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[Dublin M. Nichols](https://orcid.org/0009-0008-3819-9349), Jameson G. Berg, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Pallavi Dhagat, [Vikram V. Deshpande](https://orcid.org/0000-0001-7681-0833), Albrecht Jander, [Ethan D. Minot](https://orcid.org/0000-0002-5480-6857)

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[Charge pumping in h-BN-encapsulated graphene driven by surface acoustic waves](https://mdr.nims.go.jp/datasets/dbafe9ee-3255-492f-9584-e79cf4be198a)

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Charge pumping in h-BN-encapsulated graphene driven by surface acoustic wavesViewOnlineExportCitationRESEARCH ARTICLE |  JULY 11 2024Charge pumping in h-BN-encapsulated graphene driven bysurface acoustic waves Dublin M. Nichols  ; Jameson G. Berg; Takashi Taniguchi  ; Kenji Watanabe  ; Pallavi Dhagat;Vikram V. Deshpande  ; Albrecht Jander; Ethan D. Minot  J. Appl. Phys. 136, 024302 (2024)https://doi.org/10.1063/5.0220123 12 July 2024 00:07:23https://pubs.aip.org/aip/jap/article/136/2/024302/3303084/Charge-pumping-in-h-BN-encapsulated-graphenehttps://pubs.aip.org/aip/jap/article/136/2/024302/3303084/Charge-pumping-in-h-BN-encapsulated-graphene?pdfCoverIconEvent=citejavascript:;https://orcid.org/0009-0008-3819-9349javascript:;javascript:;https://orcid.org/0000-0002-1467-3105javascript:;https://orcid.org/0000-0003-3701-8119javascript:;javascript:;https://orcid.org/0000-0001-7681-0833javascript:;javascript:;https://orcid.org/0000-0002-5480-6857https://crossmark.crossref.org/dialog/?doi=10.1063/5.0220123&domain=pdf&date_stamp=2024-07-11https://doi.org/10.1063/5.0220123https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2416465&setID=592934&channelID=0&CID=886487&banID=521918064&PID=0&textadID=0&tc=1&rnd=5547640824&scheduleID=2335122&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Fjap%22%5D&mt=1720742843774750&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0220123%2F20041215%2F024302_1_5.0220123.pdf&hc=c0db45818c5883ac07121bfbb7d9b1ca0f39b405&location=Charge pumping in h-BN-encapsulated graphenedriven by surface acoustic wavesCite as: J. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123View Online Export Citation CrossMarkSubmitted: 22 May 2024 · Accepted: 14 June 2024 ·Published Online: 11 July 2024Dublin M. Nichols,1 Jameson G. Berg,2 Takashi Taniguchi,3 Kenji Watanabe,4 Pallavi Dhagat,5Vikram V. Deshpande,2 Albrecht Jander,5 and Ethan D. Minot1,a)AFFILIATIONS1Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA2Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA3Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044,Japan5School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon 97331, USAa)Author to whom correspondence should be addressed: ethan.minot@oregonstate.eduABSTRACTSurface acoustic waves (SAWs) on piezoelectric insulators can generate dynamic periodic potentials inside one-dimensional and two-dimen-sional materials. These periodic potentials have been utilized or proposed for various applications, including acoustoelectric chargepumping. In this study, we investigate acoustoelectric charge pumping in graphene with very low electrostatic disorder. By employing agraphite top gate on boron-nitride-encapsulated graphene, we adjust the graphene carrier concentration over a broad range, enabling us toexamine the acoustoelectric signal in both mixed-carrier and single-carrier regimes. We discuss the benefits of h-BN-encapsulated graphenefor charge pumping applications and introduce a model that describes the acoustoelectric signal across all carrier concentrations, includingat the charge neutrality point. This quantitative model will support future SAW-enabled explorations of phenomena in low-dimensionalmaterials and guide the design of novel SAW sensors.© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/). https://doi.org/10.1063/5.0220123I. INTRODUCTIONSurface acoustic waves (SAWs) offer the possibility to createdynamic superlattices in 1D and 2D materials. When a SAW prop-agates across a strong piezoelectric insulator, the extension andcompression of the insulator generates a periodic potential. SAWscan be generated with wavelengths ranging from tens of microme-ters to tens of nanometers. In the burgeoning field of van derWaals heterostructures made from 2D materials, SAWs haveemerged as a new way to interact with charge carriers. Forexample, previous work has demonstrated the transport of indirectexcitons in 2D semiconductor heterostructures1 and contactlessprobing of quantum oscillations in graphene.2Interest in applying SAWs to 1D and 2D materials is inspiredby previous experiments on GaAs/AlGaAs quantum wells and by anumber of outstanding theoretical proposals. For example,photogenerated electron–hole pairs in GaAs were separated by aSAW potential and then released to generate photons.3 SAWs wereutilized in conjunction with Coulomb blockade to sequentiallytransport single electrons through a quantum point contact.4 Newinsights into the quantum Hall effect and fractional quantum Halleffect in GaAs/AlGaAs quantum wells were obtained by utilizingcommensurability effects with a SAW superlattice.5,6 Turning toexamples of theoretical proposals, Barnes et al. formulated ascheme for quantum computing using single electrons trapped inSAW potential minima (“flying qubits”).7–9 Andreev recently pro-posed that a SAW applied to charge-neutral graphene can effi-ciently pump heat (approaching the Carnot limit).10 Talyanskiiet al. proposed a scheme in which a SAW applied to a carbonnanotube can realize a topologically protected electron pump,defining a quantum standard for the current.11Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123 136, 024302-1© Author(s) 2024 12 July 2024 00:07:23https://doi.org/10.1063/5.0220123https://doi.org/10.1063/5.0220123https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0220123http://crossmark.crossref.org/dialog/?doi=10.1063/5.0220123&domain=pdf&date_stamp=2024-07-11https://orcid.org/0009-0008-3819-9349https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0001-7681-0833https://orcid.org/0000-0002-5480-6857mailto:ethan.minot@oregonstate.eduhttps://creativecommons.org/licenses/by-nc/4.0/https://creativecommons.org/licenses/by-nc/4.0/https://doi.org/10.1063/5.0220123https://pubs.aip.org/aip/japIt is challenging to cleanly integrate SAWs with 1D and 2Delectronic systems because many insulating surfaces (including piezo-electric insulators) introduce significant electrostatic disorder to theelectronic system. This disorder disrupts the intrinsic properties ofthe low-dimensional material. To overcome this issue, Dean et al.introduced a method of encapsulating low-dimensional materialswith hexagonal boron nitride (h-BN), an ultraclean 2D insulator.12Boron-nitride-encapsulated graphene has been utilized for manyapplications; for example, demonstrating the highest-performingHall-effect sensor.13 However, there are no previous studies of acous-toelectric charge pumping in h-BN-encapsulated graphene. In thiswork, we address the need for a detailed, quantitative analysis of theinteraction between SAWs and graphene when electrostatic disorderis significantly reduced. Moreover, by using h-BN encapsulation, weexpect improvements such as larger pumping currents and increasedsensitivity of pumping current with respect to carrier concentration,which may aid future technologies.Previous authors have demonstrated acoustoelectric chargepumping in lower-quality graphene samples (see review byHernández-Mínguez et al.),14 but device quality (and sometimes non-tunable carrier concentration) has hindered quantitative comparisonwith theory. In our device design, the electric field from the SAWcouples to the graphene from below, while a graphite top gate enablesus to tune the carrier concentration in graphene over a wide range. Wedemonstrate that the SAW can drive extremely high 2D currentdensity in h-BN-encapsulated graphene when the system is tunedclose to the charge neutrality point (CNP). At the largest SAWpowers, we see signs of nonlinear effects, suggesting that the SAWcauses a perturbation in carrier density that is comparable to the equi-librium carrier density. We present a theoretical model to describe theacoustoelectric current/voltage as a function of charge carrier concen-tration. In contrast to previous work, we extend the classical relaxationmodel to account for the coexistence of electrons and holes near theCNP. Our mixed-carrier model describes the observed acoustoelectrictransport signals at all carrier concentrations, including the CNP.II. BACKGROUNDWhen the traveling electric field generated by a surface acous-tic wave (SAW) passes over a conductive 2D material, charge carri-ers move in response to the electric field. This interaction transfersenergy and momentum to the carriers and attenuates the SAW.The classical relaxation model predicts the attenuation of the SAWwill be described by an attenuation constant,15Γ ¼ K2 πλ(σ/σc)1þ (σ/σc)2� �, (1)where K2 is the piezoelectric coupling constant, λ is the wavelengthof the SAW, σ is the conductivity of the 2D material, andσc ¼ vSAW(ϵ1 þ ϵ2) is a characteristic conductivity defined by theproperties of the substrate, where ϵ1 and ϵ2 are the dielectric per-mittivities above and below the 2D material and vSAW is the SAWvelocity in the piezoelectric substrate. For a 2D material onLiNbO3, K2 ¼ 0:05 and σc � (1MΩ)�1.15,16If the 2D material is wired in a short-circuit configuration, theclassical relaxation model predicts that the SAW will drive a netflow of charge through the 2D material.16 The predicted short-circuit acoustoelectric current density is given byjae ¼ +μIvSAWΓ, (2)where the sign is determined by the sign of the carriers (negativefor electrons, positive for holes), μ is the carrier mobility, and I /PRF/W is the SAW intensity at the 2D material, where PRF is thepower applied to the interdigitated transducer (IDT) and W is theaperture width of the IDT used to drive the SAW. In experiments,there is a decrease in power between the RF generator and theSAW (insertion loss) which can be described by a proportionalityconstant. Equations (1) and (2) assume a single carrier type (eitherelectrons or holes) and predict that jae is maximized when σ ¼ σc.However, in graphene, the model must be adjusted to describe asystem in the mixed-carrier regime.III. EXPERIMENT DESIGNFigure 1(b) illustrates our experimental measurement scheme.To detect the acoustoelectric voltage, Vae, we probe the open-circuitvoltage across the graphene channel. There is an effective force oncharge carriers from the SAW which pushes charge carriers towardone side of the channel. Since there is no net current in the open-circuit configuration, an acoustoelectric voltage develops to balancethe force from the SAW. The relationship between expected Vae(open-circuit voltage) and jaew (short-circuit current) isjaew ¼ Vae/Rch, where Rch is the resistance of the graphene channeland w is the width of the graphene channel measured perpendicu-lar to the SAW propagation direction. We use Vae for our analysisbecause a true measurement of short-circuit current requireszero-resistance contacts to the graphene, and a zero-impedancecurrent amplifier. Previous attempts to quantify jae in grapheneusing the short-circuit current method likely suffered from thecomplication of large series resistance.17–21An IDT that emits a SAW with wavelength λ ¼ 20 μm froman aperture W ¼ 230 μm was fabricated on Y-cut black LiNbO3(University Wafer) using photolithography and metallization of5/25 nm Cr/Au. Black LiNbO3 was chosen because the material cantolerate faster thermal ramps than transparent LiNbO3.2,24Graphene devices were constructed next to the IDT as follows.First, we fabricated source/drain contacts (2.5/15 nm Cr/Pd) withchannel spacing l ¼ 20 μm (equal to λ) which sit 200 μm from theIDT. These contacts were cleaned using an atomic force microscope(AFM) in contact mode with a force of 100 nN.25 Then, we exfoli-ated the few-layer graphene and hexagonal boron nitride (h-BN)crystal flakes onto blank silicon wafers (300 nm oxide). We foundlarge, uniform-thickness flakes using optical microscopy and mea-sured flake thicknesses using AFM. We used a strongly adhesivepolycaprolactone (PCL) stamp to remove unwanted grapheneflakes (reducing the likelihood that unwanted graphene flakeswould short the IDT) and to tear the channel graphene flakes intorectangular pieces of a single thickness.26 We then used aPC/PDMS [poly(bisphenol A carbonate)/polydimethylsiloxane]stamp and the standard dry transfer technique22 to create the vander Waals heterostructure and to place the stack on theJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123 136, 024302-2© Author(s) 2024 12 July 2024 00:07:23https://pubs.aip.org/aip/japprefabricated source/drain contacts. Metal contact to the graphitetop gate was made by a final photolithography and metallizationstep (2.5/45 nm Cr/Au).Our aim was to create devices with different levels of electro-static disorder so we could study the effect of disorder on theacoustoelectric signal. The graphene channel of device 1 is fullyencapsulated in h-BN to minimize electrostatic disorder [see theinset of Fig. 2(c)].12 The graphene channel of device 2 is half-encapsulated such that the graphene lies directly on the LiNbO3substrate [see the inset of Fig. 2(d)]. The LiNbO3 substrate induceselectrostatic disorder in the graphene channel. For device 1, weselected two h-BN flakes, one graphene flake for the channel, andone graphite flake for the gate. The bottom h-BN flake was selectedto cover the gap between the source and drain contacts. The gra-phene flake was selected to extend beyond the bottom h-BN flakeand make electrical contact to the source and drain, as shown inFig. 2(c). The gate insulator of device 1 is 29 nm h-BN, giving gatecapacitance Cg ¼ 0:11 μF/cm2. The gate insulator of device 2 is13 nm h-BN, giving Cg ¼ 0:24 μF/cm2.IV. RESULTSFigures 2(a) and 2(b) show Vae as a function of the spatiallyaveraged carrier concentration in device 1 (fully encapsulated) andFIG. 1. Overview of the experiment. (a) Optical microscope image of the interdigitated transducer (IDT) and an h-BN-encapsulated graphene device (device 1). The three elec-trodes are labeled source, drain, and gate. (b) The acoustoelectric voltage (Vae) is measured across the source (S) and drain (D) electrodes. The gate electrode (G) is used totune carrier concentration. The total resistance of the graphene device includes the left and right contact resistance (RC1 and RC2) and the graphene channel resistance (Rch).FIG. 2. Room-temperature transport characteristics of device 1 (fully encapsulated) and device 2. (a) and (b) Acoustoelectric voltage (Vae) as a function of the carrier con-centration in the graphene channel for various levels of applied RF power PRF. Cg is the gate capacitance per unit area (see Sec. III). The inset shows the maximum Vaeas a function of PRF, with the gray dotted line as a guide for the eye. (c) and (d) Device resistance measured by setting PRF ¼ 0 and VSD ¼ 100mV. The blue dashedline shows a fit to the experimental data. The insets show the device structures. Colors indicate LiNbO3 (black), Pd (yellow), few-layer graphene (blue), and h-BN (green).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123 136, 024302-3© Author(s) 2024 12 July 2024 00:07:23https://pubs.aip.org/aip/japdevice 2. The transport curves have been shifted along the Vg-axisto align the CNP with Vg ¼ 0. The open-circuit voltage was mea-sured while driving the IDT at its resonance of 170MHz using anAgilent N5183A analog signal generator, using a Stanford SR560voltage preamplifier, filtered with the internal 30 Hz low-pass filterof the SR560. We verified that the frequency dependence of Vaeclosely follows the spectrally resolved measurement of RF powerabsorbed by the interdigitated transducer (see the supplementarymaterial). Figures 2(a) and 2(b) show other features that areexpected for acoustoelectric transport. At the CNP, the sign of Vaereverses (indicating that the SAW pushes electrons and holes in thesame direction). The magnitude of Vae changes non-monotonicallywith increasing carrier density. At large carrier concentrations, Vaedecays asymptotically toward zero, consistent with Eqs. (1) and (2).Figures 2(c) and 2(d) show DC transport in devices 1 and 2,where R ¼ Rch þ RC1 þ RC2. With the SAW power turned off, weapplied a source–drain bias Vsd ¼ 100mV and measured the DCcurrent using a Stanford SR570 current preamplifier while sweep-ing Vg . As expected, the device resistance is largest at the CNP,where the number of free carriers is minimized. The device resis-tance asymptotically approaches a finite value at large Vg . We asso-ciate this finite resistance with contact resistance RC1 þ RC2.The insets of Figs. 2(a) and 2(b) show the maximum value ofVae vs applied SAW power PRF. In both devices, we observe a linearrelationship between PRF and Vae up to 18 mW, which is consistentwith Eq. (2) and has been observed in previous acoustoelectric gra-phene devices.17 However, at PRF ¼ 31mW, the acoustoelectricvoltage is smaller than expected, suggesting a nonlinear relationshipbetween PRF and Vae. Non-linear behavior has been observed previ-ously in GaAs acoustoelectric devices at high SAW powers23 andsuggests that the perturbation of carrier density due to the SAW iscomparable in magnitude to the average carrier density in the gra-phene. More work is needed to understand the origin of this non-linear relationship in acoustoelectric graphene devices. Therefore,for the analysis below, we will use the PRF ¼ 18mW data to ensurethat the linear model is applicable.Of principal interest to this work is the shape of the peak in Vaeseen in Figs. 2(a) and 2(b). The single-carrier, classical relaxationtheory [Eqs. (1) and (2)] predicts that the acoustoelectric signalshould reach a maximum when the channel conductivity σ is equalto the characteristic conductivity of the piezoelectric substrate. ForLiNbO3, this characteristic conductivity is σc � (1MΩ)�1.15,16However, as can be seen in Fig. 2(a), the peak in Vae occurs whenRch � 2 kΩ, which corresponds to σ � (2 kΩ)�1. Prior authorsnoted similar discrepancies between the single-carrier theory andgraphene measurements, but no quantitative description for the peakhas been previously reported in the literature. The peak shape can beaccurately described using the mixed-carrier model outlined below.V. DISCUSSIONFirst, we compare the magnitude of the acoustoelectric signalmeasured in our h-BN-encapsulated graphene device to the resultsof prior graphene-based acoustoelectric experiments. For device 1,w ¼ 15 μm, Rch � 2 kΩ, and maximum jVaej ¼ 0:98mV. If thechannel was measured in a short-circuit configuration (assumingwe decreased the contact resistance such that RC1 þ RC2 � Rch),we would expect jae � 33mA/m. This current density is nearly tentimes higher than previous measurements of acoustoelectriccurrent in graphene devices.18–21 For device 2, we inferjae � 18mA/m. The higher current density obtainable in the fullyencapsulated graphene is evidence that lowering electrostatic disor-der boosts acoustoelectric signals. We further quantify this insightwith the model presented below.To understand the gate voltage dependence of Vae in graphenedevices, we consider the co-existence of electrons and holes at theCNP. In electrostatically gated graphene that has no disorder andno thermally activated charge carriers, we expect the electron andhole concentrations to be n ¼ CgVg for Vg . 0, and p ¼ Cg jVg j forVg , 0, where Cg is the gate capacitance per unit area [illustratedin Fig. 3(c)]. In a real graphene sample, there are thermally acti-vated carriers and spatial fluctuations in electrostatic potential thatmodify the electron and hole concentrations. Figure 3(a) illustratesthe spatial inhomogeneity of carrier concentration in graphene.27To model this, we assume a position-dependent gate voltage offsetVoffset(x, y) which has an average value 0 and standard deviationδV . We assume that the distribution of Voffset values follow anormal distribution. A similar disorder model has been used todescribe the gate-dependent Hall effect in graphene.28 From thefunction Voffset(x, y), we obtain integral forms for the spatiallyaveraged carrier concentrations in the graphene sample (see thesupplementary material) which can be solved analytically, givingn(Vg , δV)¼ CgeVg21þ erfVgffiffiffi2pδV� �� �þ δVffiffiffiffiffi2πp exp � V2g2δV2 ! !,(3)p(Vg , δV)¼�CgeVg21�erfVgffiffiffi2pδV� �� �� δVffiffiffiffiffi2πp exp � V2g2δV2 ! !,(4)where erf is the error function and e is the electron charge.Equations (3) and (4) are plotted in Fig. 3(c). In this model, theminimum carrier concentration in the graphene (the sum of n andp at Vg ¼ 0) is(n0þp0)¼ffiffiffi2πrCgδVe: (5)The mixed-carrier model [Eqs. (3) and (4)] yields an accuratefit to the DC transport data, as shown in Figs. 2(c) and 2(d). Thedashed lines in Figs. 2(c) and 2(d) are constructed by assumingσ ¼ eμ(nþ p), and Rch ¼ l/(wσ), where l is the length of thegraphene channel (20 μm for both devices). For device 1, we findμ ¼ 7150 cm2/(Vs) and (n0 þ p0) ¼ 0:38� 1012 cm�2. Theminimum carrier concentration in device 1 is approaching the room-temperature limit (�0:16� 1012 cm�2) which corresponds to theconcentration of thermally activated charge carriers in ultracleancharge-neutral graphene.29 For device 2, we find μ ¼ 3500 cm2/(Vs)and (n0 þ p0) ¼ 0:97� 1012 cm�2. The fully encapsulated device(device 1) has higher mobility and significantly reduced charge disor-der compared to device 2.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123 136, 024302-4© Author(s) 2024 12 July 2024 00:07:23https://doi.org/10.60893/figshare.jap.c.7285819https://doi.org/10.60893/figshare.jap.c.7285819https://doi.org/10.60893/figshare.jap.c.7285819https://pubs.aip.org/aip/japTo describe acoustoelectric voltage, we combine the mixed-carriermodel [Eqs. (3) and (4)] with the classical relaxation model [Eqs. (1)and (2)]. The SAW pushes both electrons and holes in the same direc-tion [Fig. 3(b)]. The fraction of these moving carriers which areuncompensated (carriers which do not have a partner of opposite sign)is given by ( p� n)/( pþ n) . Using this fraction, we modify Eqs. (1)and (2), finding the net current density from electrons and holes to bejae ¼ +μIvSAWK2 πλ(eμ(nþ p)/σc)1þ (eμ(nþ p)/σc)2� �p� npþ n� �: (6)In our experiment, eμ(nþ p) � 500 σc at all gate voltages,therefore, Eq. (6) simplifies tojae � +IσcevSAWK2 πλp� n( pþ n)2� �: (7)At large Vg , where n � p (or p � n), the model predictsjae / 1/Vg , consistent with the single-carrier model [Eq. (2)].Equation (7) can be extended to acoustoelectric voltage using therelationship Vae ¼ jaewRch. At large Vg, the model predictsVae / 1/V2g . Unlike the single-carrier model, Eq. (7) is also valid atsmall Vg where electrons and holes coexist.Figure 4 shows the excellent fit between our mixed-carriermodel prediction and the measured Vae curves. The key fittingparameter, δV , controls the width of the Vae peaks. For device 1(fully encapsulated), the best fit yields δV ¼ 0:65V, which is equiv-alent to (n0 þ p0) ¼ 0:35� 1012 cm�2. For device 2, the disorderparameter is more than doubled, (n0 þ p0) ¼ 0:88� 1012 cm�2.The height of the Vae peak for electron-doping differs slightlyfrom the height of the Vae peak for hole-doping. Therefore, weused separate fitting parameters for peak height on either side ofVg ¼ 0. A similar asymmetry is found in gate-dependentHall-effect measurements of graphene and the mechanism hasbeen discussed extensively in literature.30–32 Using our three-parameter fit (δV plus two peak height parameters), we achieveexcellent quantitative agreement with the experimental data.Our mixed-carrier model [Eq. (6)] gives a satisfyingexplanation for why σ = σc when Vae is maximized in a graphenedevice. To maximize Vae, the gate voltage must be tuned away fromVg ¼ 0 to avoid the cancelation of electron current by hole current.FIG. 3. (a) A spatial map of electron and hole inhomogeneity in graphene.Adapted with permission from Martin et al., Nat. Phys. 4, 144 (2008).27Copyright 2008 Springer Nature. (b) At the CNP, there are equal populations ofelectrons and holes. Electrons and holes are pushed in the same direction bythe SAW, so there is no net acoustoelectric current. (c) Top: the electron con-centration (black) and hole concentration (red) in a graphene device with nothermally activated charge carriers and no spatial fluctuation in electrostaticpotential. Bottom: the electron and hole concentrations when there is a spatialfluctuation in electrostatic potential.FIG. 4. Mixed-carrier model [Eq. (7)] fit to acoustoelectric transport in the fullyencapsulated (a) and half-encapsulated (b) graphene devices. These data aretaken with PRF ¼ 18 mW.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 024302 (2024); doi: 10.1063/5.0220123 136, 024302-5© Author(s) 2024 12 July 2024 00:07:23https://pubs.aip.org/aip/japConversely, if Vg is too large, then Vae decays as 1/V2g . Thus, thereis a sweet spot in gate voltage where most carriers have the samepolarity, but carrier concentration is still small. The position of thissweet spot is determined by the disorder parameter δV . ReducingδV will increase the height of the Vae peak.The high sensitivity of Vae with respect to Vg at the CNP(Vg ¼ 0) suggests that charge pumping in ultraclean graphene maybe useful for sensing applications. For example, adsorption of gasmolecules onto a graphene surface can modulate σ by modulatingthe concentration of charge carriers in the graphene. Prior workhas confirmed that changes in σ can be used to detect adsorbedgas (reviewed in Ref. 33). However, the σ-based transduction mech-anism does not work at the CNP where dσ/dVg ¼ 0. In contrast,the acoustoelectric voltage, Vae, is most sensitive to changes in nand p when the device is operated at the CNP (dVae/dVg ismaximal). Working at the CNP, gas detection events would corre-spond to an increase or decrease in Vae from zero (a small signalon top of zero background), which is preferable to detecting asmall change in σ on top of a large background. Additionally,open-circuit voltage measurements circumvent unwanted noise thatis generated by fluctuating contact resistance.34 Further work inthis direction could be pursued by modifying the architecture ofdevice 1: the top side of graphene could be exposed to the environ-ment, while the bottom side of graphene would rest on h-BN,which in turn would rest on LiNbO3.VI. CONCLUSIONSWe have demonstrated that the acoustoelectric signals in gra-phene (voltage and current) can be significantly increased by mini-mizing charge disorder in the graphene. h-BN-encapsulatedgraphene allows us to reach lower carrier concentration (close tothe thermal limit) so that channel resistance better matches theoptimal value to absorb SAW power. Our measurements demon-strate that room-temperature acoustoelectric current density in gra-phene can reach at least 33mA/m (nearly ten times larger thanprevious reports). We have presented a quantitative model for thegate-dependent acoustoelectric signals that describes the coexis-tence regime where both electrons and holes are present. Thisquantitative framework will aid future SAW-based experimentsdesigned to probe new phenomena in graphene and other 2Dmaterials.SUPPLEMENTARY MATERIALSupplementary material contains optical images of device 1and device 2, integral forms of Eqs. (3) and (4), spectrally resolvedmeasurements of reflected SAW power and acoustoelectric current,and comparison of pumped current density in prior gated acousto-electric graphene devices.ACKNOWLEDGMENTSThis work was supported by the National Science Foundation(NSF) under Grant No. 2004968. Part of this research was con-ducted at the Northwest Nanotechnology Infrastructure, a NationalNanotechnology Coordinated Infrastructure site at Oregon StateUniversity which is supported in part by the NSF (Grant No.NNCI-2025489) and Oregon State University. K.W. and T.T.acknowledge support from the JSPS KAKENHI (Grant Nos.21H05233 and 23H02052) and World Premier InternationalResearch Center Initiative (WPI), MEXT, Japan. V.V.D. and J.G.B.acknowledge support from the NSF under Grant No. 2005182.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsDublin M. Nichols: Conceptualization (equal); Data curation(equal); Formal analysis (equal); Investigation (lead); Methodology(equal); Software (lead); Validation (equal); Visualization (lead);Writing – original draft (lead); Writing – review & editing (equal).Jameson G. Berg: Conceptualization (supporting); Methodology(supporting); Writing – review & editing (supporting). TakashiTaniguchi: Resources (supporting). Kenji Watanabe: Resources(supporting). Pallavi Dhagat: Resources (equal); Writing – review& editing (supporting). Vikram V. Deshpande: Conceptualization(supporting); Funding acquisition (equal); Methodology (support-ing); Writing – review & editing (supporting). Albrecht Jander:Methodology (supporting); Resources (equal); Writing – review &editing (supporting). Ethan D. Minot: Conceptualization (equal);Formal analysis (equal); Funding acquisition (equal); Investigation(supporting); Methodology (equal); Project administration (equal);Resources (equal); Software (supporting); Supervision (lead);Visualization (supporting); Writing – original draft (supporting);Writing – review & editing (equal).DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1R. Peng et al., “Long-range transport of 2D excitons with acoustic waves,” Nat.Commun. 13, 1334 (2022).2Y. Fang, Y. Xu, K. Kang, B. Davaji, K. Watanabe, T. Taniguchi, A. Lal,K. F. Mak, J. Shan, and B. J. 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