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Francesca Falorsi, Shuangjie Zhao, Kejun Liu, Christian Eckel, Jonas F Pöhls, Wiebke Bennecke, Marcel Reutzel, Stefan Mathias, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Zhiyong Wang, Miroslav Polozij, Xinliang Feng, Thomas Heine, R Thomas Weitz

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[Interlayer charge transfer in graphene–2D polyimide heterostructures](https://mdr.nims.go.jp/datasets/14e82db4-f161-4a7e-8958-4c9152e8574b)

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Interlayer charge transfer in graphene–2D polyimide heterostructures2D Materials     PAPER • OPEN ACCESSInterlayer charge transfer in graphene–2Dpolyimide heterostructuresTo cite this article: Francesca Falorsi et al 2025 2D Mater. 12 025011 View the article online for updates and enhancements.You may also likeInterface engineering of van der Waalsheterostructures towards energy-efficientquantum devices operating at hightemperaturesManh-Ha Doan and Peter Bøggild-A highly polarization-sensitive near-infrared photodetector based on two-dimensional germanane/-CdSheterostructureZhengwang Chen, Jiajun Linghu, QiangZhang et al.-MXenes: exploiting their unique propertiesfor designing next-generation thermalcatalysts and photocatalystsJoshua O Ighalo, Morgen L Smith, AhmedAl Mayyahi et al.-This content was downloaded from IP address 144.213.253.16 on 07/02/2025 at 05:09https://doi.org/10.1088/2053-1583/adac6ehttps://iopscience.iop.org/article/10.1088/2053-1583/ada043https://iopscience.iop.org/article/10.1088/2053-1583/ada043https://iopscience.iop.org/article/10.1088/2053-1583/ada043https://iopscience.iop.org/article/10.1088/2053-1583/ada043https://iopscience.iop.org/article/10.1088/2053-1583/adac70https://iopscience.iop.org/article/10.1088/2053-1583/adac70https://iopscience.iop.org/article/10.1088/2053-1583/adac70https://iopscience.iop.org/article/10.1088/2053-1583/adac70https://iopscience.iop.org/article/10.1088/2053-1583/adac70https://iopscience.iop.org/article/10.1088/2053-1583/ada042https://iopscience.iop.org/article/10.1088/2053-1583/ada042https://iopscience.iop.org/article/10.1088/2053-1583/ada0422D Mater. 12 (2025) 025011 https://doi.org/10.1088/2053-1583/adac6eOPEN ACCESSRECEIVED29 August 2024REVISED13 December 2024ACCEPTED FOR PUBLICATION21 January 2025PUBLISHED4 February 2025Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERInterlayer charge transfer in graphene–2D polyimideheterostructuresFrancesca Falorsi1,11, Shuangjie Zhao2,11, Kejun Liu2,3, Christian Eckel1, Jonas F Pöhls1,Wiebke Bennecke1, Marcel Reutzel1, Stefan Mathias1,4, Kenji Watanabe5, Takashi Taniguchi6,Zhiyong Wang2,7, Miroslav Polozij2,8,9, Xinliang Feng2,7, Thomas Heine2,8,9,10 and R Thomas Weitz1,4,∗1 Georg-August-University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany2 Faculty of chemistry and food chemistry, Technical University of Dresden, Bergstrasse 66, 01069 Dresden, Germany3 Functional Nano & Soft Materials (FUNSOM), Jiangsu Key Laboratory for Carbon-Based Functional Materials & Devices, SoochowUniversity, 215123 Suzhou, People’s Republic of China4 Göttingen ICASEC, 37077 Göttingen, Germany5 Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan6 Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan7 Max Planck Institute of Microstructure Physics, 06120 Halle (Saale), Germany8 Helmholtz-Zentrum Dresden-Rossendorf, HZDR, Bautzner Landstr. 400, 01328 Dresden, Germany9 Center for Advanced Systems Understanding, CASUS, Untermarkt 20, 02826 Görlitz, Germany10 Department of Chemistry, Yonsei University, Seodaemun-gu, Seoul 120-749, Republic of Korea11 These authors contributed equally.∗ Author to whom any correspondence should be addressed.E-mail: thomas.weitz@uni-goettingen.deKeywords: 2D covalent organic framework, graphene, heterostructure, SNOM, Raman, electronic propertiesSupplementary material for this article is available onlineAbstractThe vertical integration of multiple two-dimensional (2D) materials in heterostructures, heldtogether by van der Waals forces, has opened unprecedented possibilities for modifying the(opto-)electronic properties of nanodevices. This not only allows for the exploration of newphysical phenomena but also greatly broadens the application horizon of existing monolayerdevices. Graphene, with its remarkable opto-electronic properties, is an ideal candidate for suchapplications. The other potential candidates are 2D polymers, crystalline polymeric materials withcustomizable structures and electronic properties, as they can be synthesized in all mathematicallypossible Bravais lattices. In this study, we investigated the optoelectronic properties of aheterostructure created by pristine graphene and a rectangular 2D polyimide (2DPI) film. Thisimprints a new superlattice on graphene in conjunction with a direct influence on its electronicproperties. Theoretical and experimental analyses reveal that interlayer charge exchange betweenthe 2D polymer and graphene induces hole doping in the graphene layer. We have also observedthat the properties of the heterostructure are dependent on the substrate used in experiments,likely due to the porous character of the 2DPI allowing direct interaction of graphene with thesupport. Furthermore, we demonstrate a direct correlation between the thickness of the 2DPI layerand the extent of hole doping in graphene. These findings highlight the unique ability to tailorfunctionalities in 2D polymers-based heterostructures, opening avenues for the development ofoptoelectronic devices with precisely engineered properties and stimulating further exploration ofthe diverse phenomena accessible through tailored designs of the 2D polymers.In the past decades, the rise of graphene [1, 2]and other two-dimensional (2D) materials hasoffered an unprecedented possibility to combinethem to layer-stacked heterostructures (HS) heldtogether by van der Waals (vdW) forces. Stronginterlayer effects enable access to new and interest-ing physical phenomena [3]. Prominent examplesinclude the band gap opening in bilayer graphene© 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/adac6ehttps://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/adac6e&domain=pdf&date_stamp=2025-2-4https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0009-0007-3319-7240https://orcid.org/0000-0001-7888-2574https://orcid.org/0000-0002-1085-2931https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0003-2379-6251https://orcid.org/0000-0001-5404-7355mailto:thomas.weitz@uni-goettingen.dehttp://doi.org/10.1088/2053-1583/adac6e2D Mater. 12 (2025) 025011 F Falorsi et al[4], the indirect-to-direct band gap transition intransition metal dichalcogenides [5–7], and thesemiconductor-to-metal transition in noble metaldichalcogenides [8, 9]. However, graphene and other2D crystals have fixed lattice structures that are lim-ited in their tunability and modification. To increasestructural flexibility and enable functional designs,2D polymers and their layer-stacked variant, 2Dcovalent organic frameworks (COFs), have beendeveloped for HS in recent years [10–15]. 2D poly-mers are crystalline, layered materials with organicbuilding blocks connected laterally via covalentbonds with monolayer or few-layer (<10) thickness.Notably, 2D polymers can form all mathematicallypossible 2D lattices (e.g. hexagonal, square, kagome)[16, 17], directly influencing their electronic bandstructure, which can be metallic, semiconducting,or exhibit topological bands, Dirac points, and flatbands. Additionally, their chemical composition ishighly modifiable, affecting the work function andinterlayer charge exchange, thereby altering the dens-ity of states (DoS). Having these novel materials withtunable intriguing properties, it is expected that whencoupled with graphene, novel physical phenomenacan be induced into graphene.In thiswork, we investigate the electrical and spec-troscopic properties of a HS of monolayer graphenewith a 2D rectangular polyimide (figure 1(a))(denoted below as 2DPI/graphene). The ultrafastinterlayer charge transfer between this 2D polyim-ide (2DPI) and chemically exfoliated graphene hasalready been shown by some of us [13]. Here, we fur-ther investigate these HSs by combining high-qualityexfoliated graphene with 2DPI film of different thick-nesses. This approach allows us to analyze both theinterlayer charge transfer in the HS as well as theimpact of the 2DPI on the charge transport withinthe graphene layer. As we detail below, the 2D poly-mer induces hole doping in the graphene, and thestrength of the doping increases with the layer num-ber of the polymer. In our analysis we have utilized alarge number of complementary methods, not onlyto give a full characterization of the HSs but also togive reference data for future HSs of the similar type.We first extensively utilize theoretical mod-els to explain the electronic properties of the2DPI/graphene HS. Standard theoretical models oflayered materials, which only consider standalonelayers in vacuum, are not suitable for the 2D poly-mer/graphene system. This stems from the porousnature of the 2DPI with pores large enough forthe graphene to interact through the 2DPI layerwith the substrate under it. To take this effect intoaccount, we have investigated three different models;(i) standalone 2DPI/ graphene, (ii) 2DPI/graphenedeposited on SiO2 as in transport experiments,using 2D SiO2 [18] as a substrate model, denotedSiO2/2DPI/graphene, (iii) 2DPI/graphene depositedon Si as in angle-resolved photoemission spectro-scopy (ARPES) experiments, using a H-terminated4-layer 2D model of Si(100) surface as a substratemodel, denoted Si/2DPI/graphene (figure 1(b)).There are two important structural effects influ-encing the graphene in the HS with the porous 2Dpolymer. Due to the vdW interaction between the2DPI and graphene, a superlattice forms in graphenemirroring the lattice structure of the polyimide.This is manifested by the corrugation of graphenetowards the 2DPI pore. In the case of standalone2DPI/graphene HS, the corrugation amplitude isabout 1.12 Å, however, with Si and SiO2 substrates,the maximum deformation of graphene towards thesupport is 1.5 Å and the total corrugation amplitudeis almost 3 Å (figure 1(c)). The second structuraleffect on graphene comes from the relative rotationof the graphene and 2DPI layers. Experimentally,such an angle is very hard to control due to thepolycrystalline nature of the 2DPI used and shouldbe considered random. This causes the superlatticeimposed on graphene to be in different orientationswith respect to the graphene lattice. To investigatethis, we have tested several rotation angles (0◦, 4◦,12.6◦ and, 21.6◦), which produce models with smallenough unit cells to study their electronic properties.In the case of the standalone 2DPI/graphene, theHS band structure is a simple superposition of the2DPI and graphene band structures, irrespective ofthe rotation angle (figures S1 and S2)). More pro-nounced electronic changes can be seen with theintroduction of a substrate (SiO2 or Si). Due to thesize of the systems, we were not able to include thesubstrate directly in most electronic properties calcu-lations. Instead, we only used it to obtain the HS geo-metry and removed the substrate for the band struc-ture calculation. This does not bring any significanterror; see the example of Si/2DPI/graphene in figureS3. The introduction of a SiO2 substrate does notbring any changes to the 2DPI/graphene band struc-ture (figure S4). On the other hand, with the intro-duction of a Si substrate, a gap of 7.5meVopens at theDirac cone, independent of the HS rotational angle(figures 1(d), S6). A more significant change is seenin the DoS (figures 1(e), S4 and S5) for both the SiO2and Si supportedHS,where twodistinct peaks emergebelow and above the Fermi level, instead of a singlepeak above the Fermi level in the standalone HS. Thisrelates to the difference in charge transfer between the2DPI and graphene (figures 1(f), S12), which is muchstronger in the corrugated structures of the substrate-deposited HS.22D Mater. 12 (2025) 025011 F Falorsi et alFigure 1. (a) Chemical structure of studied 2DPI. (b) Atomic structure of Si/2DPI/graphene (c) Corrugation of graphene inducedby 2D-polymer and substrate Si/2DPI/graphene (red: graphene bent towards polymer, blue: graphene bent from polymer),forming square superlattice. (d) Band structure of 2DPI/graphene moiety of Si/2DPI/graphene structure. (e) Projected density ofstates of 2DPI/graphene moiety of Si/2DPI/graphene structure. (f) Visualization of charge distribution difference 2DPI/graphenemoiety Si/2DPI/graphene. (Yellow: charge accumulation. Light blue: charge depletion).1. Electronic properties of 2DPI/grapheneHSTo experimentally analyze the optoelectronic prop-erties of the 2DPI/graphene HS, we first focus onthe SiO2 supported system. This brings the addi-tional advantage that the SiO2 is insulating and can beused as dielectric in a field-effect transistor geometryallowing to electrostatically tune the Fermi level inthe HS. The optoelectronic properties of the HSswere then analyzed with three complementary meas-urements: electrical measurements, scattering-typescanning near-field optical microscopy (SNOM) andRaman spectroscopy. Multiple samples were stud-ied, where exfoliated graphene flakes were depositedonto 2DPI films via a dry transfer method (describedin [19]). An overview of all the samples and thetechniques used for their experimental analysis ispresented in S7. The monolayer 2DPI was synthes-ized as described by our previous report [12] using theLangmuir–Blodgett method and has a homogeneousthickness of 0.8 nm [13]. To facilitate the comparisonbetween the HS configuration and bare graphene, aportion of the graphene had been stamped onto SiO2so that the optical properties of bare graphene and theHS can be compared.A typical image of a SiO2/2DPI/graphene HSis shown in figure 2(a). Here, the HS is mappedusing SNOM, where in addition to the topographicinformation we can record local differences in opticalconductivity. The near-field optical signal is indeeddirectly linked to the amplitude and phase of theelectromagnetic field inside the nanogap between thetip and the sample and is thus related to the com-plex optical conductivity of the sample [20]. Thus,the optical contrast difference between HS and baregraphene can be attributed to a difference in dop-ing and mobility between them. Figure 2(a) showsthe 3rd harmonic optical amplitude taken with alaser excitation energy of around 115 meV normal-ized to the gold signal. The optical amplitude ingraphene is larger compared to the HS region. Inthis sample, we have also studied the excitation-energy dependent relative contrast between 115 meVand 134 meV, where the contrast between the HSand the bare graphene diminishes with increasingexcitation energy. Figure 2(b) summarizes this trendwhere the difference in contrast of the gold nor-malized 3rd harmonic optical amplitude of the HSand the graphene is shown as a function of excit-ation energy. At lower excitation energies, whereDrude intraband conductivity dominates the opticalresponse, the reduced optical amplitude of the HScompared to the graphene region can be attributed toincreased electron scattering, likely caused by defectsintroduced by the 2DPI. This suggests lower elec-tron mobility in the HS. Additionally, differences indoping between the two regions could also contrib-ute to the variation in optical contrast. If the baregraphene region has a lower Fermi energy, its opticalresponse may result from a combination of Drudeintraband transitions and interband transitions [21,32D Mater. 12 (2025) 025011 F Falorsi et alFigure 2. (a) 3rd harmonic near field optical amplitude at 115 meV of one of the samples studied. In the upper part of the flake, atrilayer graphene is present, as highlighted by the colored lines. In this sample, part of the exfoliated graphene has been transferredto the 2DPI monolayer on the SiO2 to allow the comparison. A significant decrease in the σ3 in the HS is observed due to a changein the optical conductivity between the HS and the graphene. (b) Energy dependent difference between the normalized 3rdharmonic optical signal of the graphene and the HS part of the samples shown in (a). In the insets, the process associated with thehigher excitation energies is shown: both the graphene and the HS are dominated by the interband process. (c) Gate sweepmeasurement over the Si+ back gate sample prepared on a SiO2/Si+ wafer. In this sample part of the flake is stamped on the SiO2while part on the monolayer 2DPI. The measurement is performed under a vacuum. The HS shows hole doping compared to thebare graphene part of the sample. Low-temperature measurements show that the HS maintains the Dirac peak behavior until 7 K.(d) The residual charge carrier density estimates, obtained from the low-temperature sweeps of the graphene and HS curvesshown in (c), and determined by the intersection between the horizontal and the linear fits of the conductivity plotted as afunction of n in logarithmic scale. The values obtained are δnGr = 0.16× 1011 cm−2 for graphene and δnHS = 0.66× 1011 cm−2for the HS, indicating higher disorder in the HS. (e) Gate sweep measurements, (over the Si+ gate) performed under vacuum at7 K over the HS shown in the inset with an AFM picture. In the inset, the thick black line shows the borders of the graphene flakeand the black rectangle highlights the single 20 nm crystal contacted for this measurement, as described in the method section.The Dirac peak is not visible until an application of 60 V over the back gate. Similar behavior where shown by the other crystals inthe flake, for none of which the Dirac peak could be visualized. The thicknesses of the crystals are ranging from 7 to 20 nm.22]. At high excitation energies, intraband transitionsdominate the optical response, as indicated by theinset in figure 2(b), making it independent of bothdoping andmobility. As a result, the graphene and theHS exhibit the same optical contrast [23–26]. Finally,we note that the SNOM images of the HS appear veryhomogeneous, which implies that at the scale of theresolution (around 50 nm) the doping is uniform.The optical SNOM images demonstrate theimpact of 2DPI on the optical conductivity ofgraphene, attributed to a combination of doping andmobility changes in the HSs. To further understandthe effects of 2DPI on graphene’s transport proper-ties, we conducted direct electrical transport meas-urements on various samples. In figure 2(c) a gatesweep of the HS shown in figure S9a is presentedand compared to a gate sweep of the same grapheneflake which is not in contact with the 2DPI. From therelative position of the charge neutrality point of thetwo devices, we are able to identify the relative dopinglevel. The 2DPI induces hole doping in the graphene;in this case of ∆n = (1.55 ± 0.01) × 1012 cm−2.The calculations are performed as described in theelectrical measurement paragraph of the Methodssection. The 2DPI also induces additional scattering[27] as we can identify by a decrease of the chargecarrier mobility from 1580 to 901 cm2 Vs−1 (at1 × 1012 cm−2) and by an increase of the width ofthe charge neutrality peak [28]. Finally, by perform-ing temperature-dependent measurements, we couldverify that the Dirac peak behavior of graphene ismaintained up to 7 K, as expected by the DFT cal-culations shown in figure 1(d). At low temperaturesthe defects in graphene are less screened by thermalfluctuation, thus an increase in the resistance oscil-lations is seen both in the bare graphene and HSpart. The greater oscillations in the HS are attributedto the presence of a larger number of defects andtraps induced in the graphene by the 2DPI [28]. Thehigher disorder caused by these defects in the HS isalso evident by the fact that the resistivity at the CNPshows a smaller increase in the HS compared to thebare graphene region at low temperatures (represen-ted by the black and light blue plots in figure 2(c),42D Mater. 12 (2025) 025011 F Falorsi et alFigure 3. (a) Representation of graphene HS with one, two or, three layers of 2D polyimide and net electron transfer per unit cell.(b) Comparison of the Raman spectra taken on a sample with thick crystals: in black the spectrum of the untreated crystals, andin red the one of the thick 2DPI/graphene HS. To both spectra the background has been subtracted and, to the graphene one, anoffset of 2500 has been added for better visualization. The range indicated in the shaded gray region is shown in figure (c) wherethe shown spectra are normalized with respect to the peak atω∼ 1570 cm−1, circled in the figure, and prominent in eachspectrum. Here there are two additional spectra than in (a): in yellow is shown the spectrum of the protonated crystals and inorange the spectrum of the 2DPI/hBN stack sample. (d) Comparison of the Raman spectra taken 2 samples in which thegraphene is placed on top of a 2D polyimide monolayer. The pink and purple spectra are taken from the same sample respectivelyon the HS and the bare graphene part. The spectrum in blue belongs to a sample in which the monolayer 2DPI has beenprotonated before the graphene transfer. (e) Ratio between the intensity of the 2D peak and the G peak of different graphenesamples. Since the ratio decreases both with the protonation and the presence of the thicker 2DPI, confirms the hypothesis thatthe charge transfer between the two materials increases with the increasing number of polyimide layers underneath and with theprotonation of 2DPI upon stamping. (f) Raman spectra analysis comparing different samples. Here theωG is plotted in respect ofω2D all the different types of samples studied. The spots mainly lay parallel to the line corresponding to null strain (ε= 0),showing that the doping has a stronger effect than the strain on the graphene. The shift of theωG to higher values with thickersamples supports the hypothesis that the doping increases with increases in 2DPI thickness.respectively). The residual charge carrier densityinduced by the disorder around the CNP can be cal-culated from the intersection between the horizontaland linear fits of the conductivity plotted againstthe logarithmic charge carrier density, as shown infigure 2(d) [29, 30]. This analysis yields a higher valueof the residual charge carrier density in the HS part ofthe flake, respectively of δnGr = 1.6 × 1011 cm−2 forgraphene and δnHS = 6.6× 1011 cm−2 for the HS.Having established the 2DPI/graphene HS, wealso have used the versatility of the chemical synthesismethod to realize 2DPI films with varying thicknessesand transfer graphene onto them. In general, increas-ing the layer number of the 2DPI should increase theintralayer charge transfer due to an increased workfunction in the 2DPI as a function of layer thick-ness, as was seen in other 2D materials [31–34]. Infact, we do observe this in our transport measure-ments of graphene stamped on thicker 2DPI crystals,an example of which is shown in figures 2(e), S10(b)where in our accessible back gate window we are notable to electrostatically dope the graphene in the HSto the charge neutrality point, indicative of a dopingdensity larger than∼4.6× 1012 cm−2. These findingsare consistent with our first-principle calculations.As shown in figure 3(a), adding more layers of the2DPI leads to a substantial increase in charge trans-fer to graphene. It also leads to a significant down-shift of the Fermi level, which can be attributed tothe p-doping of graphene (figure S11). Our calcula-tions show that the 2DPI has a higher work functionthan graphene; 4.56 eV versus 4.45 eV, which is con-sistent with the acceptor-character of the porphyrinsites [27, 35, 36], which also show a larger chargetransfer as shown in figures 1(e) and S12. These dop-ing effects cannot be verified solely through transportmeasurements, as an accurate estimation of dopingrequires visualization of the Dirac peak. Therefore, analternative method should be employed for compar-ing samples of different thicknesses, as described inthe following.2. Spectroscopic analysis of doping andstrainTo compare the interaction effects across differenttypes of samples and to obtain large sample statist-ics, we used Raman spectroscopy, which also allows52D Mater. 12 (2025) 025011 F Falorsi et alfor the distinction between doping and strain effectsin the different HS samples. Strain is predicted to bepresent in the HS (figure 1(c)) along with doping.Typical Raman spectra of various 2DPI and2DPI/graphene HSs are shown in figures 3(b)–(d)(please note that in figures 3(b) and (c) we have used2DPI multilayers and in figures 3(d) a 2DPI mono-layer for the HS). One of the most striking effects isthe enhancement of the peak intensities in the mul-tilayer 2DPI/grapheneHS compared to the bare 2DPI.In general, twomain mechanisms are known that canlead to Raman enhancement in thin multilayers ofthis type, namely chemical enhancement and opticalinterference. The mechanism referred to as chemicalenhancement includes various factors, such as chargetransfer and orbital coupling [37–39]. Optical inter-ference involves constructive interference of multiplereflections of the excitation light beam through thevarious layers of the sample [40, 41], and thereforeis known as interference-enhanced Raman scatter-ing, and depends critically on the dielectric constantof the layers involved. For an initial understandingof which mechanism underlies the Raman enhance-ment, we have investigated different types of samples:pure 2DPI, 2DPI which was protonated to mimicdoping without the presence of additional layers,2DPI/graphene and, 2DPI/hBN, as shown in figures 3and S13. Additionally, we tested different thicknessesof the 2DPI film.To start the disentanglement between the effectsstemming from the dielectric environment andcharge transfer we placed a thin hBN flake (around5 nm thick) and a graphene flake next to one anotheron the same thick 2DPI film. In both cases (in the2DPI/graphene and 2DPI/hBN HSs) the Raman sig-nal is enhanced by more than one order of mag-nitude, with distinct enhancement factors for dif-ferent peaks. For instance, the enhancement factorsfor the peak at ω1 = 1301 cm−1 are 21 and 32 forhBN and graphene HS respectively. One aspect con-tributing to the enhancement could be interferenceeffects. Specifically at the 532 nm excitation energyused in this experiment, the conditions to obtain aninterference enhanced Raman scattered signal aremet. In contrast, while with an excitation energyof 633 nm the 2DPI peaks are still enhanced inthe 2DPI/graphene HS, they are not enhanced inthe 2DPI/hBN HSs. We attribute this difference ofenhancement to the dissimilar dielectric constant ofhBN and graphene in the visible wavelength, withthe consequence that no interference enhancement istaking place for the hBN HS (see figures (S13), (f)).A second aspect is that the chemical enhancement,induced by the charge transfer between the 2DPIand the graphene, will also contribute to enhan-cing the Raman signal. A method to validate theimpact of chemical enhancement on the Raman sig-nal is to purposely dope (protonate) the pure 2DPIwith hydrochloric acid. Indeed, protonation leads toan enhancement of the same Raman peaks (figures(S13), (c)) as in the 2DPI/graphene HS. For instance,the peak at ω2 = 1381 cm−1 is enhanced by a factorof 2. The normalized spectra presented in figure 3(c)show that the relative intensity of different peaksundergoes similar changes in the doped 2DPI andalso in the two HSs investigated.We can further validate the relative roles of chem-ical and interference enhancement by investigatingmonolayer 2DPI HSs. The study of the HSs createdwithmonolayer 2DPI (figures 3(d) and S13(b)) indic-ates that chemical enhancement continues to play arole, while interference enhancement does not con-tribute significantly. We conclude this from a studyperformed with h-BN of different thicknesses ontop of a 2DPI (figure S13), where no enhancementcan be observed. This lack of interference enhance-ment, combined with a smaller charge exchange inthe monolayer case, results in significantly smallerenhancement in monolayer 2DPI/graphene HS com-pared to the thicker samples. Nevertheless, whenthe 2DPI is protonated prior to HS formation,the peaks are further enhanced compared to theundoped 2DPI/graphene HS (figure 3(d)) since thecharge transfer between the protonated 2DPI and thegraphene increases in the doped HS. For a completepicture of the effects contributing to the Raman spec-tra more measurements should be taken, with moreexcitation wavelength and varying for example thethickness of the SiO2.This hierarchy of charge transfer (largest chargetransfer in doped thick 2DPI/graphene HSs, smallestcharge transfer undoped monolayer 2DPI/grapheneHSs) can be further confirmed by the analysis of therelative intensity of graphene’s main spectral features,the G peak (ωG ∼ 1580 cm−1) and the 2D peak(ω2D ∼ 2680 cm−1) [42, 43]. The value of I(2D)/I(G)is known to be about 4 for undoped graphene andto continuously decrease as the doping of the sampleincreases [44]. In our experiments, the relative intens-ity I(2D)/I(G) was calculated in multiple spots of dif-ferently prepared devices, as shown in figure 3(e).Here it is evident that themean I(2D)/I(G) ratio of thebare graphene decreases in the undoped monolayer2DPI/graphene HS, and it further decreases in theprotonated monolayer-2DPI HS, reaching the lowestvalues when the HS is formed by thick crystals. Theanalysis of the spectral shape of the individual 2Dand G peaks allows disentangling effects from dop-ing and strain induced into graphene by the 2DPI. Itis well-known that the Raman spectrum of grapheneis highly sensitive to the mechanical strain and dop-ing level of the flakes, as strain and doping both62D Mater. 12 (2025) 025011 F Falorsi et alhave a strong influence on the bond lengths and theelectron-phonon coupling and directly impact theshape and the position of these two peaks. To testfor the different contributions of strain and doping,the position of the 2D peak frequency ω2D is plot-ted with respect to the G peak ωG for multiple spotsof differently prepared HSs in figure 3(f). By evaluat-ing the slope of the experimental points with respectto the case of the unstrained and undoped graphene(ωG0 and ω2D0 indicated by the star), we disentanglethe effects of the strain and doping [45, 46]. Thetwo gray lines in figure 3(e) separate the ωG—ω2Dplane in different regions. The gray area indicatedwith n = 0, with a slope (∆ω2D/∆ωG) =2.2 ± 0.2,represents the area for which the only effect inducedon the graphene is strain. Starting from (ωG0, ω2D0),the valuesmoving along the dotted line indicatedwithε= 0, characterized by a slope of (∆ω2D/∆ωG)= 0.8,define a region in which the only effect induced onthe graphene by the substrate is hole doping. By pro-jecting the experimental values on the (ωG,ω2D) ontothe two characteristic n= 0 and ε= 0 lines, it is pos-sible to deduce the strain and doping of the stud-ied sample: the further the projected point is fromthe unstrained and undoped value (ωG0, ω2D0) thehigher the sample is doped/strained. By performinga linear fit on the experimental data, shown by faintgray lines in figure 3(f), we obtained values of theslope of: SGr=−0.03 ± 0.26, SMono = 1.24 ± 0.24,SThick cryst = 0.94 ± 0.28, SMono+ = 0.75 ± 0.21. Wetherefore conclude that in all samples doping plays themain role since the 2D peaks of the HSs are locatedmostly parallel to the ε = 0 line. The doping dens-ity (as deduced from the G-peak position) increasesaccording to the doping hierarchy discussed above.Finally, while some strain seems to be present in themonolayer 2DPI/graphene samples, it overall plays aminor role compared to the doping.3. Direct analysis of graphene bandstructure in 2DPI/graphene HS by ARPESUp to now, the analysis has indicated that the 2DPIinduces interlayer charge transfer, charge scatteringand, strain in the HS, but we have not been able toexperimentally identify the expected change in theDoS in the HS. To test for these effects, we havemanufactured HSs directly on conductive substrates(doped Si) to allow direct band structure measure-ments by ARPES (technique described in [47, 48]).In the momentum cut of the detected spectra, shownin Figure S14b, it is possible to identify that there is adip in the acquired spectral weight at the Dirac peak.This spectral weight dip of about 215 meV, meas-ured consistently in a second sample, can be attrib-uted to the interaction between 2DPI and graphene,which induces a dip in the DoS in the HS, as calcu-lated for the substrate-supportedHS dip in theDoS inthe HS (figure 1(d), where two distinct density peaksemerge below and above the Fermi level). The dip inthe ARPES spectral weight and in the calculated thusindicates a strong interaction between graphene and2DPI, more details of the analysis are shown in figureS14 in the SI. There, we also discuss that interactionbetween 2DPI and graphene when placed on a Si sub-strate is stronger than when SiO2 substrates are used,as confirmed by our Raman analysis and theoreticalcalculations (figure S6(b)).4. Towards larger device sizes: 2DPI/CVDgraphene HSIn the measurements up to now exfoliated graphenehas been used, which is ideal for fundamental stud-ies. However, in such devices, the HS size is limitedby the size of graphene to the µm regime. Since the2DPI monolayers can be also synthesized on largerscales, we have testedHS composed of chemical vapordeposition (CVD) graphene and the 2DPI (figure(S15)). In these samples similar inter-layer chargetransfer between the 2DPI and the graphene wasmeasured, whereas the overall charge carrier mobil-ity was lower, as expected for CVD graphene.5. ConclusionIn conclusion, we conducted an in-depth study of theinteraction between a 2D COF and graphene, usingvarious experimental techniques and density func-tional theory calculations. Through electronic, scan-ning near-field optical microscopy and Raman spec-troscopy measurements we showed that graphene ishole doped by the 2DPI. This charge transfer pro-cess is likely attributed to the work function differ-ence between the 2DPI and graphene. Our investiga-tion of different samples revealed that controlling thecharge transfer between the polymer and graphenecan be finetuned by adjusting the thickness of the2DPI and/or protonating the 2DPI. Specifically, as the2DPI thickens, the hole doping effect on grapheneincreases. The remarkable tunability observed in theinteraction between this 2DPI and graphene sug-gests a promising avenue for further exploration.With diverse 2D polymers characterized by distinctchemical and topological properties, we anticipate theinvestigation of new and intriguing physical phenom-ena in this emerging field of study.6. Experimental methods6.1. Device fabricationThe stamped samples were fabricated by transferringthe graphene flakes on the 2DPI substrate using thedry transfer method described in [19]. The grapheneflakes were obtained through mechanical exfoliationfrom natural graphite crystals (from NGS tradingand consulting) Silicon/Silicon dioxide (300 nm) sub-strate. The electrical contacts were patterned using72D Mater. 12 (2025) 025011 F Falorsi et alelectron beam lithography (from Raith), with the fol-lowing parameters: an accelerating voltage of 10 kV,a dose of 110 µC cm−2 for the 7.5 µm aperture(used for small contacts) and a dose 170 µC cm−2for 60 µm (used for wider contact lines). The layerof resist for the e-beam procedure was obtained fol-lowing the procedure described in [49]. Finally, the1 nm chromium (with a rate of around 0.43 Å s−1)and 60 nm gold (with a rate of around 0.9 Å s−1) con-tacts are evaporated via thermal evaporation (evapor-ation chamber from BesTec) at pressures of around10−6 mbar. The top electrolyte gate for the meas-urements, shown in figure 2, was deposited throughthe technique described in [50]. To separate the CVDgraphene and the thick crystals samples from the sur-roundings, the flakes were etched through a dry etch-ing process performed with a flow of 40 sccm O2plasma at 80 W and 40 mTorr for 18 s in a react-ive ion etching chamber (from Oxford PlasmaLab).The etchingmaskswere designed using electron beamlithography. In the protonated sample the protona-tion was performed by depositing a droplet of 10%of Hydrochloridric acid and letting it dry at 80◦overnight (around 12 h).Before preparing the samples, the stability of thestudied 2DPI to the applied chemicals was assessedthrough the analysis of atomic force microscopy(AFM) pictures andRaman spectra; no differencewasfound before and after the application of any of theused chemicals.6.2. Scanning probe techniquesThe AFM measurements were performed withAsylum Jupiter AFM by Oxford Instruments withTap300Al-G (from NanonAndMore) tips.The near field scattering microscopy images aretaken with a commercial s-SNOM (from NeaspecCompany) coupled to a tunable CO2 laser (fromAccess laser, model L4G) with wavelengths of 9.2–10.78 µm. The infrared nanoimaging was based onan AFM operated in tapping mode with a tappingamplitude of∆z = 90 nm. All the images were takenwith the tips Arrow-NCPt (fromNanoworld) charac-terized by a tapping frequency Ω of ∼270 KHz. Thepower of the laser during the measurement was set toaround 0.8 mW.6.3. RamanmeasurementsThe Raman measurements shown in the manu-script were taken with the commercially availablesetup is the commercially available LabRam HREvolution (from Horiba). This setup is coupledtwo 2 lasers: an HeNe laser with a 6329 nm andYAG-Laser (Neodymium-doped Yttrium AluminumGarnet) with a wavelength of 532 nm (torus 532 fromLaser Quantum). The setup is equipped with 2 dif-ferent gratings of 1800 gr mm−1 and 600 gr mm−1,both were used during this work. The images shownin figure 4 are taken with the 600 gr mm−1 grating.6.4. Electrical measurementsElectrical measurements, both at room temperatureand low temperature, were performed by contact-ing the gate and the source-drain of the samplesthrough the application of voltages to needles connec-ted to a Keithley 2450. Inmeasurements involving theelectrolyte gate, the needles were applied directly tothe droplet of electrolyte on top of the sample. Themeasurements under vacuum were conducted in aLakeshore CRX-VF probe station under vacuum con-ditions (temperature range 5–450 K). The sampleswere fixed to the sample holder using silver conduct-ing paint to ensure thermal connection between theholder and the sample.From gate sweep measurements shown infigure 2(c), considering the field effect transistor geo-metry of the samples it is possible to derive the chargecarrier density n induced capacitively by the Si gate,with:n=ε0εed(VBG −V0)where d is the thickness of the SiO2 (300 nm), is thedielectric constant of the dioxide, is the vacuum per-mittivity, e is the elementary electron charge, VBGis the applied voltage to the back-gate and V0 isthe voltage corresponding to the CNP of the con-sidered sample [51]. Themobility, corresponding to adefined n, was calculated from the 2 point-probe res-istivity ρ from: µ= 1/(ρne) .6.5. Quantum chemistry calculations detailsAll structures are generated by hetbuilder [52] byrotating and expanding unit cells of target 2D-polymer and graphene w/wo substrate to look forthe shared coincident supercell. The geometries ofall multi-layer structures were optimized by dens-ity functional based tight binding method [53, 54](DFTB), which is a computationally efficient tightbinding approach based on density functional the-ory. DFTB+ [55], as an implementation of DFTB,was used to perform the geometry optimizationsby matsci–0–3 parameters [56]. Electronic proper-ties like band structures and DoS were performedby Fritz-Haber-Institute ab-initio materials simula-tions package (FHI-aims [57]) with PBE [58] func-tional plusmany-body dispersion [59]. Tier 2 basis setand tight integrationmeshwere used. Charge transfercalculations were performed using Vienna Ab initioSimulation Package [60–62] with PBE functional plusD3BJ (D3 with Becke–Johnson damping) dispersion[63] and Bader charge analysis was done by codefrom Dr Henkelman’s group [64–66]. Strain analysis82D Mater. 12 (2025) 025011 F Falorsi et alwas done by a self-made script using atomic simula-tion environment [67], which can be found in Github(https://github.com/shuangjiezhao).Data availability statementThe data that support the findings of this study areavailable upon reasonable request from the authors.AcknowledgmentWe acknowledge stimulating discussions withStephanie Reich and Sabrina Jürgensen. F. F., J.P., R. T. W., X. F. and T. H. acknowledge fundingfrom the SPP 2244 (2DMP) and from the SPP 1928(COORNETs). S. Z. acknowledges funding of theDFG priority program SPP 2244. The authors grate-fully acknowledge the computing time made avail-able to them on the high-performance computers atthe NHR Centers at TU Dresden and NHR CenterPC2. These are funded by the Federal Ministry ofEducation and Research and the state governmentsparticipating on the basis of the resolutions of theGWK for the national high-performance computingat universities (www.nhr-verein.de/unsere-partner).K.W. and T.T. acknowledge support from the JSPSKAKENHI (Grant Numbers 20H00354, 21H05233and 23H02052) and World Premier InternationalResearch Center Initiative (WPI), MEXT, Japan.ORCID iDsFrancesca Falorsi https://orcid.org/0009-0007-3319-7240Christian Eckel https://orcid.org/0000-0001-7888-2574Marcel Reutzel https://orcid.org/0000-0002-1085-2931Kenji Watanabe https://orcid.org/0000-0003-3701-8119Thomas Heine https://orcid.org/0000-0003-2379-6251R Thomas Weitz https://orcid.org/0000-0001-5404-7355References[1] Novoselov K S, Geim A K, Morozov S V, Jiang D,Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A2005 Two-dimensional gas of massless Dirac fermions ingraphene Nature 438 197–200[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y,Dubonos S V, Grigorieva I V and Firsov A A 2004 Electricfield effect in atomically thin carbon films Science 306 666–9[3] Novoselov K S, Mishchenko A, Carvalho A and CastroNeto A H 2016 2D materials and van der Waalsheterostructures Science 353 aac9439[4] Zhang Y, Tang T-T, Girit C, Hao Z, Martin M C, Zettl A,Crommie M F, Shen Y R and Wang F 2009 Directobservation of a widely tunable bandgap in bilayer grapheneNature 459 820–3[5] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010Atomically thin MoS: a new direct-gap semiconductor Phys.Rev. 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