Enhanced Optical Second-Harmonic Generation from the Current

generation induced by electric current in graphene on Si and SiC substrates. Yong Q. An , J. E. Rowe , Daniel B. Dougherty , Ji Ung Lee , Alain C...
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Enhanced Optical Second-Harmonic Generation from the CurrentBiased Graphene/SiO2/Si(001) Structure Yong Q. An,* Florence Nelson, Ji Ung Lee, and Alain C. Diebold College of Nanoscale Science and Engineering, University at Albany, Albany, New York 12203, United States ABSTRACT: We find that optical second-harmonic generation (SHG) in reflection from a chemical-vapor-deposition graphene monolayer transferred onto a SiO2/Si(001) substrate is enhanced about 3 times by the flow of direct current electric current in graphene. Measurements of rotational-anisotropy SHG revealed that the current-induced SHG from the currentbiased graphene/SiO2/Si(001) structure undergoes a phase inversion as the measurement location on graphene is shifted laterally along the current flow direction. The enhancement is due to current-associated charge trapping at the graphene/SiO2 interface, which introduces a vertical electric field across the SiO2/Si interface that produces electric field-induced SHG. The phase inversion is due to the positive-to-negative polarity switch in the current direction of the trapped charges at the current-biased graphene/SiO2 interface. KEYWORDS: Graphene, second-harmonic generation, rotational anisotropy, current-induced SHG, field-induced SHG

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recently observed by studying the interference between the SHG contribution from graphene and that from the underlying SiO2/Si(001) substrate.18,19 The symmetry may also be broken by an electric current or field in graphene, resulting in current or field-induced SHG. It was recently reported that a direct current (dc) electric current in multilayer graphene supported on a SiO2/Si(001) substrate could enhance SHG20 by nearly 30% when the current was applied to graphene through a pair of needle electrodes. Electric current-induced SHG (CI-SH)21 has been observed in other materials, such as silicon22 and GaAs.23 However, observation of CI-SH in graphene is particularly remarkable, because confining the electric current in a few atomic layers or a monolayer allows one to directly infer the mechanism of CI-SH effects. There are mainly two reasons that the mechanism of CI-SH enhancement in graphene is not well understood. First, the CISH effect is always accompanied by the electric field-induced SHG (FI-SH) effect, and this entanglement makes it difficult to identify which one is the primary effect. Second, the SH response from the Si substrate may significantly contribute to the measured CI-SH or FI-SH and thus complicate the isolation of the CI-SH response in graphene. Rotationalanisotropy SHG (RA-SH) provides a convenient approach for disentangling different SH sources of surface SHG from the graphene/SiO2/Si(001) structure. In a typical RA-SH scan, the SH signal varies with sample azimuthal angle, because the SHG from the surface or its adlayers, such as graphene, and that from the Si(001) substrate interfere constructively or destructively depending on the sample azimuthal angle. The interference

raphene is a monolayer of carbon atoms arranged in a hexagonal lattice. It possesses superior electronic and transport properties, as its carriers are massless Dirac fermions with a high mobility,1,2 and thus has potential applications in nanoelectronics. The linear optical and ultrafast optical properties of graphene have been intensively studied in order to correlate with its Dirac-cone band structure and cone-related carrier dynamics.3−7 In contrast, the nonlinear optical properties of graphene8−11 have been studied to a lesser extent due to its weak nonlinear response. Recently, theoretical calculations have shown that graphene can be a nonlinear optical material with giant nonlinearity when it is electrically biased or optically excited.12,13 The second-order nonlinear susceptibility χ(2) is predicted to be enhanced by several orders of magnitude when applying electric current to bilayer graphene12 or when exciting surface plasmons in single layer graphene.13 Experimental verification of the theoretically predicted giant optical nonlinearity is an important step toward implementing this effect in optical devices. Field-effect transistors (FET) with graphene channels 2,14 appear to be suitable structures for the investigation of such electro-optical effects, because the graphene film in the channel region can be easily biased by either an electric current or field and the optical transparency of graphene allows for nonlinear optical measurements. Nonlinear optical studies of graphene FET channels will elucidate new opportunities for combining high electron mobility with giant optical nonlinearity resulting in new optoelectronic devices. For a free-standing graphene monolayer, the second-order nonlinear optical response of second-harmonic generation (SHG)15−17 is forbidden because of the centro-symmetry of its crystal lattice. However, SHG from a graphene/substrate system becomes allowed, in principle, because the substrate breaks the symmetry of the system. Accordingly, surface SHG from exfoliated graphene on a SiO2/Si(001) substrate was © XXXX American Chemical Society

Received: February 3, 2013 Revised: March 26, 2013

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may amplify the SH signal from graphene and also determine the phase of the SH field. Here we show that RA-SH measurements of a current-biased graphene/SiO2/Si(001) structure reveal a new phenomenon: the CI-SH signal varies strongly with the graphene location along the current direction. Our graphene film was grown on a copper foil by chemical vapor deposition (CVD) and then transferred onto a SiO2/ Si(001) substrate by a PMMA-based method.24,25 The SiO2 layer was 300 nm thick. Graphene produced from this procedure is polycrystalline and consists of domain sizes on the order of several micrometers. The graphene monolayer covered a ∼10 × 10 mm2 area on the SiO2/Si(001) substrate. On top of the graphene, we patterned a pair of parallel copper electrodes, separated by a 1.3 mm gap and aligned in the Si[110] direction, through which electric current was applied in the Si[1̅10] direction. The [110] and the [1̅10] directions are equivalent when there is no current in graphene, both lying in a mirror plane of symmetry in Si. We also deposited a third electrode on the back of the heavily doped Si substrate for application of a dc bias voltage across the SiO2/Si interface. These three electrodes resemble the source (S), drain (D), and gate (G) terminals of an FET structure but here the graphene channel is large, allowing RA-SH measurements at different channel locations. SHG measurements used laser pulses of 120 fs duration at a repetition rate of 76 MHz produced from a Ti:Sapphire laser. The laser beam was focused to a 30 μm spot on the sample at an incident angle of 45°. The peak intensity was 2.3 GW/cm2. The reflected SH signal was measured in air at room temperature by a photomultiplier tube (PMT). The sample was mounted on a rotation stage to allow RA-SH measurements. Both p and s-polarizations were used for either the incident beam or the SH analyzer to separate different SH components. The pp polarization represents the p-polarized fundamental and p-polarized SH configuration, and so forth. The fundamental wavelength was fixed at 740 nm to match the E1 critical point transition in Si, so that the interference between the isotropic SHG from graphene and the anisotropic SHG from the Si(001) substrate is the strongest.26 A set of color glass filters were placed in the optical path before the PMT to select the light wavelength in the vicinity of SHG. A bandpass filter with a 10 nm bandwidth was used to verify that the detected light was at the SH wavelength of 370 nm. Special care was taken to ensure that the photoluminescence27 from graphene excited by the laser pulses was not significantly mixed into the SH signal. In the experiment, the solid angle for collecting photoluminescence was small ( 0) current directions are illustrated as an inset in (a) and (b), respectively. Current flow direction is in the plane of incidence when the sample azimuthal angle is at 90°. (c) Fit coefficients a0 and 4 × a4 for different current amplitudes and directions.

randomly oriented graphene domains inside the beam spot further ensure that any SHG contribution from graphene is isotropic. Without current in graphene, the pp-polarized RA-SH intensity at 2ω frequency from the graphene/SiO2/Si(001) sample takes the form19 (2ω) Ipp (ϕ) = [a0 + a4 cos(4ϕ)]2

(1)

where the coefficients a0 and a4 are the amplitudes of the isotropic and anisotropic terms, respectively, and ϕ is the sample azimuthal angle between the incident plane and the B

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[110] direction in the Si(001) surface. a4 arises entirely from the Si(001) bulk, and it can be independently measured from the ps-polarized RA-SH. We neglect the noninterference term26 that adds a background to eq 1, because our measurements of the term by comparing pp and ps-polarized RA-SH signals found that it is much smaller than a02. Figure 1a,b shows that reversing the current direction in graphene may cause a phase inversion of SHG, as RA-SH peaks of a negative current correspond to valleys of a positive current. If an electric current, I, exists in graphene, a0 in eq 1 may be split into three terms 3

a0 = a0Si + a0C +

∑ anI I n=0

cos[n(ϕ + 90°)] (2)

Here aSi0 comes from SHG at the SiO2/Si interface, aC0 is due to SHG from graphene when I = 0, and aIn is due to CI-SH in graphene, where n = 0, 1, 2, or 3. Because CI-SH disappears when there is no current, the summation term in eq 2 is presumably proportional to I. When I = 0, the RA-SH signal from graphene/SiO2/Si(001) is about 7% less than that from the bare SiO2/Si(001) substrate (data not shown), consistently for all 4 p and s polarization combinations. This ∼7% signal reduction is consistent with 1− (1−2.3%)3 due to the linear optical absorption of graphene for SHG from the SiO2/Si(001) interface, where 2.3% is the optical absorption of a graphene monolayer.5 Therefore, SHG from CVD graphene is found to be negligible, that is, aC0 = 0, when there is no current. When graphene is current-biased in the [1̅10] direction of Si, the current breaks the symmetry in graphene, reducing the 4-fold symmetry of the I = 0 graphene/SiO2/Si(001) system to a mirror symmetry with the mirror plane along the [1̅10] direction. The [110] direction is not in the mirror plane of symmetry of the I ≠ 0 system anymore. For a surface with one mirror plane of symmetry, the pp-polarized RA-SH field is the sum of 0, 1, 2, and 3-fold symmetric cosine terms,28,29 as shown in eq 2. In the experiment, electric current is perpendicular to the plane of incidence when ϕ = 0. Current should introduce n(≤3)-fold symmetric terms, of which the 1-fold symmetric term aI1 sin(ϕ) should dominate. However, the measured RASH patterns in Figure 1 all appear 4-fold symmetric, indicating that the observed CI-SH is isotropic with respect to the sample orientation, that is, aI1, aI2, and aI3 = 0. Figure 1c shows the eq 1 fit coefficients a0 and a4 of the measured RA-SH scans for different current values and directions. For the negative current, a0 increases almost linearly with current. For the positive current, however, a0 crosses zero at I = 0.7 A/m and then linearly increases in magnitude. Reversing the current direction at a fixed graphene location can introduce a sign change of a0. The slight variation of a4 with current suggests that the current in graphene likely affects the SH response in the Si(001) substrate. Surprisingly, we find that the observed CI-SH signal varies strongly with the measurement location along the current flow direction. Figure 2 shows RA-SH scans measured at three different locations on the graphene: near (0.15 mm from) the S electrode (a), midway between S and D (b), and near (0.15 mm from) the D electrode (c), at a fixed current of ±2.4 A/m. For a fixed current direction, we find that a phase inversion in the RA-SH appears between the S and the D-side of currentbiased graphene. The RA-SH scans near the S or D electrode are 4-fold symmetric, but those midway between S and D are clearly 1-fold symmetric. The in-plane variation of CI-SH

Figure 2. (Polar plot) Rotational-anisotropy SHG scans from the graphene/SiO2/Si(001) sample with a fixed current I = 2.4 A/m for both ± current directions measured at three different graphene locations: nearby the S electrode (a), halfway between S and D (b), and nearby the D electrode (c). Measurement locations are illustrated in each panel. Smooth curves in (a) and (c) are fits to eq 1. Current flow direction is in the plane of incidence when the sample azimuthal angle is at 90°.

means that the observed CI-SH is not solely a function of current but rather a function of both current and local voltage. The observed 1-fold symmetric RA-SH scans in Figure 2b shows a mirror symmetry along the ϕ = 0 direction, while the predicted RA-SH patterns from the summation term proportional to current in eq 2 should show a mirror symmetry along the ϕ = 90° direction. The results indicate that the CI-SH component cannot be described by the summation term in eq 2 and aI0 = 0. The anode-side CI-SH of the positive current C

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direction is essentially equivalent to the cathode-side CI-SH of the negative current direction. The result suggests that the inplane translational phase inversion of SHG is due to the current flow, rather than sample nonuniformity. As current flows in graphene, a potential difference exists between the graphene and the Si substrate, resulting in a vertical electric field, E, and thus a FI-SH effect across the SiO2/ Si interface.30 The FI-SH itself can be independently studied by applying a dc bias voltage between the S (or D) and G electrodes without applying a current in graphene. The pppolarized RA-SH signals in reflection from a measurement location midway between the S and D electrodes of the graphene/SiO2/Si(001) sample for zero and the positive bias voltages (0, 6, 12, 18, and 25 V) are shown in Figure 3a, and those for the negative bias voltages are shown in Figure 3b. Here positive bias is defined as bias with a higher voltage on S than G. The RA-SH scans measured at different locations between the S and D electrodes appear approximately the same in amplitude and consistently the same in phase. Figure 3a,b shows that switching the bias polarity can cause a phase inversion of SHG. If an electric field, E, is present across the SiO2/Si interface, a0 in eq 1 may be split into two terms

a0 = a0Si + a0EE

(3)

Here aSi0 has the same interpretation as in eq 2, and aE0 arises from the FI-SH at the SiO2/Si interface. The bias field E is proportional to the bias voltage, while the surface charge (electron) density on field-biased graphene is proportional to E. The maximum bias of 25 V corresponds to an electric field of 8.3 × 107 V/m and also to a surface electron density of 1.8 × 1012 electrons/cm2. Figure 3c shows the eq 1 fit coefficients a0 and a4 of the RA-SH scans at different bias voltages. For either bias polarity, a0 increases linearly with the bias magnitude above 6 V. For positive bias, however, a0 crosses zero at a bias of 5 V. The FI-SH in Figure 3 resembles the CI-SH in Figure 1 in two respects: the polarity-correlated phase inversion and the voltage dependence of a0. In the FI-SH measurements, the graphene monolayer serves as a transparent electrode for application a vertical bias across the SiO2/Si interface. However the observed FI-SH results resemble earlier studies when a chromium layer served as such an electrode.30−32 Therefore, we attribute the observed CI-SH from the graphene/SiO2/Si(001) structure to current-associated FI-SH at the SiO2/Si interface. Even in the absence of an external bias between the S and G electrodes, the local voltage associated with the current in graphene should bias the SiO2/Si interface. As current flows in graphene for CI-SH, the cathode (either S or D) electrode on graphene and the G electrode on Si are all grounded in the experiment. Therefore, the local voltage is positive everywhere on graphene regardless of the current direction. Assuming that current-associated FI-SH at the SiO2/Si interface is fully responsible for the observed CI-SH, we would expect that the CI-SH patterns measured everywhere on graphene has the same phase as the FI-SH patterns independently measured with positive bias. In other words, the phase of SHG is expected to stay the same on every measurement location along the current flow direction because the bias field is always positive (downward). The anode-side RA-SH scans in Figure 1b show the same phase as those in Figure 3a, but the cathode-side RASH scans in Figure 1a show the opposite phase, which contradicts the expected behavior. We attribute the opposite phase of SHG close to the cathode to trapped electrons at the

Figure 3. (a) (Polar plot) Measured rotational-anisotropy SHG scans from the graphene/SiO2/Si(001) sample for zero and different positive bias voltages (+6, +12, +18, and +25 V). (b) The above scans for different negative bias voltages. Smooth curves in (a) and (b) are fits to eq 1. (c) Fit coefficients a0 and 4 × a4 for different bias voltages and polarities. Linear fits of the bias-dependence of a0 are shown for bias amplitudes above 6 V.

graphene/SiO2 interface.33,34 These negative charges can introduce a negative (upward) bias field at the SiO2/Si interface to reverse the phase of SHG. It is known that transport properties of graphene on SiO2 are strongly affected by the surface conditions of SiO2.35,36 Charge trapping is believed to occur at the graphene/SiO2 interface because of the presence of structural defects, such as domain boundaries in graphene, and morphological imperfections. To study the development of the phase inversion along the current direction, we measured RA-SH at different graphene locations with smaller (0.1 mm) sampling steps. Figure 4 shows the eq 1 fit coefficients a0 and a4 of the measured RA-SH scans as a function of the graphene location, x (distance measured D

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Figure 4, approximately half of the maximum density of FI-SH in Figure 3c. The one-fold distortion of the RA-SH scans in the transition region, as shown in Figure 2b, can be explained by the lateral distribution of trapped charges. When current flows in graphene, positive charges accumulate on the anode side, while negative charges accumulate on the cathode side, and these charges are trapped at the graphene/SiO2 interface. The trapped charges and the local voltage that sustains the current can be treated equivalently as an x-dependent surface charge density on graphene that yields a vertical bias field at the SiO2/ Si interface. At a certain current, it is possible to form such a bias field that varies from positive on one-half of graphene to negative on the other half. At large currents, aSi0 in eq 3 is negligible, and thus a0(x) is proportional to E(x). The bias field, E(x), varies with x, resulting in a0(x) to vary with x, and thus a translational phase inversion. When a0 = 0, eq 1 predicts RASH to be 8-fold symmetric, but this is not observed. We always observe 1-fold symmetric RA-SH scans in the transition region. This is because E(x) varies quickly with x even within the small area of the sampling ring. At x = 0.65 mm, half of the ring covers the E(x) > 0 region, and the other half covers the E(x) < 0 region, as illustrated on top of Figure 4. Such a distribution results in two RA-SH peaks appearing at locations where valleys are supposed to be, as evidenced in Figure 2b for either current direction. If current is reversed, E(x) is reversed everywhere and thus a phase inversion occurs at every azimuthal angle, and therefore, all RA-SH peaks turn into valleys upon current reversal, as evidenced also in Figure 2b. The observed CI-SH is attributed to the current-associated FI-SH at the SiO2/Si interface, thus it is a Si substrate effect. However, a question remains as to whether it is the only source for CI-SH, as the FI-SH at the graphene/SiO2 interface may also contribute to CI-SH. Just like bias-controlled optical reflectivity on bilayer graphene,2 the SH signal in reflection from the graphene monolayer might vary with the bias voltage. To eliminate the Si substrate effect on CI-SH, we transferred a graphene monolayer onto a 1 mm thick glass plate and patterned with electrodes. The graphene film and the electrodes on the graphene/glass sample were nearly identical to those on the graphene/SiO2/Si(001) sample. Transmission RA-SH at a 45° incident angle was measured in order to obtain maximum SH signal levels. Using the same current of 2.4 A/m, the measured CI-SH signal from the graphene/glass sample was about 20 times weaker than the CI-SH signal in reflection from the graphene/SiO2/Si(001) sample, while it is expected that the transmission and reflection SH signals should be about the same if the enhanced SHG originates from graphene only. This result means that CI-SH from graphene itself without the Si substrate is negligible. In conclusion, we have used a millimeter-sized FET-like graphene/SiO2/Si(001) structure to study the character and mechanism of CI-SH in graphene. We found that a dc electric current in a graphene monolayer may enhance surface SHG more than 3 times. We also found that the CI-SH signal is a strong function of the measurement location between the source and drain electrodes on current-biased graphene, and that a phase inversion of CI-SH may form between the upstream and the downstream locations of the current. Through measurements of FI-SH on the graphene/SiO2/ Si(001) structure and CI-SH on a graphene/glass structure, we determined that the CI-SH effect originates from currentassociated FI-SH at the SiO2/Si interface due to charge

Figure 4. Fit coefficients a0 and 4 × a4 at different graphene locations, x, for a fixed current amplitude I = 2.4 A/m and both positive and negative current directions. A phase inversion of SHG (sign flip of a0) develops through a 0.3 mm wide transition region in the central area. On top of the graph, a schematic drawing scaled to the whole x axis is plotted to illustrate the S and D electrodes, graphene channel, definition of positive current direction (I > 0), laser sampling ring, and lateral distribution of the local bias field.

from S to D), for a fixed current of ±2.4 A/m. Within 0.5 mm from either S or D, the RA-SH scans appear 4-fold symmetric and thus can be fit to eq 1. Approximately midway between S and D, the RA-SH scans gradually distort to be 1-fold symmetric with the maximum distortion occurring at the middle location x = 0.65 mm, as shown in Figure 2b. The transition region for completing a phase inversion is found to be about 0.3 mm wide. The resolution for the width determination is limited by the sampling ring size of 0.1 mm in the experiment. One-fold symmetric RA-SH scans in the transition region cannot be simply fit to eq 1. As shown in Figure 4, the anisotropic coefficient a4 drops roughly 50% as x varies from the current downstream to the upstream region. This is because negative charges at the graphene/SiO2 interface repel near-interface electrons in Si away from the SiO2/Si interface, enlarging the space charge region and resulting in a stronger SH contribution from the Si bulk. The explanation is corroborated not only by the FI-SH results in Figure 3c, showing a larger a4 under negative bias than positive bias for all bias voltages, but also by the CI-SH results in Figure 1c, showing a larger a4 when I < 0 than I > 0 for all current values. The isotropic coefficient a0 varies abruptly with x from positive to negative in the transition region, corresponding to polarity switch of the trapped charges. In eq 3, aSi0 is negligible when E is large, and thus the x-dependent surface density of trapped charges is proportional to −a0(x). Figure 4 shows that the along-current lateral distribution of the trapped charges at the current-biased graphene/SiO2 interface appears similar to the electron distribution in a p-n junction. The surface electron density trapped at the graphene/SiO2 interface ranges between 0.7 × 1012 to 1.2 × 1012 electrons/cm2 for the data points in E

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(21) Khurgin, J. B. Appl. Phys. Lett. 1995, 67, 1113. (22) Aktsipetrov, O. A.; Bessonov, V. O.; Fedyanin, A. A.; Val’dner, V. O. JETP Lett. 2009, 89, 58. (23) Ruzicka, B. A.; Werake, L. K.; Xu, G.; Khurgin, J. B.; Sherman, E. Y.; Wu, J. Z.; Zhao, H. Phys. Rev. Lett. 2012, 108, 077403. (24) Nelson, F. J.; Kamineni, V. K.; Zhang, T.; Comfort, E. S.; Lee, J. U.; Diebold, A. C. Appl. Phys. Lett. 2010, 97, 253110. (25) Li, X.; Zhu, Y.; Cai, W.; Borysiak, M.; Han, B.; Chen, D.; Piner, R. D.; Colombo, L.; Ruoff, R. S. Nano Lett. 2009, 9, 4359. (26) An, Y. Q.; Cundiff, S. T. Appl. Phys. Lett. 2002, 81, 5174. (27) Lui, C. H.; Mak, K. F.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2010, 105, 127404. (28) Lupke, G.; Bottomley, D. J.; Vandriel, H. M. J. Opt. Soc. Am. B 1994, 11, 33. (29) An, Y. Q. Ph.D dissertation, University of Colorado at Boulder, Boulder, CO, 2003. (30) Dadap, J. I.; Hu, X. F.; Anderson, M. H.; Downer, M. C.; Lowell, J. K.; Aktsipetrov, O. A. Phys. Rev. B 1996, 53, R7607. (31) An, Y. Q.; Cundiff, S. T. J. Appl. Phys. 2004, 96, 2638. (32) He, L.; Walker, J. D.; Branz, H. M.; Rogers, C. T.; Teplin, C. W. Appl. Phys. Lett. 2012, 101, 161604. (33) Lee, Y. G.; Kang, C. G.; Jun, U. J.; Kim, J. J.; Hwang, H. J.; Chung, H.-J.; Seo, S.; Choi, R.; Lee, B. H. Appl. Phys. Lett. 2011, 98, 183508. (34) Kalon, G.; Jun Shin, Y.; Giang Truong, V.; Kalitsov, A.; Yang, H. Appl. Phys. Lett. 2011, 99. (35) Kang, Y.-J.; Kang, J.; Chang, K. J. Phys. Rev. B 2008, 78, 115404. (36) Nagashio, K.; Yamashita, T.; Nishimura, T.; Kita, K.; Toriumi, A. J. Appl. Phys. 2011, 110, 024513.

trapping at the graphene/SiO2 interface. Our observed variation of CI-SH along the current direction in graphene means that the symmetry-breaking caused by current flow in graphene is not the main factor responsible for enhancement of SHG. This contradicts the earlier interpretation of the mechanism for CISH.20 The comparable signal level of CI-SH and FI-SH in this work suggests that the CI-SH effect in materials is likely due to current-associated electric field-effects. We demonstrate that scanning RA-SH is a phase-sensitive probe for characterizing electric current and charge distribution in graphene based devices, and our results of CI-SH suggest an opportunity for electrically modulating SHG inside a focused laser spot by using micrometer-sized graphene FET channels.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the Institute for Nanoelectronics Discovery and Exploration (INDEX) and Nanoelectronics Research Initiative (NRI) for partial funding of this work. We thank Chris Bevis of KLA-Tencor for donation of a Tsunami femtosecond laser. Y.Q.A. thanks Dr. Tianhao Zhang for help in constructing the experimental infrastructures for the measurements and Dhiraj Sinha for helpful discussions.

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REFERENCES

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