Mechanism and modulation of terahertz generation from a semimetal - graphite

Semi-metals might offer a stronger interaction and a better confinement for terahertz wave than semiconductors, while preserve tunability. Particularly, graphene-based materials are envisioned as terahertz modulators, filters and ultra-broadband sources. However, the understanding of terahertz generation from those materials is still not clear, thus limits us recognizing the potential and improving device performances. Graphite, the mother material of graphene and a typical bulk semi-metal, is a good system to study semi-metals and graphene-based materials. Here we experimentally modulate and maximize the terahertz signal from graphite surface, thus reveal the mechanism - surface field driving photon induced carriers into transient current to radiate terahertz wave. We also discuss the differences between graphite and semiconductors; particularly graphite shows very weak temperature dependency from room temperature to 80 °C. Above knowledge will help us understand terahertz generations, achieve maximum output and electric modulation, in semi-metal or graphene based devices.

(second or third order) nonlinear optical rectification 33,35 , is used to explain experimental results. However, how the carriers become transient current and the details of the mechanism are still unanswered.
Here, we report on the modulation and maximization of terahertz pulses radiated from voltage biased graphite. Our result clearly proves the physical nature of THz generation in graphite, surface field driving photon induced carriers into transient current to radiate THz wave. We also perform ab initio simulations to verify the gating field effect on graphite. The calculation result supports the gating modulation and saturation behavior, observed from our experiment. It also quantitatively supports that the THz saturation amplitude difference between positive and negative gate voltages is the result of the effective mass difference between electrons and holes, which have a ratio about 2.3. Compared to THz generation from semiconductors, the graphite shows differences: much quicker amplitude saturation for the surface field tuning, and very weak temperature dependence. All these two differences are the results of a much higher free-carrier density in graphite, a semi-metal, than semiconductors. This work not only helps us understand the physics of THz generations in bulk semi-metals or graphene based devices, but also demonstrates the electric modulation ability and signal maximization in semi-metallic THz generation devices.

Results
Electrically modulated THz generation setup. Figure 1a shows the sketch (side view) of the graphite sample and experiment setup. The graphite sample is a ZYA grade Highly Ordered Pyrolytic Graphite (HOPG) with a size of 12 × 12 × 2 mm 3 from Structure Probe Inc. Before THz emission measurements, a fresh flat surface was prepared by mechanical exfoliation. An ion-gel top gate was made for the application of a tunable electric field normal to and at the graphite surface. A Keithley 2400 is used as the gate voltage source (V g ) and monitors the gate current as well. An aluminum plate supports and connects the back side of the graphite to the negative electrode of the gate source. A circle of copper adhesive foil functions as the positive electrode of the gate voltage, is separated by a layer of insulting adhesive tape from the graphite, and is connected by ion-gel 36 with the top surface of the graphite. The resulting gate capacitance of the setup is about 1.3 μF. The center openings of the copper adhesive foil and insulting tape are about 25 mm 2 in squares, in order for the placing of ion-gel on and the optical addressing to the graphite top surface.
A linear polarized femtosecond laser, operating at 800 nm central wavelength with 80 MHz repetition rate and 70 fs pulse duration, was focused onto the graphite surface. The incident laser power was about 400 mW, the incident angle was 60°, and the spot diameter was about 2 mm. The radiated THz pulses in the reflective direction were measured with a ZnTe (110) electro-optic crystal, and the detection 800 nm laser power was about 30 mW. The measured THz waveforms and their peak-to-peak amplitudes as functions of the gate voltage (V g ) are plotted in Fig. 2. The transformed spectra data is plotted and discussed in the supplementary information file. Figure 2 clearly illustrates the modulation of the THz signals with the gate voltage. Figure 2a shows the temporal waveforms of the THz signals generated from the basal plane of graphite, when the gate voltage decreases from positive 2.5 V to negative 3 V. Figure 2b shows the peak-to-peak amplitude of the THz pulse as a function of the gate voltage. The gate voltage was scanned from 0 V to 2.5 V, and then was scanned back to − 3 V. Figure 2b shows the data from both the voltage increasing scan (black square points) and decreasing scan (red circle points). In Fig. 2b, the gate voltage upward scan curve matches the downward scan curve very well; this indicates hysteresis of the gate scan is negligible. Therefore, we only plot the V g downward scan THz waveforms in Fig. 2a, which clearly shows that a higher gate voltage will give a stronger THz signal until saturation. Changing the gate voltage direction will result in the THz signal turning to the opposite direction. The bias voltage for minimum THz amplitude is not exactly 0 V, because of a residue or chemical doping of the graphite surface. In Fig. 2b, we also notice that the THz pulses under different gating directions show different saturation amplitudes. We define I p , the saturation amplitude for positive V g , and I n , the saturation amplitude for negative V g . I p is 2.3 times of I n , or, I p /I n = 2.3. This difference is due to the effective mass difference of electrons and holes in Z direction of graphite. We will prove this point later with our theoretical calculation. We also performed a second measurement with a different but same kind HOPG sample, in order to test the dispersion of the value of I p /I n ; details and discussions are in the supplementary information file. Figure 2, together with previously reported experiments 33,37 , clearly proves the mechanism of graphite THz generation. The excitation 800 nm laser pulse is absorbed by the graphite surface to generate electron hole pairs; then, a surface field normal to the graphite basal plane drives the pairs into transient current to generate the THz radiation. A previous report shows that the THz signal is independent to the excitation light's polarization at various conditions (e.g. different incident angles) 37 , and supports that the excitation pulse contributes the photo-carriers through sample light absorption. Here, our gating measurement proves that the surface field normal to the graphite basal plane is the driving force of the transient current, which radiates the THz pulse. Figure 1b,c show the sketch of the surface field and electric potentials of graphite under different V g , (b) for a large positive V g , and (c) for a large negative V g . When the V g is positive, it generates an electric field pointing into and at the surface of graphite with the help of the ion-gel. This field penetrates into the graphite surface, thus builds a surface field normal to the basal plane. However, the field inside graphite is reduced due to the screening of graphite as it goes deep into the body. When the V g increases, the field on and inside graphite increase as well; the ion-gel will not fail in working until V g is outside the range of ±3 V. When the V g is negative, the ion-gel works similarly but with the opposite field direction. When V g = 0, graphite still has a small surface field because graphite is naturally n-doped. Therefore, we achieve the modulation of the surface field of graphite using ion-gel, and our result in Fig. 2 proves the direct connection between the surface field and the generated THz signal, both in magnitude and direction. Ramakrishnan et al. first attributed the terahertz generation of graphite to the transient photocurrent in the direction normal to the basal plane 33 ; our work here, with well controlled experiment conditions, clearly demonstrates that how the photo-carriers are driven into transient current and the key role of surface field in the process.

Surface field modulation.
Simulation parameters and results. We use ab initio theoretical method to calculate the surface field and electron dispersion curve of graphite in Z direction, prove that the saturation behavior of THz amplitude in Fig. 2b is the result of graphite screening of the external field, and quantitatively verify that the difference in saturation amplitudes for opposite field directions is indeed due to the effective mass difference of electrons and holes. The band structure and local potential of graphite are calculated based on density functional theory (DFT) with the Vienna Ab initio Simulation Package (VASP) 38 . Projector-augmented wave pseudo-potential and plane wave energy cutoff of 600 eV are employed. Generalized gradient approximation in the PBE form 39 is used to express the exchange-correlation functional. The K-point grid of 15 × 15 × 5 is used to sample the first Brillouin zone of bulk graphite. The atomic structure is relaxed until the force on each atom is less than 0.01 eV/Å. The local potential in graphite in response to external electric field is calculated using a 10-layer graphite slab. When calculating a graphite slab, a sufficiently large vacuum space of more than 15 Å in the surface normal direction is adopted. An external field is applied using a dipole placed in the middle of vacuum region. The induced field strength inside graphite as a function of external field applied is calculated and shown in Fig. 3a. It is clear that the field at the surface layer of graphite (the outmost layer of the graphite slab) has approximately a linear relationship with the external field applied with a dimensionless slope of ~0.3. On the contrary, the field on layers below the first layer initially increases linearly with the external field E ext up to 0.4 × 10 10 V/m, then it quickly saturates around a value of 0.02 × 10 10 V/m for |E ext | ≥ 0.5 × 10 10 V/m. Under a positive field (with field vector outgoing from the graphite surface), although the induced field at the second layer keeps increasing, local field at layers below the second layer all slightly decreases with the increase in external field after E ext ≥ 0.5 × 10 10 V/m. The calculated band structure along the K-H direction (Z direction, normal to basal plane) is shown in Fig. 3b. We find that besides the flat band around Fermi level, there are two additional dispersive electronic bands, which separate by ~1.4 eV at K point, and join each other at the Fermi level at H point. These two bands come from the interlayer interaction between the p z orbitals of graphite layers, which are sensitive to the interlayer distance of graphite. We find that the curvature of the two bands changes dramatically as the electron potential deviates from the Fermi level. The effective electron/hole masses are thus calculated from the curvatures of the two bands using the equation Temperature dependence. Furthermore, we look into the similarities and differences between graphite, a semi-metal, and semiconductors in the THz generation (surface field induced). Both of them generate THz with a surface field in the normal direction, and both of them show that a surface field tuning results in a THz signal modulation 40 . However, graphite THz generation appears with a much quicker amplitude saturation for the surface field tuning (in Fig. 2b), in comparison to the semiconductors 40 . Graphite also shows very weak temperature dependence, as semiconductors give highly enhanced THz radiation at a high temperature 41 . Figure 4 shows the THz waveforms of the graphite surface at different sample temperatures. The graphite was heated by a small heater on the backside and the temperature was monitored with a sensor on the graphite front surface. Other measurement settings were the same as those of the gating measurement, but without the ion-gel on graphite for the V g = 0 V measurement. The slight amplitude drops at high temperatures in Fig. 4 are due to an off-focus effect, as the mounting of the graphite sample extends about 0.3 mm at the highest temperature. For the V g = 3 V data, the THz signal drops intensity at 28 °C, then goes to opposite phase at 46 °C, and stays about same for further higher temperatures. This phase reversion for V g = 3 V, probably is due to graphite's naturally n doping surface field overcomes and surpasses the ion-gel induced gating field. Either graphite's naturally n doping surface field gets enhanced or the ion-gel starts to fail, when the sample temperature goes higher from room temperature. In general, Fig. 4 demonstrates that the THz signal from graphite is not responding to the temperature change from  room temperature to 80 °C. All those two differences, the faster amplitude saturation and very weak temperature dependency, are the results of a much higher free-carrier density in graphite, a semi-metal, than semiconductors. The high free-carrier density provides a strong field screening in the surface field tuning measurement and makes graphite much less sensitive to temperature than semiconductors, whose defect associated carrier levels are normally very sensitive to the temperature. Figure 3a indicates a strong screening effect exists in graphite: within 2-3 layers beneath the graphite surface, the external field is largely screened out and the local field saturates quickly around a relatively small value (2% of the external field). This field screening behavior in Fig. 3a is consistent with the saturation behavior of THz amplitude in Fig. 2b; this proves the saturation of the THz amplitude is the result of screening of the surface field. Considering the saturation field in graphite is about 0.02 × 10 10 V/m and surface field extends only about 3 atom layers into the bulk (layer spacing is 0.335 nm), we have a maximum Fermi level of ±0.2 eV at graphite surface while the bulk body is always considered to be the Fermi level zero point. When V g is a sufficiently large positive value, graphite surface (with ion-gel) has a potential of V sur ≈ + 0.2 eV (in Fig. 1b). This positive V sur corresponds to − 0.2 eV Fermi level in electron dispersion curve, and cuts the lower band (the blue one in Fig. 3b upper panel). The cutting position is the Fermi surface, determines the effective mass of the quasi-particles, and gives an effective mass m * = 2.5 m 0 (m 0 is the electron mass). For a large negative V g value (in Fig. 1c), V sur ≈ − 0.2 eV; the Fermi level cuts the upper band (the red one in Fig. 3b) at + 0.2 eV level, and gives an effective mass m * = 5.5 m 0 . For the THz generation in a semiconductor under the surface field effect, its amplitude is proportional to ⁎ E/m , where E is the surface field and m * is the quasi-particle effective mass. It is reasonable to assume that the THz amplitude from graphite satisfies the same rule and is proportional to ⁎ E/m . Our test shows that the ion gel works fine for gating when the V g is within ± 3 V, however the THz signal already flats out at about ± 1 V. This suggests that the saturation in THz signal is due to the saturation of the field within graphite, even as the external field keeps increasing with a larger V g . This picture is supported by the result in Fig. 3a from our calculation. Considering the saturation surface field within graphite is same for positive and negative V g (see Fig. 3a The agreement quantitatively proves that the difference in saturation amplitudes for opposite field directions is due to the effective mass difference of electrons and holes, and greatly supports our physical picture for the THz generation mechanism.

Discussion
In conclusion, we carry out a surface field modulation and a temperature variation experiments on THz signal emitted from graphite. Our result clearly proves the THz generation mechanism, the surface field driving photo-carriers into transient current to radiate THz wave. We also perform ab initio calculation for the field screening effect and electron dispersion curves in Z direction of graphite. Theoretical result strongly supports our physical picture and shows that external field is screened after 2-3 atom layers of graphite. The THz saturation amplitudes of positive and negative gate voltages have a ratio of 2.3, because the effective mass of electrons is about 2.3 times of the effective mass of holes in Z direction (normal to basal plane) of highly gated graphite. Despite the similarities in the mechanism to semiconductors, graphite has quicker amplitude saturation and is insensitive to the temperature in the range of room temperature to 80 °C.