SCIENCE ADVANCES | RESEARCH ARTICLE CONDENSED MATTER PHYSICS Copyright © 2021 The Authors, some Electrical tunability of terahertz nonlinearity rights reserved; exclusive licensee in graphene American Association for the Advancement of Science. No claim to Sergey Kovalev1, Hassan A. Hafez2*, Klaas-Jan Tielrooij3, Jan-Christoph Deinert1, Igor Ilyakov1, original U.S. Government Nilesh Awari1, David Alcaraz4, Karuppasamy Soundarapandian4, David Saleta3, Semyon Germanskiy1, Works. Distributed Min Chen1, Mohammed Bawatna1, Bertram Green1, Frank H. L. Koppens4,5, Martin Mittendorff6, under a Creative Mischa Bonn7, Michael Gensch8,9*, Dmitry Turchinovich2* Commons Attribution License 4.0 (CC BY). Graphene is conceivably the most nonlinear optoelectronic material we know. Its nonlinear optical coefficients in the terahertz frequency range surpass those of other materials by many orders of magnitude. Here, we show that the terahertz nonlinearity of graphene, both for ultrashort single-cycle and quasi-monochromatic multicycle input terahertz signals, can be efficiently controlled using electrical gating, with gating voltages as low as a few volts. For example, optimal electrical gating enhances the power conversion efficiency in terahertz third-harmonic generation in graphene by about two orders of magnitude. Our experimental results are in quantitative agree- ment with a physical model of the graphene nonlinearity, describing the time-dependent thermodynamic balance maintained within the electronic population of graphene during interaction with ultrafast electric fields. Our re- Downloaded from http://advances.sciencemag.org/ on May 10, 2021 sults can serve as a basis for straightforward and accurate design of devices and applications for efficient electronic signal processing in graphene at ultrahigh frequencies. INTRODUCTION hundred gigahertz and with a field strength in the range of 10 to The development of efficient broadband electronic frequency multi- 100 kV/cm, which is even lower than typical channel fields in the pliers and modulators operating at the technologically important current generation of high-speed transistors (4, 16). Conveniently, terahertz frequency range and under normal ambient conditions is graphene is also compatible with complementary metal-oxide semi- of great relevance, but also challenging (1–5). These technologies re- conductor (CMOS) technology (6, 17). This suggests the possibility quire the integration of a highly nonlinear material in an electronic to develop hybrid graphene-CMOS technology, with the subterahertz device with the possibility to control its nonlinear behavior. In addi- CMOS device acting as a reliable and cost-effective pump source, tion, compatibility between the device constituents is crucial. These providing the input signal for the efficient nonlinear processing in requirements are not easy to meet, especially in simple electronic graphene at terahertz frequencies. One of the straightforward appli- circuits (4–6). Here, we demonstrate the possibility of accomplishing cations of such a technology is all-electronic terahertz frequency these requirements in a graphene-based device. A straightforward mixing or upconversion of the subterahertz CMOS–generated and efficient wide-range control of the terahertz nonlinearity of signals into the terahertz range, with the potential to outcompete graphene is enabled by electrical gating of only a few volts. the current generation of diode-­based ultrahigh frequency mixers One of the essential technological consequences of the Dirac- (1–3, 18, 19) in terms of conversion efficiency, operation bandwidth, type electronic bandstructure of graphene (7, 8) is its extremely compactness, and cost. nonlinear response to electric fields in the terahertz frequency Recent experiments on terahertz high-harmonic generation range, which persists at room temperature and under normal ambi- (HHG) in graphene directly provided the measurement of its non- ent conditions. Graphene is a highly efficient terahertz nonlinear linear coefficients up to the seventh order (14). These nonlinear absorber, capable of displaying a nonlinear power transmission coefficients were found to exceed the respective coefficients of all modulation of about 50% per single monolayer (9–12). It is also an other known electronic materials by many orders of magnitude extremely efficient terahertz frequency multiplier, allowing for the (12, 14). In a nonoptimized terahertz HHG experiment in (14), the straightforward generation of multiple terahertz harmonics (12–15). field conversion efficiency from the driving subterahertz electric Such a nonlinear response is directly attainable with quite moderate signal to terahertz higher harmonics of  ~ 1% was demonstrated in input electric fields, oscillating at frequencies not exceeding a few just a single–atomic layer graphene sample. Such a strong terahertz nonlinearity of graphene is attributed to the collective thermo- dynamic response of its background free-carrier population (elec- 1 Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, trons or holes) to the driving terahertz field (11, 12, 14). Increasing Germany. 2Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany. 3Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST and the density of these free carriers in graphene (or equivalently, its CSIC, Campus UAB, 08193, Bellaterra (Barcelona), Spain. 4Institut de Ciencies Foto- Fermi energy EF) enhances the power absorption of the terahertz niques (ICFO), The Barcelona Institute of Science and Technology, Barcelona, driving field and consequently provides a control knob that allows Spain. 5Institució Catalana de Recerça i Estudis Avancats (ICREA), 08010 Barcelona, Spain. 6Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, for tuning the nonlinear response. On the other hand, too high car- Germany. 7Max-Planck-Institut für Polymerforschung, Ackermannweg 10, 55128 rier density and hence the strongly metallic phase of graphene with Mainz, Germany. 8Institut für Optische Sensorsysteme, DLR, Rutherfordstraße 2, increased electronic heat capacity will diminish the material’s thermo- 12489 Berlin, Germany 9Institut für Optik und Atomare Physik, Technische Univer- dynamic nonlinearity. This suggests the existence of optimal dop- sität Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany. *Corresponding author. Email: hafez@physik.uni-bielefeld.de (H.A.H); michael.gensch@ ing in graphene, favoring its terahertz nonlinearity, which can be dlr.de (M.G.); dmtu@physik.uni-bielefeld.de (D.T.) controlled externally. Here, we demonstrate such an efficient control Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 1 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE of graphene nonlinearity by varying its free carrier density by elec- leading to a weaker nonlinear response. Hence, there is an optimal trical gating. carrier density that provides the largest nonlinearity (see the Sup- Being only one atomic layer thick and having a gapless band- plementary Materials for further information). structure, graphene is a material for which wide tuning of the Fermi To examine the degree of control over the nonlinearity that we energy is easily achievable using a small gating voltage of only a few can expect, we first consider two levels of carrier densities corre- volts, not only in one band but also between the valence and con- sponding to EF of 80 and 180 meV and simulate two nonlinear duction bands across the Dirac point. This offers a simple route to experiments. We use two different terahertz waveforms, single-cycle control the terahertz nonlinearity of graphene. Here, we demon- broadband and multicycle quasi-monochromatic terahertz pulses, strate the effects of the carrier density (or the material Fermi energy, as shown in Fig. 1 (A and B), respectively, similar to the terahertz EF) on terahertz saturable absorption (SA) and HHG, as well as the signals used in our experiments, with identical peak field strengths associated nonlinear carrier dynamics in gated graphene. We of 80 kV/cm. We see from Fig. 1 (C to H) that for both cases of tera- achieve this using nonlinear terahertz spectroscopy using single- hertz driving signals, the nonlinear terahertz field–induced effects and multicycle terahertz driving fields with a peak electric field in graphene are more pronounced for the larger EF. strength reaching 80 kV/cm. Within the experimentally tested Another important feature shown in Fig. 1 is that for the case of range of EF, increasing from ~50 to 200 meV relative to the Dirac multicycle quasi-monochromatic driving terahertz signal, the mod- point, transient changes in the terahertz field transmission of graphene ulation effect in graphene is generally stronger both in amplitude in response to a terahertz driving field of 80 kV/cm are enhanced by and in temporal dynamics, as compared to the excitation with the a factor of ~70. For the same range of increasing EF, an enhance- single-cycle pulse, at the same value of EF and peak electric field ment in the power conversion efficiency in third terahertz harmonic strength in the signal. This is clearly visualized in Fig. 1 (G and H) Downloaded from http://advances.sciencemag.org/ on May 10, 2021 generation by almost two orders of magnitude has been achieved. through the spectra of the terahertz signals transmitted through the graphene layer. The reason for the stronger nonlinear modulation Physical picture of gate-tunable terahertz nonlinearity of terahertz properties of graphene in case of multicycle driving The nonlinear interaction between free carriers in graphene and the field is that (i) the power carried by the multicycle pulse is larger, field of a driving terahertz signal resembles a thermodynamic pro- assuming the same peak field as for the single-cycle and (ii) the cess exhibiting an interplay of heating-cooling dynamics (11, 12, 14), accumulated electronic heat persists more than a few hundred as illustrated in Fig. 1 for two different terahertz pulse shapes: single-­ femtoseconds, which, in turn, allows for enhancing the electronic cycle (Fig. 1A) and a multicycle (Fig. 1B) pulses. The terahertz interaction with the longer-lasting multicycle driving signal. This energy absorbed in graphene by the free carriers via the intraband presents novel opportunities for the efficient nonlinear signal pro- optical conductivity mechanism is quasi-instantaneously (on a sub– cessing of quasi-monochromatic terahertz electronic signals. 50-fs time scale) converted into electronic heat, corresponding to a Our calculations based on the thermodynamic model presented rise in the carrier temperature and consequently to a suppression of here use a single-band picture, in which only intraband free carrier both the THz conductivity and power absorbance (i.e., SA) of dynamics, subjected to the conservation of carrier density within the graphene (see Fig. 1, C to F). This heating process is then followed by terahertz-excited band, is considered (i.e., either electrons in the a slower, picosecond-timescale carrier cooling process, occurring via conduction band or holes in the valence band). Whereas this ap- emission of optical and acoustic phonons, which then restores the proach is strictly valid for graphene with a large EF, it is expected to initial high conductivity of graphene. The interplay of the carrier heat- be less accurate for the situation with EF < kBTe, where a two-band ing and cooling processes during the interaction of graphene with the thermalization picture should instead be considered. Here kB is the driving terahertz signal results in a temporal modulation of both the Boltzmann constant and Te is the carrier temperature. However, we terahertz conductivity and the instantaneous terahertz absorbance use the single-band approach universally for the whole range of (see Fig. 1, C to F). This leads to a nonlinear temporal deformation tested Fermi energies, because it very well reproduces the entirety of of the driving terahertz field passing through graphene, which even- our experimental observations using a minimum of adjustable tually results in a spectral broadening for the single-cycle pulse, as parameters (namely, only the proportionality constant between the shown in Fig. 1G, and a highly efficient terahertz frequency multi- electron energy and electron scattering time). At the same time, the plication, i.e., terahertz higher odd-order harmonic generation for two-band model would require the introduction of additional adjust- the multicycle pulse, as shown in Fig. 1H (see also the Supplemen- able parameters (see the Supplementary Materials). tary Materials for further information). Because the electronic terahertz nonlinearity of graphene is Sample and nonlinear terahertz spectroscopy facilitated by the absorption of the driving terahertz field by the free On the basis of our simulations that predict a large gate tunability of carriers and the subsequent thermodynamic process involving the the nonlinear response in both single-cycle and multicycle cases, we electronic and phononic subsystems, it is the density of these free have conducted two types of nonlinear terahertz spectroscopy carriers that provides the key to controlling the terahertz nonlinearity experiments on our electrically gated graphene sample: (i) table top in this material. That is, the terahertz nonlinearity relies on the laser–based intense terahertz pump–terahertz probe (TPTP) spec- presence of free carriers, and increasing the free carrier density in- troscopy using single-cycle broadband terahertz pulses, as shown in creases the power absorption and leads to a stronger nonlinear re- Fig. 2A, and (ii) accelerator-based nonlinear terahertz time-domain sponse (scaling approximately with the square of the Fermi energy, spectroscopy (nonlinear terahertz-TDS) with multicycle quasi-­ EF), as shown in Fig. 1 (C to H). However, in the regime where the monochromatic terahertz fields, as shown in Fig. 2B. The former density becomes extremely high (likely above EF = 200 meV), the rise provided the measurements of the terahertz field–induced SA and in the carrier temperature becomes modest, as the absorbed tera- the associated carrier (temperature) dynamics, while the latter en- hertz energy is to be shared among a very large number of carriers, abled the observations of terahertz HHG. The graphene sample is Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 2 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE 80 80 Pump-induced heat, Pump THz E field Power absorption Pump-induced heat, Pump THz E field A B (kV/cm) 40 (kV/cm) 40 0 0 −40 −40 −80 0.4 0.4 Q(t) ( J/cm2) C D Q(t) ( J/cm2) 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 18 E 18 F Power absorption coefficient (%) coefficient (%) 16 16 14 14 12 12 4 4 2 2 Downloaded from http://advances.sciencemag.org/ on May 10, 2021 0 2 4 6 8 0 10 20 30 40 50 Time (ps) Time (ps) G 10 H 10 (1) 1 Amplitude (a.u.) 1 Amplitude (a.u.) 0.1 0.1 (3) 0.01 0.01 (5) 0.001 (7) 0.001 1 × 10−4 1 × 10−5 1 × 10−4 1 × 10−6 1 × 10−5 1 × 10−7 0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Frequency (THz) Frequency (THz) Fig. 1. Thermodynamic model calculations for the Fermi energy dependence of the terahertz nonlinearity of graphene. (A and B) Driving single-cycle and multicycle terahertz fields, respectively. (C and D) and (E and F) The associated terahertz field–induced heat and SA, respectively, for two-doping levels corresponding to Fermi energies of 80 and 180 meV. The terahertz-induced heat (or equivalently the rise in the electron temperature) leads to a reduction and a temporal modulation of both the intraband conductivity, (t) and the power absorption coefficient (t), as shown in (C) and (D). This results in a nonlinear terahertz field–induced current J(t) = (t, ETHz)ETHz(t) in the graphene layer, yielding terahertz field–induced transparency (SA) and electromagnetic reemission at higher odd-order harmonics. Both the terahertz-induced heat and SA become more pronounced when the doping concentration (the Fermi energy, EF) increases, scaling nearly with ​​E​2F​​​.(G and H) The spectral amplitudes of the terahertz fields transmitted through graphene relative to the pump field (gray background), for the tested Fermi energies of 80 and 180 meV. a.u., arbitrary units. composed of a chemical vapor deposition (CVD)–grown single-layer never uniformly zero at ∣V − V0∣ = 0 due to inhomogeneity in the graphene on a 1-mm-thick infrasil quartz substrate and is connected doping and gating field across the graphene layer, as well as a finite at two opposite edges to two electrodes acting as source and drain. thermal broadening of the electron distribution, given kBT = 26 meV The gating is enabled by another pair of electrodes and a polymer at room temperature T = 300 K, resulting in the finite peak resist­ance electrolyte [LiClO4:polyethylene oxide (PEO)] deposited on the at ∣V − V0∣ = 0. Increasing the absolute gating voltage away from graphene layer and the gate electrodes, as shown in Fig. 2C. The V0 leads to an increase in the absolute value of EF, whether for electrons Fermi energy of graphene is then varied by a small gate voltage in or holes, as shown in Fig. 2D. Quantitatively, _ EF is related to the free the range between −2 to +2 V (see Materials and Methods for further carrier density, Nc, through E ​​ ​ F​​  = ℏ ​v​  F​​ ​√ ​Nc​  ​​ ​​, where ℏ is the reduced information about the experiments and the sample preparation). Planck’s constant and vF = 1 × 106 m/s is the Fermi velocity in graphene. Figure 2D shows the gating response of the graphene sample, indicated by the graphene sheet electrical resistance, retrieved by measuring the source-drain current through the graphene layer at a RESULTS AND DISCUSSION drain voltage of 10 mV, as a function of the gating voltage. The ini- Saturable absorption tial doping of the graphene layer (doping at zero gate voltage) was Figure 3 shows both the as-measured and processed results of the p-type, as usually provided unintentionally by chemical residues single-cycle TPTP experiment, demonstrating the efficient control during the preparation process and due to interaction with the sub- of the nonlinear terahertz transmission of graphene using a small strate (12, 20, 21), and the deposited polymer electrolyte. Here, a gating voltage of 2 V at maximum. Here, we refer to ∣V − V0∣ sim- nonzero gate voltage V0 has compensated for this hole doping and ply as the gating voltage. The graphene sample was excited by shifted the Fermi energy to a minimum near the Dirac point, which terahertz pump pulses with peak electric field strength ranging corresponds to the peak resistance of the sample in Fig. 2D. We from 1 to 80 kV/cm. The effects induced by the terahertz pump note here that EF is considered relative to the Dirac point and is were probed by a weak terahertz probe pulse, at various values of EF Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 3 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE A C 5 B Sheet resistance (kOhm) D 4 3 Downloaded from http://advances.sciencemag.org/ on May 10, 2021 2 −2 −1 0 1 2 V − V 0 (V) Fig. 2. Schematics of the terahertz experiments and the gated graphene sample. (A) TPTP experiment with gated graphene. The electric field of the terahertz pump is vertically polarized and has a peak field strength up to 80 kV/cm, while the electric field of the terahertz probe is horizontally polarized with a peak field strength of less than 1 kV/cm. (B) Nonlinear terahertz-TDS, using multicycle quasi-monochromatic terahertz pulses oscillating at a fundamental central frequency of 0.3 THz and having a peak electric field up to 80 kV/cm. The transmitted field through the graphene sample consists of higher odd-order harmonics in addition to the fundamental frequency. Note that EF refers to the Fermi energy of the graphene sample, while Ef refers to the peak electric field of the driving THz signal oscillating at the fundamental frequency f. (C) The gated graphene sample device in which the graphene film acts as a channel between source and drain electrodes subjected to a constant potential difference of 0.2 mV. The graphene film is covered on top by an electrolyte subjected to a varying gating voltage to tune the Fermi level of the graphene layer. (D) Experimentally de- termined gating response of the graphene sample given by the sheet resistance of the graphene film as a function of the gating voltage relative to the voltage V0 corre- sponding to the minimum Fermi energy in the vicinity of the Dirac point, exhibiting a maximum resistance. Positive V − V0 leaves electrons in the graphene layer with the Fermi level elevated in the conduction band, while hole doping with the Fermi level pinning the valence band is induced by negative V − V0. controlled by the gating voltage. Figure 3 (A and B) shows the differential transmission T/T0 of the terahertz probe obtained terahertz probe pulses transmitted through the graphene sample from the data of Fig. 3C, revealing that the nonlinear terahertz with and without the intense terahertz pump at 80 kV/cm for two field transmission of graphene is modulated from a minimum of different gating voltages. After the pump, the probe transmission less than 0.1% to ~7%, i.e., by 70 times, when a gating voltage of increases, indicating terahertz absorption bleaching (or equivalently only 2 V is applied. This demonstrates an efficient, straightforward SA) in graphene, which corresponds to a reduction of the graphene control of the graphene nonlinearity with a very modest gating terahertz conductivity. This effect becomes more pronounced with voltage. increasing the gating voltage (the increase in transmission of the We further observe from Fig. 3D that the transient increase in “red” pulse relative to the “black” pulse is more pronounced in transmission reaches a peak after ~2 ps and is then followed by an Fig. 3A compared to the situation in Fig. 3B). This is further clarified exponential decay over a few picoseconds. The dots represent the by the difference pulses shown in blue (∆E = Ered − Eblack, multiplied experimental data from Fig. 3C, while the solid lines guide the eye by four for clarity) that show a larger pump-induced change in trans- (see the Supplementary Materials for further information). This mission for the case of the larger gating voltage. temporal evolution of T/T0 in Fig. 3D is attributed to the nonlin- Figure 3C shows the as-measured transmission of the probe ear thermodynamic modulation of the graphene properties illus- peak field as a function of the pump-probe delay time for various trated in Fig. 1 and its related discussion above. It is also consistent gating voltages. We note that the background probe transmission with observations reported in numerous studies where the electron T0 before the pump decreases with the gating voltage due to increas- temperature dynamics were ascribed to heating-cooling effects ing absorption when the carrier density increases by gating. With using various techniques, including time-resolved angle-resolved the intense terahertz pump, a transient increase in the transmission photoemission spectroscopy (22), TPTP (9), optical pump–terahertz occurs. This nonlinearity becomes much more pronounced at a probe spectroscopy (23–25), and time-resolved photocurrent larger gating voltage. The secondary smaller features observed at microscopy (26, 27). We note here that the time resolution of our ~16.5 ps in Fig. 3C are due to internal round-trip etalon reflection measurement, which is of the order of 2 ps, is limited by the non- within the quartz substrate. Figure 3D shows the analyzed terahertz collinear pump-probe geometry used in the experiment, as shown Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 4 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE A B Normal THz probe E field Normal THz probe E field 1.0 1.0 |V − V 0| =1 V Before pump |V − V0 | = 0.3 V Before pump After pump After pump E×4 E×4 0.5 0.5 0.0 0.0 −0.5 −0.5 2.5 3.0 3.5 4.0 2.5 3.0 3.5 4.0 C Time (ps) D Time (ps) THz probe transmission, T T0 with 80 kV/cm THz pump |V − V 0| 1.00 |V − V0| 0.0 V 6 1.7 V 0.2 V 1.2 V 0.95 T/T0 (%) 0.7 V 0.3 V 4 0.5 V 0.90 0.3 V Downloaded from http://advances.sciencemag.org/ on May 10, 2021 0.5 V 0.2 V 0.85 0.0 V 2 0.7 V 0.80 1.2 V 1.7 V 0 0.75 0 5 10 15 20 25 0 5 10 15 Time delay (ps) Time delay (ps) E 8 F 8 80 kV/cm 1.7 V 60 kV/cm 6 40 kV/cm 1.2 V 6 T/T0,max (%) T/T0, max (%) 20 kV/cm 0.7 V 1 kV/cm 4 0.5 V 0.3 V 4 0.2 V 2 0.0 V 2 0 0 0 20 40 60 80 0.0 0.5 1.0 1.5 2.0 THz pump electric field (kV/cm) |V − V 0 | (V) Fig. 3. Dependence of terahertz field–induced SA on the gating voltage revealed by TPTP spectroscopy. (A and B) The terahertz probe fields before (black) and after (red) intense terahertz pump excitation, normalized to the peak field after excitation with pump peak electric field (80 kV/cm), and their difference (blue) multiplied by four for clarity, for gating voltages of 1 and 0.3 V, respectively. (C) The as-measured peak field transmission of the probe pulses at various gating voltages when the graphene is pumped at 80 kV/cm. T0 is the background probe transmission of the graphene sample before the pump, which increases by decreasing the doping (gating) level. (D) The terahertz probe differential transmission T/T0 = (T − T0)/T0, where T is the probe transmission after the pump, as a function of the pump-probe delay time, obtained by analysis of the experimental data of (C). The dots represent the experimental results, while the solid lines are guides for the eye. (E) The peak of the probe differential signal T/T0 as a function of the terahertz pump field at various doping levels and (F) the peak of T/T0, extracted from (E), as a function of the gating voltage at some selected pump peak electric fields. The pink arrows indicate that the data in (D) and (F) are obtained by analysis of data from (C) and (E), respectively, while the violet arrows in (E) and (F) indicate increase in T/T0 with the gate voltage and the driving field, respectively. in Fig. 2A. The dependence of the peak values of T/T0 on both the branch of the gating voltage, the sample maintains a very similar terahertz pump electric field and the gating voltage is shown in (but not perfectly the same) behavior. Fig. 3 (E and F). The as-measured data of Fig. 3E were obtained, for each gating voltage, via systematic variation of the terahertz peak Terahertz high harmonics field of the pump pulses using a pair of wire-grid polarizers. We see In Fig. 4, we show the results of the nonlinear multicycle terahertz-­ that T/T0, i.e., the nonlinear response of graphene, increases with TDS experiment using the same gated graphene sample. In this both the terahertz pump field and the gating voltage. We further see experiment, the sample was excited by a multicycle terahertz field the saturation of T/T0 setting in for gating voltages exceeding 0.7 V, with a central frequency of 0.3 THz, as shown in the inset of which mimics the behavior of the graphene sheet resistance shown Fig. 4A. The peak electric field of the driving pulse was as high as in Fig. 2D. We also note here that the data shown in Fig. 3 were 80 kV/cm, i.e., the same as the pump peak field in the single-cycle collected for the negative branch of the gating voltage. On the positive TPTP experiment. The response of the graphene sample was revealed Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 5 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE A B Higher harmonic E field (V/cm) 1000 Spectral amplitude (a.u.) 80 (3) THz driving field 1 (1) 40 (kV/cm) 0.56 V 0 0.1 0.4 V −40 100 −80 0.01 (3) 0 10 20 30 40 50 Time (ps) (5) 0.001 (5) 10 1 × 10−4 (7) (7) 1 × 10−5 0.28 V 0.14 V 1 Noise floor 1 × 10−6 0.0 0.5 1.0 1.5 2.0 0.1 0.2 0.3 0.4 0.5 0.6 Frequency (THz) |V − V0| (V) Fig. 4. Gating dependence of terahertz HHG. (A) The terahertz amplitude spectra of the terahertz fields of the incident driving field and the transmitted fields through the graphene sample exhibiting generation of higher odd-order harmonics up to the seventh order for two doping levels, with the driving terahertz signal shown in the inset, and (B) the peak electric field of the generated harmonics as a function of the gating voltage. Downloaded from http://advances.sciencemag.org/ on May 10, 2021 through transmission measurements using calibrated free-space the corresponding EF shown in Fig. 5C. We see a good agreement electro-optic sampling detection of the transmitted terahertz field. between the experiment and the model calculations for the assumed In Fig. 4A, we show the frequency-domain spectra of the terahertz range of EF up to 200 meV, in which the graphene nonlinearity pulses transmitted through the graphene sample at various gating (both differential transmission and HHG) is enhanced substantially voltages. The spectrum includes odd-order higher harmonics of the with increasing EF. Above this doping level and up to EF~260 meV, fundamental frequency f1 = 0.3 THz up to the seventh order, namely we see from Fig. 5A that the experimental data show saturation in centered at the higher-harmonic frequencies f3 = 0.9 THz, f5 = the nonlinearity, which is also captured by the model calculations. 1.5 THz, and f7 = 2.1 THz. We note here that a conservative estimate We attribute this saturation behavior to the fact that the electronic of the corresponding nonlinear electronic susceptibilities for HHG heat capacity of graphene increases with EF at high doping levels from graphene in the perturbative regime (namely at lower driving (28–30), restricting the increase in the carrier temperature with fur- terahertz fields below 30 kV/cm) are as high as (3)~10−9 m2/V2, ther increase in terahertz field excitation, which leads to a smaller (5)~10−22 m4/V4, and (7)~10−38 m6/V6, for the third-, fifth-, and increase in the graphene nonlinearity at these high Fermi energies seventh-order harmonics, respectively (14). These values are several (see the Supplementary Materials for further information). These effects orders of magnitude larger than the analogous coefficients of other are automatically included in the thermodynamic model by respect- known materials investigated in many different frequency ranges ing the conservation of energy and total carrier density (11, 12, 30). (12, 14). As we see from Fig. 4A, the amplitudes of the generated In our model calculations, we considered a range of EF from 50 harmonics, normalized to the peak at the fundamental frequency, to 260 meV (as a variable parameter) to be equivalent to the values are strongly enhanced by increasing the gating voltage from 0.14 corresponding to the experimentally applied gating voltage ∣V − V0∣ to 0.56 V. in the range from 0 to 2 V, as shown in Fig. 5C. As previously noted, Figure 4B shows the dependence of the actual peak electric fields EF is never uniformly zero at ∣V − V0∣ = 0. Therefore, we assigned of the generated harmonics on the gating voltage, for a terahertz a value of EF= 50 meV to the gating voltage ∣V − V0∣ = 0, which is driving field of 80 kV/cm at the peak. Here, increasing the gating consistent with the puddle energy estimates reported in previous voltage from 0.14 to 0.56 V leads to a magnification of the generated works on similar graphene samples (25, 31, 32). The initial linear harmonic fields by factors of 9 for the third harmonic, 4 for the fifth increase in EF with the gating voltage is consistent with Hall mea- harmonic, and 3 for the seventh harmonic, which correspond to surements (see the Supplementary Materials). Another free param- enhancement factors of 81, 16, and 9 for the power conversion effi- eter used in our calculations is the momentum scattering time 0 ciencies of these harmonics, respectively. These results display a associated with the linear response of graphene to low terahertz wide range of tunability of the graphene nonlinearity and can pave fields and is considered to be a function of EF (24, 25, 33), as shown ways for practical graphene-based ultrahigh-frequency electronics. in Fig. 5D. Here, we considered the linear terahertz peak transmission T0 indicated in Fig. 3C, which is related to the “frequency-integrated Modeling the experimental results conductivity” of the graphene layer, to estimate 0 and EF as carefully We now reproduce the experimental results through simulations chosen pairs of values that reproduce the nonlinear response to the based on the thermodynamic model discussed above [see the Sup- intense driving signals as well. We note that choosing other pairs of plementary Materials and (12, 14) for further information]. In our 0 and EF in our calculations resulted in a significant deviation calculations, we simulate the nonlinear propagation of the driving between the model and the experimental data. With the obtained terahertz signals, in the time domain, through the graphene layer at range of EF and 0, we extract a carrier mobility of ~3000 cm2/Vs, various Fermi energies corresponding to the experimentally tested which is consistent with values reported for typical CVD graphene gate voltage. In Fig. 5 (A and B), we show the model calculations (34, 35). Moreover, the increase in 0 with EF indicates that long- (solid lines) along with the experimental results (symbols) of Figs. 3F range Coulomb scattering dominates the carrier scattering process and 4B, respectively, after replacing the gating voltage ∣V − V0∣ by (24, 25, 33). Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 6 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE A 8 C 300 80 kV/cm Fermi energy, EF (meV) 60 kV/cm 6 40 kV/cm T/T0, max (%) 20 kV/cm 200 1 kV/cm 4 100 2 0 0 50 100 150 200 250 300 0.0 0.5 1.0 1.5 2.0 2.5 Fermi energy, EF (meV) |V − V0| (V) B D Higher-harmonic E field (V/cm) 10000 100 3rd 90 0 (fs) 5th Downloaded from http://advances.sciencemag.org/ on May 10, 2021 1000 80 7th 70 Scattering time, 100 60 50 10 40 30 1 20 Noise floor 10 0.1 50 100 150 200 250 300 100 200 300 Fermi energy, EF (meV) Fermi energy, EF (meV) Fig. 5. The thermodynamic model calculations. (A and B) The thermodynamic model calculations (solid lines) and the experimental results (solid circles) of the peak of T/T0 and the electric field of the generated harmonics up to the seventh order, respectively, as functions of the EF and various terahertz pump fields, (C) EF as a function of the gating voltage, and (D) the carrier momentum scattering time as a function of EF. Conclusions MATERIALS AND METHODS The gigantic terahertz nonlinearity of graphene can be efficiently In the TPTP experiment, intense single-cycle terahertz pulses with tuned by modest gating voltages. Our findings thus pave the way for a peak electric field strength up to 80 kV/cm are generated by opti- exploiting graphene in applications that require a straightforward cal rectification of 800 nm, 40 fs Ti:sapphire laser pulses in a LiNbO3 control of its nonlinear behavior. Therefore, applications such as crystal, following the pulse-front tilting technique (39, 40), and are graphene-CMOS hybrid devices for tunable frequency conver- used as the pump pulses to excite the graphene sample. The tera- sion, efficient nonlinear terahertz modulators, shutters, switches, hertz probe pulses, with a much weaker peak electric field of less and conceivably other applications, are all expected to benefit from than 1 kV/cm, are generated by optical rectification of 800-nm pulses both the gigantic nonlinearity of graphene and the possibility to from the same Ti:sapphire laser in a 1-mm-thick (110) ZnTe crystal. efficiently tune it by a small gating voltage. Graphene also allows Both pump and probe pulses are detected by free-space electro-­ for electrical modulation at exceptionally high speeds, limited optic sampling in another 1-mm-thick (110) ZnTe crystal. Spatial ultimately by the carrier cooling time of a few picoseconds, thus separation between the pump and probe beams after the graphene corresponding to a bandwidth of a few hundreds of gigahertz. sample was attained by following a noncolinear incidence onto the Graphene-based amplitude (36) and phase (37) modulators with sample. Combined with a cross-polarization scheme (s-polarization bandwidths as large as a few tens of gigahertz have been already for the intense pump beam and p-polarization for the weak probe), demonstrated. Whereas these speeds cannot be reached with the this sufficiently suppressed the intense pump beam after the sample polymer electrolyte that we used here, it is attainable for example to allow for a sensitive detection of the weak probe pulses that carry with a doped silicon back gate or by hybridizing the electrolyte-­ the desired information about the pump-induced effects in graphene. gated graphene with back-gating (38). This opens prospects for In the multicycle experiments, the graphene sample was excited efficient nonlinear conversion of terahertz signals that can be mod- by terahertz pulses generated by the accelerator-based TELBE su- ulated with a bandwidth of tens of gigahertz or even higher, which perradiant source (41, 42), with a central fundamental frequency of is of great interest for ultrahigh-speed information and communi- 0.3 THz, as shown in Figs. 2B and 4A. The incident and transmitted cation technologies. terahertz pulses through the graphene sample have been detected Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 7 of 9 SCIENCE ADVANCES | RESEARCH ARTICLE by electro-optic sampling in a 1.9-mm-thick (110) ZnTe crystal. To 14. H. A. Hafez, S. Kovalev, J. C. Deinert, Z. Mics, B. Green, N. Awari, M. Chen, S. Germanskiy, enable sensitive detection of the generated harmonics and reduce U. Lehnert, J. Teichert, Z. Wang, K. J. Tielrooij, Z. Liu, Z. Chen, A. Narita, K. Müllen, M. 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Probing ultra-fast processes with high dynamic range at 4th-generation light sources: Arrival H.A.H., K.-J.T., and D.T. wrote the manuscript with contributions from M.Bo., J.-C.D., M.M., and time and intensity binning at unprecedented repetition rates. Struct. Dyn. 4, 024301 (2017). M.G. All coauthors discussed the results and commented on the manuscript. Competing 43. A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V. Waghmare, K. S. Novoselov, interests: The authors declare that they have no competing interests. Data and materials H. R. Krishnamurthy, A. K. Geim, A. C. Ferrari, A. K. Sood, Monitoring dopants by Raman availability: All data needed to evaluate the conclusions in the paper are present in the paper Downloaded from http://advances.sciencemag.org/ on May 10, 2021 scattering in an electrochemically top-gated graphene transistor. Nat. Nanotechnol. 3, and the Supplementary Materials. Additional data related to this paper may be requested 210–215 (2008). from the authors. 44. I. Gierz, F. Calegari, S. Aeschlimann, M. Chávez Cervantes, C. Cacho, R. T. Chapman, E. Springate, S. Link, U. Starke, C. R. Ast, A. Cavalleri, Tracking primary thermalization events Submitted 2 December 2020 in graphene with photoemission at extreme time scales. Phys. Rev. Lett. 115, 086803 (2015). Accepted 19 February 2021 Published 7 April 2021 Acknowledgments: We would like to thank J. Teichert, U. Lehnert, and Z. Wang for assistance. 10.1126/sciadv.abf9809 We would like to acknowledge discussions with Z. Mics. We thank J. Sierra, M. Costache, X. Jia, and S. Valenzuela for assistance with the Hall measurements. Funding: D.T. and H.A.H. Citation: S. Kovalev, H. A. Hafez, K.-J. Tielrooij, J.-C. Deinert, I. Ilyakov, N. Awari, D. Alcaraz, acknowledge funding from the European Union’s Horizon 2020 Framework Programme under K. Soundarapandian, D. Saleta, S. Germanskiy, M. Chen, M. Bawatna, B. Green, F. H. L. Koppens, grant agreement no. 964735 (EXTREME-IR). M.G. and B.G. acknowledge support from the M. Mittendorff, M. Bonn, M. Gensch, D. Turchinovich, Electrical tunability of terahertz nonlinearity European Cluster of Advanced Laser Light Sources (EUCALL) project that has received funding in graphene. Sci. Adv. 7, eabf9809 (2021). Kovalev et al., Sci. Adv. 2021; 7 : eabf9809 7 April 2021 9 of 9 Electrical tunability of terahertz nonlinearity in graphene Sergey Kovalev, Hassan A. Hafez, Klaas-Jan Tielrooij, Jan-Christoph Deinert, Igor Ilyakov, Nilesh Awari, David Alcaraz, Karuppasamy Soundarapandian, David Saleta, Semyon Germanskiy, Min Chen, Mohammed Bawatna, Bertram Green, Frank H. L. Koppens, Martin Mittendorff, Mischa Bonn, Michael Gensch and Dmitry Turchinovich Sci Adv 7 (15), eabf9809. DOI: 10.1126/sciadv.abf9809 Downloaded from http://advances.sciencemag.org/ on May 10, 2021 ARTICLE TOOLS http://advances.sciencemag.org/content/7/15/eabf9809 SUPPLEMENTARY http://advances.sciencemag.org/content/suppl/2021/04/05/7.15.eabf9809.DC1 MATERIALS REFERENCES This article cites 44 articles, 1 of which you can access for free http://advances.sciencemag.org/content/7/15/eabf9809#BIBL PERMISSIONS http://www.sciencemag.org/help/reprints-and-permissions Use of this article is subject to the Terms of Service Science Advances (ISSN 2375-2548) is published by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. The title Science Advances is a registered trademark of AAAS. Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).