Photo-induced terahertz near-field dynamics of graphene/InAs heterostructures

In this letter, we report optical pump terahertz (THz) near-field probe (n-OPTP) and optical pump THz near-field emission (n-OPTE) experiments of graphene/InAs heterostructures. Near-field imaging contrasts between graphene and InAs using these newly developed techniques as well as spectrally integrated THz nano-imaging (THz s-SNOM) are systematically studied. We demonstrate that in the near-field regime ( / 6000 λ ), a single layer of graphene is transparent to near-IR (800 nm) optical excitation and completely “screens” the photo-induced far-infrared (THz) dynamics in its substrate (InAs). Our work reveals unique frequency-selective ultrafast dynamics probed at the near field. It also provides strong evidence that n-OPTE nanoscopy yields contrast that distinguishes single-layer graphene from its substrate. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

probing the local far-infrared properties of nanomaterials on select substrates and provides an interesting frontier for future research on THz emission dynamics in novel quantum materials [10][11][12][13][14].
In this work, we perform optical pump terahertz (THz) near-field probe (n-OPTP) and optical pump THz near-field emission (n-OPTE) experiments on graphene/InAs heterostructures. This specific sample is chosen to illustrate the unique near-field reflection and emission phenomena at THz frequencies in these two technologically important THz materials. Specifically, graphene has been demonstrated to possess unique far-infrared behavior in the extreme subwavelength regime [15,16]. Unlike in the mid-IR frequency range where plasmon propagation can be readily measured [17][18][19][20][21][22], the high momentum coupling between the photon and electrons in THz s-SNOM yields a strong tip-sample interaction and a close-to-perfect near-field THz reflection in high mobility graphene [16]. This interesting phenomenon arises naturally when evanescent optics with high in-plane light-momentum meet the high in-plane THz conductivity of graphene. As we will further demonstrate in this work, this near-perfect THz near-field reflectivity of graphene can effectively "screen out" the pump-induced carrier dynamics in its InAs substrate while graphene remains "transparent" to the optically induced THz emission from beneath. Fig. 1. Schematic of the near field optical-pump THz-probe (n-OPTP) setup, equally capable of performing optical pump near-field THz emission (n-OPTE) experiments. : 800 nm, 300 mW pump pulses pass through the ITO then go through the center of, while parallel to, the THz beam . Optical pump  and THz probe  are focused onto the AFM tip apex using an off-axis parabolic mirror. : THz gate (detection) beam. Tip scattered THz signals can be mapped out in the time domain by modifying the arrival time of THz gate beam  to the THz photoconductive antenna detector, thus changing the delay between  and  (t 1 ). Changing the delay between  and  (t 2 ) by modifying arrival time of pump pulse  probes the photoexcited ultrafast dynamics of the sample (see main text), where in this work, t 1 is fixed at the peak position of the scattered THz electric field while t 2 is varied to yield n-OPTE (with THz probe  blocked) and n-OPTP (with THz probe  unblocked) measurements.

Methods
In Fig. 1, we illustrate our home-built THz near-field system based on a commercial AFM (NT-MDT NTEGRA Lite). The 800 nm pulses are generated using a 35 fs, 78 MHz Tisapphire oscillator (Spectra-Physics MaiTai SP). We split the 800 nm beam into three separate optical paths: the optical pump beam, the THz probe generation beam and the THz gate (detection) beam (, ,  respectively, as shown in Fig. 1), which is the same as a typical far-field OPTP setup. The THz pulses are generated and detected through a pair of THz photoconductive antennas (PCA, TeTechS inc.). To perform near-field THz measurement and achieve ~50 nm spatial resolution, the THz beam is focused onto the AFM tip with a diffraction-limited spot using a 50.8 mm diameter parabolic mirror with a focal length of 38.1 mm. The back scattered THz light from the tip is collected by the same parabolic mirror and then directed into another PCA detector following a separate beam path. By modifying the arrival time of gate beam to the PCA detector, we are able to adjust the time delay between the 800 nm gate beam and THz beam (t 1 ), allowing us to effectively map the THz electric field in the time-domain (THz time-domain spectroscopy, THz-TDS). When performing the pump-probe measurement, t 1 is fixed at the peak position of the THz pulse and the time delay between the pump and the gate beam (t 2 ) is varied by modifying the arrival time of the pump pulse. By convention, in the following discussions of n-OPTP, time zero is set to when the optical pump pulse and the peak of THz probe pulse overlay one another.
To yield genuine near-field signal from the tip-sample interaction and eliminate the far field backgrounds, we demodulate the scattered THz signal at the second harmonic of the tip tapping frequency. The signal-to-noise ratio of the near-field signal S 2 is approximately 14:1, using an integration time per pixel of 100 ms. The graphene samples are exfoliated onto PDMS (polydimethylsiloxane) and then transferred onto 2 µm InAs thin film grown on 500 μm GaAs substrate. The InAs layer was grown via molecular beam epitaxy (MBE) and Sidoped to ~10 17 cm −3 [23].

Results
Prior to the discussion of the ultrafast dynamic responses, we first compare the THz s-SNOM imaging with the IR s-SNOM imaging of a graphene/InAs heterostructure. The static THz near-field imaging is done by blocking beam  and allowing beams  and  to operate. In Fig. 2, we show the AFM topography (left) and near-field images (right) of the same sample using mid-IR (top row) and THz (bottom row) s-SNOM without the 800 nm pump. (The nearfield IR imaging is performed using a separate system with a CO 2 laser at ~10.8 μm [24,25].) The AFM topography mappings in both systems yield similar results which verifies that the location and quality of the sample is maintained between measurements. For IR near-field imaging, the difference between the InAs substrate and graphene is relatively small, while the contrast between the different number of layers of graphene is evident; one can easily distinguish single layer graphene (SLG) and bilayer graphene (BLG). In comparison, for THz near-field imaging, there is a strong contrast between the bare InAs substrate and the graphene, while the single layer and bilayer graphene are indistinguishable. We have previously reported on the similarity of THz near field signals among different layers of graphene and its close to unity signal level [16]. We note that for high quality graphene samples with typical doping at ambient environment conditions such as ours, it has been documented that the single layer and bilayer graphene are indistinguishable [26]. However, it is possible that when the Fermi level is much closer to the Dirac point (within several meV), the differences between single layer and bilayer graphene can still be resolved with THz nearfield imaging. The mobility and asymmetry of electrons or holes may also contribute to this distinguishability, providing an interesting subject for future studies. The dotted line shows that there is no notable change for the baseline of THz reflection signal before and after the pumping of SLG/InAs. Next, we discuss the n-OPTP measurements, which are the main results of this letter. Figure 3(a) illustrates the experimental setup where the optical pump and THz probe are both present. Therefore, the photo-induced n-OPTP dynamics contain contributions from both the THz emission and the THz near-field scattered signal. In contrast to the THz near-field imaging without the pump ( Fig. 2(d)), near-field OPTP imaging reveals slightly higher signals from the bare InAs than that from single-layer graphene/InAs (SLG/InAs) ( Fig. 3(b), with t 2 fixed at the peak of THz field). This small signal contrast will be discussed later. In Figs. 3(c) and 3(d), we demonstrate the n-OPTP dynamics of the bare InAs and SLG/InAs, respectively. In bare InAs, with 800 nm optical excitation, both near-field THz generation and photo-induced ultrafast carrier dynamics are present. The emitted near-field THz signal is the oscillatory part of the curve in Fig. 3(c), while the pump-induced carrier dynamics in InAs cause the rising baseline indicated by the dotted black curve. Oppositely, for SLG/InAs the rise of the baseline does not appear (indicated by the dotted black curve in Fig. 3(d)), suggesting that the signal from the carrier dynamics, here the change of near-field reflectivity in THz range, in InAs is effectively screened out by graphene. Since the THz near-field signal in this n-OPTP measurement includes both the near-field THz emission and the THz scattering, extra steps must be executed to identify the contributions of the two different dynamics.
With the incident THz beam  blocked, we record only the THz emission signal via n-OPTE experiments. The experiment is schematically shown in Fig. 4(a). It is clear that the near-field THz emission microscopy yields very small contrast between bare InAs and SLG/InAs ( Fig. 4(b)). The emission signal is taken with t 2 at the THz peak (green circle in Figs. 4(c) and 4(d)). Upon comparison of the n-OPTE dynamics between Figs. 4(c) and 4(d), it becomes evident that InAs shows comparable THz near-field emission signal with or without the graphene coverage. The bare InAs is only slightly (<10%) higher. This suggests that the optically generated THz emission from the InAs substrate is not blocked by SLG. Moreover, this small contrast between graphene and InAs in Fig. 4(b) proves that the THz near-field emission nanoscopy works with an optical contrast that distinguishes a single atomic layer. In addition, since the incident THz probe light is absent, neither SLG nor InAs shows a rising "baseline" in n-OPTE experiments (Figs. 4(c) and 4(d)). This suggests that the rising baseline in the n-OPTP experiment (Fig. 3(c)) indeed results from pump induced carrier dynamics in InAs, which manifests itself as an increase of THz near-field reflectivity following optical excitation. Such photoinduced THz dynamics in InAs can be effectively screened by a single layer of graphene, which agrees with our previous observations: with high light momentum, graphene shows close to unity reflectivity at the THz frequencies despite the change of optical properties in the substrate [16].

Discussion
For completeness, we also performed a rigorous calculation to understand the near field contrast at various frequencies. The details of the model are described in the Appendix, which produces similar results to the point dipole analysis [27]. The complex dielectric function of InAs and the complex 2d conductivity of graphene are used to yield simulated s-SNOM S 2 signals. The conductivity of graphene was modeled by Eq. (4) in the Appendix, as derived in [28], where a scattering rate of ν = 10 meV and a temperature of T = 300 K is used. The dielectric properties of InAs were determined by the Drude formula, which is extensively used in probing semiconductors with s-SNOM technique [4,[29][30][31]. The effect of optical pumping is modeled by the rise of carrier density N d to ~10 19 cm −3 [32]. The parameters for the Drude formula are the following: 14. is the effective electron mass and μ = 3.5·10 3~2 .5·10 4 cm 2 /Vs is the mobility [23,33]. Figure 5 shows the simulation results of the S 2 signal acquired from bare InAs, as well as InAs covered by SLG with various carrier mobilities and carrier densities of InAs and Fermi energies of graphene. From the solid curves in Fig. 5, it is seen that SLG exhibits its screening properties at frequencies below about 1-2 THz (photon energy is about 4-8 meV), more or less independently from its Fermi energy. This is in agreement with the relatively simple concept of oscillation theory which states that an action on a system with a frequency below its reversed relaxation time (that equals ν = 10 meV in the case of SLG) can be considered as (quasi)static. Similar behavior of the S 2 frequency dependence occurs in the case of bare InAs (dotted curves in Fig. 5 when InAs can be considered as intrinsic [4]. The width of transmission region ω Δ is about ν, where ν is electron scattering rate in InAs. From a qualitative point of view, the dependencies are in agreement with the S 2 contrasts between bare InAs and InAs covered by SLG or BLG obtained in the experiments. Approximately, BLG can be considered as SLG under the same conditions, but with twice the conductivity (see Appendix). In our case, it's difficult to reproduce the specific contrasts observed in experiment due to several reasons. The first is that the exact values of the Fermi energy and of the electron scattering rate in graphene are unknown. The second is that we are probing the surface depletion layer of InAs where the carrier density is effectively reduced [34]. The third is that the tip enhanced THz field effectively reduces the carrier mobility [23]. Simulations that can achieve exact replication of experimental results demands further research work.

Conclusion
From the coherent study of the pump induced THz near-field dynamics, we conclude that a single layer of graphene is a near-perfect THz near-field "scatterer". It can couple the THz field from above or below, incident or generated, to the AFM tip and lead to near-unity nearfield scattering dynamics. Concurrently, graphene serves as a near-perfect shield to the dynamic changes of the physical properties (e.g. THz conductivity) of the substrate. Combined with the InAs-based THz near-field emission microscopy techniques, our study provides a useful route for manipulating the ultrafast far-infrared responses of low dimensional materials at the nanoscale. Future studies can investigate the gate control of the THz pump probe or emission dynamics of low dimensional materials with confined geometry, preferably at cryogenic temperatures.

Appendix
To simulate the s-SNOM signal in the experiment, we consider the tip as an infinite cylinder of radius a=30 nm oriented along the y-axis and located at a varying height h(t) above the sensed surface (located in XY plane). The electric field measured at the cylinder's center is the superposition of the incident field is the wavelength of the plasmons excited in the graphene, we can find the electric field generated by the dipole, neglecting the radiation compound, as: where the "XZ" subscript represents the projection operation to the XZ plane: is the radius vector of the dipole position. For better convergence and possibility to apply the Fourier method to solve Maxwell equations, we consider a periodic geometry along the x-direction with a period of , , L p is the graphene plasmon propagation length. To allow the excited electric field to satisfy the Poisson equation, we consider periodic dipoles that give the field the expression: is the periodic translation vector and M → ∞ is the number of neighbors (at one side) taken into account. In this case, at the investigated surface (at z = 0) we represent the component of the excited electric field parallel to the surface ( , ) x E x t and the component of the electric displacement vector normal to the surface ( , ) z D x t as the following Fourier series: respectively. N → ∞ is the highest Fourier harmonic taken into account. The reflected electric field can be represented as where a j are unknown amplitudes of Fourier harmonics and ε 0 is the dielectric permittivity of the media at which the tip is located. The wafer can be made of n+1 layers of materials with different dielectric permittivities ε l and thicknesses h l . We imply that the last material has an infinite thickness, 1 n h + = ∞ . The electric field in the medium with index l can be represented as follows: In addition to the equations above, we enact the following additional conditions: • Boundary conditions between the media with l = 0 and l = 1: , 4 where σ is the distribution of the sheet density of free charges at the interface.
• Continuity equation at the interface: where j is the sheet current density at the interface.
• Transport equation (Ohm's law in our case) for the current: where the "ω"-subscript represents the Fourier transform of a function in the time domain and λ ω is the conductivity of the 2d-material covering the bulk material layer with dielectric permittivity ε l . For instance, if the 2d-covering is absent, λ ω = 0; if the 2d-material is single layer graphene, λ ω can be calculated using the formula [28]: where μ c is its chemical potential, ν is the electron scattering rate in it, T is the temperature, k B is the Boltzmann's constant and f d (E) is Fermi distribution: The equations above have been widely used in similar works, for example, in verification of graphene plasmon using s-SNOM measurements [36,37].
If the 2d material is an AB-stacked bilayer of graphene, in the THz and IR frequency ranges (where the photon energy is less than ~400 meV) its conductivity can be taken to be approximately twice that of the single layer graphene. This can be checked by comparing numerical results obtained using equations 3 and 4 in [28] and the ones obtained by equations 19-21 in [38] and equations 4-6 in [39]. Note that in our case, the basis functions are ( ) exp i t i ω + − ⋅ k r with a "+" sign before iω and Kramers-Kronig relation (equation 4 in [39]) has the opposite sign: Solving all of the listed equation together, we find the harmonic amplitudes of the reflected field: Once amplitudes a j are known, we can calculate the reflected electric field at any point in the region 0 z ≥ using Eq.
where a is radius of spherical tip, h is the height of its center above the surface and 0 ' p is complex amplitude of oscillations of the dipole moment.
Assuming that the distance between the tip and the surface oscillates as where z min = 5 nm and z max = 50 nm are its minimum and maximum and Ω is the frequency of the mechanical oscillations, we can calculate the resulting s-SNOM signal p 0 (t) (in arbitrary units) in the time domain. Shifting the signal along the t-axis to make it symmetric, the value S n is obtained as 0 ( )cos d n S p t n tt π π π Ω − Ω Ω = Ω  according to [27]. Finalizing, we compare the S 2 signal from the bare InAs surface using the described model (cylindrical tip) with the signal in which we assumed that the tip is spherical [27] to determine whether or not they give the same results. Fig. 6 shows that the simulated signals, which are normalized to the corresponding reference signals from the gold surface, are very close to each other. Fig. 6. Solid lines: frequency dependence of the S 2 signal from the InAs surface calculated for different doping levels N d using Eq. (5) for the E-field reflectance, normalized to the S 2 signal the signals from InAs and from gold are calculated using the Eq. (7) for the E-field reflection.
The radius of the cylindrical or spherical tip is taken to be a = 30 nm. The dielectric permittivity of InAs and gold are modeled by the Drude formula with the parameters stated in the main text.