid leading to the formation of electrical double layers (EDLs), near SLG and Au interfaces,71,82 that modulate the carrier density. Since the EDL thickness is ∼1 nm for ionic liquids,83,84 the solid−liquid interfacial electric field and the induced charge densities on the surface reach values as large as22,83 ∼10−20 MV cm−1 and 1014 cm −2 even at moderate V g ∼ 1−2 V. The transfer Figure 2. (a) Total resistance RTOT as a function of Vg-VCNP (black dots) with Drude model fitting (blue solid line) to estimate characteristics of our device for source-drain bias Vds = 100 residual charge carrier density, n0, and gate capacitance C. Inset, Ids mV is in Figure 2a. This exhibits a typical ambipolar behavior, for Vds = 100 mV. (b) δT/T for different Vg−VCNP (indicated next as seen by the V-shaped gate dependence of the source-drain to the curves) as a function of photon energy ℏω, showing the gate current Ids. The channel resistance peaks at VCNP = 0.84 V, tunability of the absorption edge for interband transitions; (c) EF corresponding to the charge neutrality point (CNP), where the determined from δT/T as a function of Vg−VCNP (full dots) density of states in SLG reaches its minimum.22,23,85 VCNP interpolated by f(x) = A0 + A1x + A2x2 + A3x3 with A0 = −0.03 eV, depends on EF, on the gate-metal work function,22 and on the A1 = 0.37 eV/V A2 = 0.17 eV/V2 A3 = 0.08 eV/V3 (gray dashed choice of contact materials.86 line), together with the trend (blue solid line) E F = ℏvF πne(Vg) In order to determine EF as a function of Vg, we measure the where ne(Vg) = (Vg − VCNP)(C/e) is the gate-tunable charge carrier static transmission T in NIR (500−1500 meV) with an Agilent density Cary 7000 spectrometer. Figure 2b plots a selection of transmission spectra for different Vg, compared with that at the T (Vg) − T (VCNP) attributed to intraband transitions enabled by disorder.73 The CNP, evaluated as δT /T = . T increases with T (VCNP) T modulation due to the bleaching of interband absorption is respect to the CNP, i.e., δT/T > 0, when absorption is ∼1.5% against the ∼2.3% expected for suspended SLG,8 inhibited by Pauli blocking, due to e in CB (n-doping) or h in because of the presence of the glass substrate and of VB (p-doping). In terms of probe photon energy, this diethylmethyl (2-methoxyethyl) ammoniumbis(trifluoro- corresponds to ℏωprobe < 2|EF|. We estimate EF considering methylsulfonyl)imide,87 with a refractive index ∼1.418− that δT/T halves73 for ℏωprobe = 2|EF| at values indicated by 1.420.88 black stars in Figure 2b. For probe photon energies ℏωprobe < EF extracted from the T measurements is plotted in Figure 2|EF|, interband absorption is blocked, and the sample has T ∼ 2c as a function of Vg. At Vg = 0 V, there is a p-doping EF ∼ 99.6−99.8%, with ∼0.2−0.4% residual absorption being −250 meV in agreement with the Raman estimation (∼−230 3615 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article Figure 3. (a) Sketch of pump−probe experiment on SLG with tunable EF controlled by Vg. (b) Experimental ΔT/T at t = 150 fs as a function of |EF| for p-doping acquired at different ℏωprobe = 0.729, 0.855, 1.033, 1.127, 1.240 eV (legend of panel d) for a pump fluence F ∼ 28 μJ cm−2. Top-right inset: fluence dependence of ΔT/T amplitude above Pauli blocking for pump absorption, at ℏωprobe = 0.729 eV and EF = −590 meV (hexagonal yellow symbol in main figure), together with a superlinear power-law dependence on F (solid red line). Bottom-left inset: fluence dependence of ΔT/T amplitude, for ℏωprobe = 0.729 eV and EF = −260 meV (cyan rhombus symbol in main figure). (c) |E0F| at ΔT/T = 0, extracted from panel b, as a function of ℏωprobe. (d) Simulated ΔT/T at t = 150 fs as a function of |EF| for p-doping at the same ℏωprobe as in panel b. ± 80 meV) without ionic liquid. From the analysis of the Figure 2c. At high gate voltages |Vg − VCNP| > 0.9 V, the charge-transfer curve with the Drude model as in ref 23 (see disagreement between calculated EF and the values obtained blue line in Figure 2a), we evaluate a residual n0 = 5.6 × from δT/T is attributed to the dependence of mobility on 1011cm−2, responsible for the finite conductivity at the CNP, charge carrier density,6 not included in the analysis of the and a gate capacitance C = 766 nF cm−2. We note this is a transport properties used for the calculated EF, that is valid typical n0 for as-grown and transferred SLG.89 A lower residual near the CNP and fails to describe the sample behavior for |Vg doping ∼1011 cm−2 can be achieved with cleaning techniques,6 − VCNP| > 0.9 V. Accordingly, we assume the values extracted not used here. The finite electrical conductivity and doping at from δT/T (Figure 2c gray dashed line) in the range |Vg − the CNP22,23 are due to electron−hole puddles,90 caused by VCNP| > 0.6 V, and those calculated from ne(Vg) (Figure 2c, charged impurities91 located either in the dielectric, or at the blue solid line), in the range |Vg − VCNP| < 0.6 V. At each Vg of SLG/dielectric interface.91 Near the CNP, for |Vg−VCNP| < 0.6 Figure 2. We also monitor the source-drain current Ids (inset of V, the interband absorption edge is outside the spectral Figure 2a) to determine the empirical relation with EF. The window of our δT/T measurements, and we evaluate8 transfer curve that we obtain allows us to track EF by monitoring Ids during all subsequent measurements. We test E F = ℏvF πne(Vg) , with vF the Fermi velocity, directly from the EF tunability of the ionic liquid top-gate device up to −800 the gate tunable charge carrier density ne(Vg) = (Vg − meV, corresponding to a wide range of charge carrier densities VCNP)(C/e), with e the electron charge, see blue solid line in from ∼4.5 × 1012 cm−2 (n-doping) to ∼−4.7 × 1013 cm−2 (p- 3616 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article Figure 4. Time-evolution of ΔT/T(t) for different EF at (a,b) ℏωprobe = 0.729 eV, with (a) experiment, and (b) simulations, and (c,d) ℏωprobe = 1.033 eV, with (c) experiment and (d) simulations. t = 0 corresponds to the pump arrival. The signal at negative delays indicates a finite build-up time, exceeding the pump−probe time duration at |EF| = 250 meV for ℏωprobe = 0.729 eV and 350 meV for ℏωprobe = 1.033 eV, approaching the Pauli blocking EF. doping), much wider than possible with a 285 nm SiO2 back varied with an optical delay line. Given that the pulses duration gate, usually limited to ±6 × 1012cm−2 by the gate exceeds the time-scale of carrier−carrier thermalization,60 we capacitance.85 We got similar EF(Vg) in ref 73 from Raman can assume charge carriers thermalized to HFDs and spectra and NIR transmission. investigate their cooling dynamics. We perform ultrafast pump−probe spectroscopy as sketched Figure 3b plots ΔT/T at t = 150 fs, chosen as the delay at in Figure 3a. The pump is a 100 fs NIR pulse centered at which the maximum signal amplitude is reached for Vg = 0 V. ℏωpump = 0.8 eV, while the probe spectrum covers ℏωprobe = The signal is plotted as a function of EF for different probe 0.729−1.240 eV (see Methods for details). The relaxation photon energies. Since the transient response is symmetric dynamics is monitored through the differential transmission with respect to the CNP for n- and p- doping and our SLG is p- Tpump ‐ ON(t ) − Tpump ‐ OFF doped at Vg = 0, we explore negative EF in order to reach ΔT (t )/T = evaluated from the probe Tpump ‐ OFF higher |EF| by applying a smaller Vg. We observe a strong transmission with (Tpump−ON) and without (Tpump−OFF) pump modulation of ΔT/T with EF, higher at the low-energy tail of excitation, after a time delay t between probe and pump pulses, the probe pulse, with the signal changing from 4 to −2 × 10−4 3617 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article (see the curve at 0.729 eV in Figure 3b). The signal amplitude 2 decreases for increasing ℏωprobe, as expected for a thermal by ne = 1 π ( ) . ΔT/T in Figure 3d is computed from the EF ℏvF distribution of carriers.58 In all the probed range, near the changes in optical conductivity, Δσ, induced by photo- CNP, we observe, as expected, a PB signal, i.e., ΔT/T(t) > 0. excitation as a function of EF. To evaluate ΔT/T at t = 150 By increasing |EF|, first PB increases in amplitude, and then a fs we consider the charge carriers as distributed in energy and change of sign occurs at a threshold |EF| dependent on the momentum along a HFD with a time-dependent chemical probe photon energy. The Fermi energy at which the sign potential, μc , and Te(t) > RT. Our model takes into account change occurs, |E0F| in Figure 3c, corresponds to ℏωprobe/2, i.e., that, even though the pump fluence is constant, the initial Te the Pauli blocking threshold for probe photons. Above this, the changes with EF due to the change of pump absorption. We pump pulse, exciting e (h) to higher (lower) energy states, consider the absorption from the tail of the Fermi−Dirac partially unblocks the probe interband absorption, otherwise distribution as source of residual pump absorption for |EF| > inhibited, resulting in a PA signal, i.e., ΔT/T < 0. The PA 400 meV. The charge carrier distribution modification with EF intensity increases with EF up to a peak, whose position in is sufficient to reproduce qualitatively the experimental PB terms of EF raises with probe photon energy. A constant ΔT/T signal increase, the change of sign at ℏωprobe/2, and the PA ∼ −1 × 10−5 is then approached in the high |EF| limit (EF < decrease for EF > 400 meV, Figure 3d. −690 meV) in all the probed range. Our data and model indicate that the PA signal amplitude is We note that ref 93 reported a study of EF dependence of maximized at EF ∼ 0.4ℏωprobe, unlike claimed in ref 93, i.e., that the transient optical properties of SLG, without reaching Pauli the maximum occurs at EF = 0.5ℏωpump. We attribute this blocking, i.e., |EF| > ℏωprobe/2, which we investigate here, difference to the coarser sampling of EF in ref 93 (50 meV revealing the PA regime. Our results show that, by varying Vg, steps against our 4 meV, Figure 3b), to the fact that ref 93 used we can not only control the relaxation dynamics of SLG, but a reflection geometry, mixing contributions from transient also change the ΔT/T sign. reflection and transmission with opposite sign,96 and to the Above the Pauli blocking threshold for pump interband larger probe photon energy at which intraband transitions transitions (|EF| ≥ 400 meV for ℏωpump = 800 meV), ΔT/T is contribute with opposite sign to that of interband transitions.97 expected to vanish, because the pump should not be able to Furthermore, the EF thresholds that control the ΔT/T photoexcite SLG. However, a finite value is observed, caused amplitude and sign are identified by ℏωprobe, not by ℏωpump by residual pump absorption, related to both extrinsic14,73,92 as incorrectly stated in ref 93, since ℏωpump has no role in and intrinsic14,94 effects. Among the former, charged impurities defining the cooling dynamics of the HFD after the first and scatterers (e.g., edge defects, cracks, vacancies) can induce ultrafast (<100 fs) step of electron−electron thermaliza- residual conductivity73,92 activating intraband absorption. tion.60,63 Amongst the latter is the residual absorption from the tail of To examine the dependence of the cooling dynamics on EF, the carrier Fermi distribution, i.e., off-resonance absorption, we monitor ΔT/T as a function of pump−probe delay. Figures which has a finite broadening at RT.94 The fluence dependence 4a,c show the gate-dependent relaxation dynamics at ℏωprobe = of ΔT/T at ℏωprobe = 0.729 eV in the inset of Figure 3b is 0.729, 1.033 eV, lower and higher than the pump photon superlinear above the threshold for Pauli blocking of pump energy. At both energies, the relaxation dynamics progressively absorption (as measured at |EF| = 590 meV), suggesting a non- slows down with increasing |EF|, evolving from a biexponential negligible contribution from two-photon absorption.95 This to a monoexponential decay, due to a reduction of the fast could also explain the vanishing signal when approaching |EF| = decay component. We can appreciate this slowdown by noting 800 meV (the Pauli blocking threshold for two-photon that, to see a signal reduction by a factor 10, we need to wait absorption). ∼1 ps at |EF| = 100 meV and ∼5 ps at 300 meV. Both signal While height and width of PB and PA bands slightly change intensity and relaxation dynamics are symmetric for n- or p- with ℏωprobe, we observe similar features in all the probed doping, as a consequence of the CB, VB symmetry. range upon increasing |EF|: an increase of PB, followed by a The observed gate-dependence can be qualitatively decrease, and a sign change above the Pauli blocking threshold explained considering that, for increasing |EF|, the excess for probe absorption. The measurements are performed using energy of the photoexcited charge carriers with respect to a low excitation fluence (28 μJ cm−2) to work in a perturbative equilibrium is reduced, affecting the scattering with optical regime corresponding to Te < 1000K, thus reducing the impact phonons that drives the cooling. To gain a deeper insight into of the hot-phonon bottleneck and focusing on the electron- the phenomena responsible for quenching the fast relaxation optical phonon cooling. The amplitude of ΔT/T increases by component, we solve a set of phenomenological equations of increasing the excitation fluence, as for the inset of Figure 3b, motion (EOMs)98 for Te and for the occupation of the phonon by almost 2 orders of magnitude for the PA signal (see top- modes. We include the optical phonon modes at the K and Γ right inset of Figure 3b at |EF| = 590 meV) and 1 order of points of the SLG Brillouin zone, and we consider that they magnitude for the PB signal (see bottom-left inset of Figure 3b can be emitted/absorbed by e and h and decay into acoustic at |EF| = 260 meV). We previously reported the use of ungated modes due to anharmonic coupling62,63,65 (see Methods). SLG as SA (GSA) in mode-locked lasers, in which an We calculate the time-evolution of the differential absorption modulation ≤1.3% is sufficient to induce and conductivity for several values of μc , corresponding to EF, control the pulsed (mode-locked) regime.44 The ability to (i.e., μc at Te = 094), in the range 250 to −650 meV. The results electrically control amplitude, sign, and recovery time of ΔT/T in Figure 4b,d explain the observed slowdown of the dynamics in a GSA is thus of practical relevance for optimizing mode- with increasing EF, with the saturation of the phase space for locking for stability, pulse width, and average output power. optical phonon-emitting electronic transitions. As EF increases, To understand the EF dependence of the nonequilibrium there are fewer carriers with an energy high enough (>160 optical response of SLG, we calculate ΔT/T (see Methods for meV) to emit an optical phonon, and optical phonon emission details) as a function of initial carrier density ne, related8 to EF is quenched. This is a fundamental process, not dependent on 3618 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article the SLG substrate, like supercollision cooling through slowdown, we need to consider that additional relaxation defects,99 nor on its dielectric environment, like the cooling channels may start playing a role once the cooling via optical to hyperbolic phonons in hBN-encapsulated SLG.66 It is phonons gets slower. Defects can accelerate cooling,67−70 determined by the intrinsic coupling of e with the K and Γ mediating the scattering with acoustic phonons of finite phonons.100 The initial increase of PB amplitude with EF in momentum and energy.69 This supercollision mechanism67−70 Figure 3b,c is a consequence of the quenching of relaxation via may become the dominating process once optical phonon optical phonons,60,63 which reduces the initial fast decay. emission is quenched. Cooling times ∼4 ps are expected for Figure 4 also shows that |E0F| is independent of t, both in supercollision cooling67 in SLG with EF ∼ 400 meV and experiments and simulations. The vanishing ΔT/T does not mobility of a few thousand cm2 V−1 s−1, as that of our device. correspond to zero absorption, but it means that the The EF independence of the decay dynamics in the high EF conductivity remains at its equilibrium value for all delays. limit could be explained by the lack of dependence on carrier For t > 0, the e system is photoexcited. This can happen only density of the supercollision cooling time away from the Dirac because the e distribution undergoes a time-evolution such point.67 According to refs 78 and 79, the e scattering time with that the conductivity remains time-independent at ℏω = 2|EF|. defects in SLG is not expected to significantly change with EF. Figure 5a shows that for EF > 340 meV and ℏωprobe = 0.729 The electrical tunability of the SLG relaxation dynamics, eV, the simulations predict a further slowdown of the sketched in Figure 6a−c, is promising for the realization of tunable SA. Saturable absorption, i.e., the quenching of optical absorbance under intense illumination,101 can occur in SLG at low light intensity (e.g., ∼ 0.750MW cm−2 at 0.8 eV102). We measured a saturation intensity44 IS = 0.5−1.7MW cm−2 for photon energies in the range ∼0.5−2.5 eV, comparable to semiconductor saturable absorber mirrors (SESAMs) (P = 0.01−0.1MW cm−2 at 0.944 eV103), but maintained over a much broader spectral range.44 The modulation depth, defined as the maximum change in absorption,101 can be optically tuned exploiting cross absorption modulation.104 GSAs are promising for passive mode-locking,44,105,106 Q-switching,107 and Q-switched mode-locking.108 Figure 6 shows that the SLG equilibrium photoresponse can be electrically tuned, providing an additional knob for controlling its SA performance in terms of modulation depth and recovery dynamics. For EF ≪ ℏωprobe/2, the intrinsic biexponential-like relaxation dynamics makes SLG an ideal fast SA, Figure 6a. The presence of two different time scales, in analogy with SESAMs,109 is considered an advantage for mode locking.109 As discussed in refs 109 and 110, the longer time scale reduces the saturation intensity, facilitating self-starting mode-locking, while the fast relaxation component is efficient in shaping subps pulses. For EF ≤ ℏωprobe/2 as in Figure 6b, SLG can act as slow SA111 with recovery times 10 to 30 times longer than the pulse duration,111,112 favoring soliton shaping,112 or the temporal shift of the pulses caused by the SA,109 which limits the time in which noise behind the pulse can be amplified.111 Longer recovery time also gives an increased tolerance towards instability induced by self-phase modulation.111 The PA at EF > ℏωprobe/2 can be exploited to operate SLG as reverse SA,113 for which absorption increases with increasing impinging intensity, because of depletion of the final state population (see Figure 6c). The PA of highly doped SLG could be exploited to realize an optical limiter,114 based on the decrease in transmittance under high-intensity or fluence Figure 5. (a,b) Experimental (colored dots) and theoretical (solid illumination. An ideal optical limiter, with the functionality of lines) ΔT/T at different EF for (a) ℏωprobe = 0.729 eV and (b) protecting delicate optical elements, should strongly attenuate ℏωprobe = 1.033 eV for pump−probe time delays between −500 fs and 5 ps (pump arrival at t = 0). intense, potentially dangerous, laser beams, while exhibiting high transmittance for low-intensity light. Carbon nano- tubes115 and few-layer graphene116 dispersions in organic relaxation dynamics, not observed in our experiments. These solvents have been used to prepare optical limiters. However, all saturate to a similar decay trend independent of EF (see these rely on nonlinear scattering,117 rather than on nonlinear overlapping black and green dots in Figure 5). Analogous absorption.118 The nonlinear scattering of graphene disper- behavior is found at all ℏωprobe, provided that when we increase sions116 is based on the avalanche ionization of carbon when ℏωprobe, we tune EF to higher levels to find overlapping decay interacting with an incident laser pulse, and subsequent bubble dynamics (see Figure 5b). To understand the saturation of this formation in the solvent due to the heat released by expanding 3619 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article Figure 6. (a−c) Sketch of interband absorption of a NIR probe pulse (vertical blue arrow) within the SLG Dirac cones populated at equilibrium up to EF (gray filling). The pump pulse perturbs the probe absorption by promoting e from VB to CB (red filling), which then relax through emission of optical phonons (downward black arrows). The three sketches correspond to (a) EF at the Dirac point, (b,c) moderate n-doping with EF (b) below and (c) above the threshold for interband probe absorption. By increasing EF, optical phonon emission is quenched (dashed downward arrows) and relaxation becomes slower. Above the threshold for interband absorption of the probe (dashed vertical blue arrow), photoexcitation results in ΔT/T < 0, leading to reverse saturable absorption, consisting in an increased absorption upon increasing illumination. microplasmas.115,116 The 10 ps PA lifetime of the nonlinear generating 70 fs pulses at 0.8 eV with 300 mW average power. The absorption of highly doped SLG is 10 times shorter than the output of the first EDFA is attenuated to obtain pump pulses with 1 typical time scales for thermal effects and bubbling of graphene mW maximum average power. The second EDFA feeds a highly dispersions, which are of the order of 100 ps,115 allowing the nonlinear optical fiber that produces a supercontinuum tunable application to lasers with shorter pulse duration. The nonlinear between 0.729 and 1.240 eV, which serves as probe pulse. The pump absorption in SLG is not related to a specific absorption and probe pulses, synchronized by a computer-controlled optical resonance. Thus, it covers a broad spectral range, as shown in Figure 3b, where for |EF| = 600 meV we detect PA for photon delay line and collinearly recombined by a dichroic beam splitter, are energies in the range 0.729 to 1.127 eV. The SA to reverse SA focused on the sample over spots of ∼25 μm radius. The portion of transition could be used for all-optical logic gates.119 Gate- the probe transmitted by the sample, spectrally selected by a dependent effects on cooling dynamics are also important for monochromator with a bandwidth ∼5 nm, is detected by an amplified the design of transceivers for data communication.3 E.g., ref InGaAs photodiode (bandpass 4.5 MHz, gain 104) and analyzed by a 120 showed that longer cooling times give larger photocurrent. lock-in amplifier (Zurich Instruments HF). Pump and probe pulses have perpendicular polarizations and a linear polarizer is used to filter CONCLUSIONS out the pump light scattered from the sample. The pump pulse is We demonstrated that electrostatic tuning of the non- modulated at 1 MHz by an acousto-optic modulator, resulting in a equilibrium optical response of SLG results in changes of ΔT(t)/T sensitivity of the order of 10−7, for an integration time of amplitude, sign, and recovery dynamics of ΔT/T. Increasing EF quenches emission of optical phonons, i.e., of the fastest 300 ms. From the FWHM of the instrumental response function, we intrinsic relaxation channel for SLG hot charge carriers. The estimate an overall temporal resolution ∼100 fs. The absorbed photon ability to tune EF above the threshold for Pauli blocking of density is in the range 2−3 × 1012cm−2 (depending on EF), as interband absorption of NIR light results in photoinduced calculated from incident fluence and sample transmission. absorption in SLG, because of pump-induced unblocking of Simulation of Differential Transmission Dynamics. To model interband transitions for the probe. Our results anticipate the the time-evolution of the differential transmission we assume that, on use of voltage-controlled SLG for nonequilibrium optoelec- the time-scale given by the time-resolution of the experiment (100 fs), tronic devices as gate tunable optical elements, which can e in both CB and VB are thermalized at the same Te, and reach a behave either as fast, slow, or reverse SA. common μc(t), such that the e energy distribution is a HFD. μc(t) is METHODS calculated at each instant in time, as it depends on Te and is fixed by the condition that the carrier density, defined as 9 4 High-Sensitivity Transient Absorption Microscopy. The +∞ setup for pump−probe experiments comprises a mode-locked Er- n=∫ dεν(ε)[1 + exp((ε − μ)/kBT )]−1, with ν(ε) the electronic doped fiber oscillator (Toptica Photonics, FemtoFiberPro), emitting −∞ 150 fs pulses at 0.8 eV (1550 nm) at 40 MHz repetition rate. The density of states in SLG,122 is constant.94 As for refs 98 and 121, we oscillator feeds two Er-doped fiber amplifiers (EDFAs) each can write the following EOMs for Te and phonon occupations: 3620 https://doi.org/10.1021/acsnano.1c04937 ACS Nano 2022, 16, 3613−3624 ACS Nano www.acsnano.org Article dTe(t ) R (t )ℏωΓ + RK (t )ℏωK Sandro Mignuzzi − Cambridge Graphene Centre, University =− Γ , of Cambridge, Cambridge CB3 0FA, U.K. dt ce(t ) + ch(t ) Klaas-Jan Tielrooij − Catalan Institute of Nanoscience and dnΓ(t ) R (t ) n (t ) − nΓ(0) Nanotechnology (ICN2), BIST & CSIC, Barcelona 08193, = Γ − Γ , dt MΓ τph Spain; orcid.org/0000-0002-0055-6231 Marco Polini − Dipartimento di Fisica, Università di Pisa, dnK (t ) R (t ) n (t ) − nK(0) 56127 Pisa, Italy; Istituto Italiano di Tecnologia, 16163 = K − K . dt MK τph (1) Genova, Italy Complete contact information is available at: Here, nΓ(t) and nK(t) are the occupations of the optical phonon https://pubs.acs.org/10.1021/acsnano.1c04937 modes at Γ and K, with energy ℏωΓ ∼ 0.196 eV and ℏωK ∼ 0.161 eV,100 respectively, as these have the strongest electron−phonon coupling.100 The parameter τph is the finite optical phonon lifetime, Notes via relaxation into acoustic phonons due nonlinearities of the lattice,65 The authors declare no competing financial interest. until global thermal equilibrium with densities n(0) (0) Γ , nK is reached. We find good agreement between theory and experiment for τph ∼ 1.2 ps, ACKNOWLEDGMENTS consistent with ref 65. The constant coefficients MΓ, MK correspond to the number of phonon modes in an annular region between the We thank A. Principi for useful discussions. We acknowledge minimum and maximum energy that can be exchanged with e.98,121 funding from the European Union Graphene Flagship, ERC The time-dependent parameters ce(t) and ch(t) are the heat capacities Grants Hetero2D, GSYNCOR, and CUHL, EPSRC Grants of e in CB and h in VB, respectively. The time-dependent parameters EP/K01711X/1, EP/K017144/1, EP/N010345/1, EP/ RΓ(t) and RK(t) are electronic relaxation rates per unit area, due to L016087/1, EP/V000055/1, the German Research Founda- phonon emission and absorption, proportional to a Boltzmann tion DFG (CRC 1375 NOA), the Daimler und Benz scattering integral.98,121 In line with our assumption that, on the time-scale probed by our foundation, RYC fellowship No. RYC-2017-22330, IAE project experiments, a common μc(t) is established between CB and VB, the PID2019-111673GB-I00, and the Severo Ochoa program from heat capacities are calculated separately in the two bands, (i.e., Te Spanish MINECO Grant No. SEV-2017-0706. variations are decoupled from interband transitions) and only intraband transitions are included in the relaxation rates. The initial REFERENCES Te(0), following the pump pulse, is estimated as for ref 37. The initial phonon populations nΓ,K(0) are evaluated at RT. The optical (1) Ferrari, A. 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