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Teppei Shintaku, Afsal Kareekunnan, Masashi Akabori, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Hiroshi Mizuta

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[Berry Curvature Induced Valley Hall Effect in Non‐Encapsulated hBN/Bilayer Graphene Heterostructure Aligned with Near‐Zero Twist Angle](https://mdr.nims.go.jp/datasets/deaeefe5-73b4-4391-8ebc-bc9513962a17)

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Berry Curvature Induced Valley Hall Effect in Non‐Encapsulated hBN/Bilayer Graphene Heterostructure Aligned with Near‐Zero Twist AngleRESEARCH ARTICLEwww.advphysicsres.comBerry Curvature Induced Valley Hall Effect inNon-Encapsulated hBN/Bilayer Graphene HeterostructureAligned with Near-Zero Twist AngleTeppei Shintaku, Afsal Kareekunnan,* Masashi Akabori, Kenji Watanabe,Takashi Taniguchi, and Hiroshi MizutaValley Hall effect is observed in asymmetric single-layer and bilayer graphenesystems. In single-layer graphene systems, asymmetry is introduced byaligning graphene with hexagonal boron nitride (hBN) with a near-zero twistangle, breaking the sub-lattice symmetry. Although a similar approach is usedin bilayer graphene to break the layer symmetry and thereby observe the valleyHall effect, the bilayer graphene is sandwiched with hBN on both sides inthose studies. This study looks at a much simpler, non-encapsulated structurewhere hBN is present only at the top of graphene. The crystallographic axes ofboth hBN and bilayer graphene are aligned. A clear signature of the valley Halleffect through non-local resistance measurement (RNL) is observed. Theobserved non-local resistance can be manipulated by applying a displacementfield across the heterostructure. Furthermore, the electronic band structureand Berry curvature calculations validate the experimental observations.1. IntroductionWith the introduction of 2D materials, the valley degree of free-dom of carriers has gained much prominence in recent years.[1–3]Materials like graphene and MoS2 have two in-equivalent valleysat the K and K′ high symmetry points of their Brillouin zone,which can be interpreted as valley-up and valley-down, much likethe spin degree of freedom of carriers. However, the fundamen-tal criterion for a material to be valleytronic is to have a brokeninversion symmetry. While single-layer graphene is symmetric,aligning graphene with hexagonal boron nitride (hBN) with aT. Shintaku, A. Kareekunnan, M. Akabori, H. MizutaJapan Advanced Institute of Science and Technology1-1 Asahidai, Nomi 923-1292, JapanE-mail: afsal@jaist.ac.jpK. Watanabe, T. TaniguchiNational Institute for Materials Science1-1 Namiki, Tsukuba 305-0044, JapanThe ORCID identification number(s) for the author(s) of this articlecan be found under https://doi.org/10.1002/apxr.202300064© 2023 The Authors. Advanced Physics Research published byWiley-VCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distributionand reproduction in any medium, provided the original work isproperly cited.DOI: 10.1002/apxr.202300064near-zero twist angle has proven to breakthe sub-lattice symmetry of the graphenelayer.[4–7] Such a system has exhibited thevalley Hall effect (VHE) due to the emer-gence of Berry curvature at the valley as aresult of broken inversion symmetry.[8–10]As for bilayer graphene, the asymmetrycan be introduced by either applying anout-of-plane electric field across the lay-ers or by aligning with an hBN layer, bothof which break the layer symmetry of thesystem as they introduce different poten-tials between the top and bottom layersof the bilayer.[11–15] Both methods havebeen employed to observe VHE in bilayergraphene in recent years.[16–19]In the case of single-layer graphene, ithas been shown that both encapsulatedand non-encapsulated graphene exhibitthe valley Hall effect, provided either ofthe hBN (top or bottom) is oriented with graphene.[8] As for bi-layer graphene, the valley Hall effect is observed by hBN align-ment only in encapsulated systems.[18,19] Here, hBN is presentat the top and bottom of the bilayer graphene with one of thehBN aligned and the other misaligned by more than 10° to avoidthe formation of a double moiré pattern. However, it has beenshown theoretically that aligning hBN with bilayer graphene ina non-encapsulated configuration can also break the symme-try of the system and induce Berry curvature.[20] Consideringthe complexity in fabricating an encapsulated heterostructure, inthis study, we explore the VHE in non-encapsulated hBN/bilayergraphene heterostructure (hBN/bilayer graphene/SiO2) with thehBN aligned with the bilayer graphene. We observed a strongVHE signal at the primary Dirac point through non-local elec-trical measurement. The VHE signal could be further manipu-lated by applying a displacement electric field across the layers.We also performed ab initio calculations, which show that alignedhBN/bilayer graphene heterostructure has an intrinsic bandgapand a non-zero Berry curvature. The bandgap and the Berry cur-vature can be manipulated with an out-of-plane electric field ap-plied across the layers.2. Results and DiscussionThe hBN/bilayer graphene heterostructure is fabricated follow-ing the dry transfer method.[21] Two devices, denoted as Device AAdv. Physics Res. 2024, 3, 2300064 2300064 (1 of 6) © 2023 The Authors. Advanced Physics Research published by Wiley-VCH GmbHhttp://www.advphysicsres.commailto:afsal@jaist.ac.jphttps://doi.org/10.1002/apxr.202300064http://creativecommons.org/licenses/by/4.0/http://crossmark.crossref.org/dialog/?doi=10.1002%2Fapxr.202300064&domain=pdf&date_stamp=2023-08-31www.advancedsciencenews.com www.advphysicsres.comFigure 1. a) Optical image of hBN/bilayer graphene heterostructure aligned with near-zero twist angle. The dotted line shows the graphene region.The arrow indicates the edges of graphene and hBN, which are aligned. The inset shows the optical image of the final device. b) The heterostructureschematic diagram shows the passivation hBN layer and the top gate electrode. C) Measured gate characteristics of the device as a function of carrierdensity n. The arrow indicates the two secondary Dirac peaks at the electron and hole sides. The measurement is performed at 10 K.and Device B, are fabricated. The results presented in the maintext are from Device A (see Supporting Information for the re-sults from Device B). Figure 1a shows the optical image of thehBN/bilayer graphene heterostructure from which Device A isfabricated. The dotted line outlines the bilayer graphene area.The bilayer graphene is AB-stacked, and the layer number is con-firmed through Raman spectroscopy. The arrows indicate theedges of hBN and bilayer graphene, which are aligned with anear-zero twist angle. After etching the heterostructure into aHall bar, edge contacts were fabricated.[21] Later a passivationhBN layer is transferred on top of the heterostructure, abovewhich the top gate electrode is fabricated. Figure 1a inset andFigure 1b show the optical image and schematic diagram of thefinal device. Figure 1c shows the gate characteristics of the de-vice. The field-effect carrier mobility extracted from the linear re-gion around the main Dirac peak (MDP) is ≈ 19 000 cm2 V−1 s−1and ≈ 26 000 cm2 V−1 s−1, respectively, for the holes and elec-trons. Apart from the MDP, secondary Dirac peaks (SDP), whichis the signature of the formation of moiré superlattice, can be ob-served on both sides of the main Dirac peak. The SDP appearsat ± 1.78 × 1012 cm−2, which corresponds to a moiré superlatticeperiod of 15.3 nm. This period is slightly larger than the maxi-mum period (13.8 nm) expected for an hBN-graphene moiré su-perlattice. The slight increase in the periodicity is attributed tothe stretching of the bilayer graphene (supporting InformationII),[5,22,23] which could be originated from the non-uniformity ofthe SiO2 substrate.The local and non-local electrical measurements are per-formed following the standard four-terminal method usingKEITHLEY 4200 semiconductor parameter analyzer with a highinput impedance (1013 Ω) at the voltage terminals. A separatesource meter (KEITHLEY 2400) is used to apply gate voltage.Figure 2a compares the local (RL) and non-local (RNL) resistancemeasurement results for Device A at 10 K. For RL, a current is ap-plied between terminals two and three, and the voltage drop be-tween terminals nine and eight is detected, giving RL = V9, 8/I2, 3.For RNL measurement, the current is applied at the local termi-nals three and eight, and the voltage drop at terminals two andnine is measured, giving RNL = V2, 9/I3, 8. The length and widthof the Hall bar in the measured region are 2.5 μm and 1 μm, re-spectively (A schematic diagram showing the device dimensionsin detail is given in the Supporting Information). A strong RNLsignal is detected around the charge neutrality point (CNP) withzero electric or magnetic field applied across the layers. The peakof the RNL generally appears at the CNP. The shift in the RNL peakis attributed to the in-homogeneity in the bilayer graphene chan-nel, especially since the graphene is on SiO2 substrate. To ruleout the possibility of diffusive charge contribution to the mea-sured non-local signal, we also calculated the Ohmic contribu-tion using the formula ROhmNL = RL( W𝜋L)exp(− 𝜋LW).[24] The calculatedOhmic contribution is at least one order of magnitude less thanthat of the measured RNL, thereby ruling out the possibility of dif-fusive charge contribution. One possible origin of the observedRNL would be the VHE. The Berry curvature induced VHE, andthe resultant transverse valley Hall conductivity (𝜎VHxy ) is relatedto the measured RNL asRNL = 12(𝜎VHxy𝜎xx)2W𝜎xxlvexp(− Llv)(1)where L and W are the length and width of the device, lv is thevalley diffusion length and 𝜎xx = 1/𝜌 is the conductivity. Here, 𝜌is defined as RL(W/L) where W and L are the width and length ofthe measured part of the channel, respectively. In the small valleyHall angle regime (𝜎VHxy ∕𝜎xx) ≪ 1), RNL and 𝜌 holds a cubic scal-ing relation (RNL∝𝜌3). Thus we plotted RNL as a function of 𝜌 asshown in Figure 2b, which exhibits a clear cubic relation imply-ing that the measured RNL indeed originates from the VHE. Theorigin of the VHE can be explained as follows. Aligning hBN withbilayer graphene creates a moiré superlattice with periodic re-gions where the heterostructure is commensurately stacked.[5,8]Such commensurately stacked regions induce a global asymme-try between the non-dimer atoms (which constitute the low en-ergy bands) in the top and bottom layers, resulting in global layerAdv. Physics Res. 2024, 3, 2300064 2300064 (2 of 6) © 2023 The Authors. Advanced Physics Research published by Wiley-VCH GmbH 27511200, 2024, 1, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/apxr.202300064 by National Institute For, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advphysicsres.comwww.advancedsciencenews.com www.advphysicsres.comFigure 2. a) Measured local (RL) and non-local (RNL) resistance for theheterostructure at 10K. The blue line is the calculated Ohmic contributionto the non-local resistance. b) RNL and 𝜌 follows a cubic scaling relation(RNL∝𝜌3) indicating that the measured RNL originates from VHE.asymmetry. The broken layer symmetry will open a bandgap andinduce a finite Berry curvature at the CNP, resulting in VHE.Next, we investigate the effect of an electric displacementfield applied across the bilayer graphene on both RL and RNL.Figures 3a, b show the heat map of the RL and RNL, respectively,as a function of both top-gate and bottom-gate voltage. It can beseen that the RNL is narrower than RL, indicating the differencein the physical origin of both peaks. Applying voltages on the topand bottom gates allows the independent control of carrier con-centration and the displacement field. The displacement fieldsrelated to the top and bottom gates (VTG and VBG) are defined asDTG = −𝜖TG(VTG − V0TG)∕dTGDBG = −𝜖BG(VBG − V0BG)∕dBG(2)where ϵTG(ϵBG) and dTG(dBG) are the dielectric constant and thick-ness of the top(bottom) layer. V0TG,BG is the voltage offset, which is-1.2 and 10 V, respectively, for Device A. The difference betweenthe two displacement fields gives the carrier doping, and the av-erage of the two is the net displacement fields. Figure 3c showsthe evolution of RL and RNL as a function of the displacementfield. Here RL and RNL are plotted as a function of top gate volt-age with the back gate fixed at different values. As mentioned ear-lier, the heterostructure at the pristine state (VBG = 0V) shows aclear non-local signal, suggesting an in-built asymmetry presentin the heterostructure. Application of a negative electric field (VBG= -20 and -10V) increases the intensity of both RL and RNL. Thisimplies that a negative electric field widens the bandgap and en-hances the asymmetry between the layers. Whereas the applica-tion of the offset bottom-gate voltage (V0BG = 10V) reduces theintensity of both peaks, suggesting a reduction in the bandgapand the asymmetry. However, the application of a strong positiveelectric field (VBG = 30V) yet again increases the intensity of bothRL and RNL, implying an increase in bandgap and asymmetry ofthe heterostructure.To validate the above hypothesis, we measured the tempera-ture dependence of the RL at different gate voltages to calculatethe bandgap. The maximum of the local resistivity (𝜌maxL ) at thehigh-temperature regime is related to the bandgap as:1𝜌maxL= 1𝜌Lexp(− ELkBT)(3)where 𝜌L is the local resistivity, EL is the activation energy, kB is theBoltzmann constant, and T is the temperature. The bandgap Eg,defined as 2EL, can be extracted by plotting 1∕𝜌maxL as a functionof 1/T as shown in Figure 4. The dotted line is the fit to Equation(3) at the high-temperature regime. Table 1 shows the extractedbandgap values at different VBG. The heterostructure has an in-trinsic bandgap of 25 meV (at VBG = 0 V), suggesting that thebandgap originates from the alignment of bilayer graphene withthe hBN. Application of a negative displacement field enhancesthe bandgap (35.3 meV at VBG= -10 V and 45.5 meV at VBG= -20V). At the same time, the bandgap reduces to a value of 17.5 meVat the offset bottom-gate voltage (V0BG = 10V). This is consistentwith the earlier observation of an increase(decrease) in the RL andRNL peak intensity at the negative(positive) displacement field.We have also performed ab initio calculations to substanti-ate the experimental observations (see [25–28] for calculationdetails). The heterostructure is formed by stacking a unit cellof bilayer graphene on top of an hBN unit cell. The lattice pa-rameter of hBN is matched to that of graphene to create acommensurate stacking to mimic the experimental scenario.Figure 5a–e shows the electronic band structure calculated for thehBN/bilayer graphene heterostructure at different electric fieldsapplied across the layers. The heterostructure has an intrinsicbandgap of 36 meV (Figure 5c), implying asymmetry betweenthe layers. As the low energy bands are constituted by the non-dimer atoms in the bottom and top layers of the bilayer graphene,the hBN induces different potentials between them, which opensa bandgap. Applying a negative electric field (Figure 5a,b) intro-duces additional asymmetry between the layers, enhancing thebandgap (75 meV for -0.25 Vnm-1 and 92 meV for -0.5 Vnm-1).However, applying a positive electric field initially works againstthe inbuilt asymmetry between the layers, reducing the bandgapto 21 meV (Figure 5d). At higher positive electric fields, the elec-tric potential surpasses the intrinsic potential difference betweenthe layers and widens the bandgap further (40 meV for 1.25Vnm-1), as shown in Figure 5e. The results of the band struc-ture calculation strongly agree with the experimental observa-Adv. Physics Res. 2024, 3, 2300064 2300064 (3 of 6) © 2023 The Authors. Advanced Physics Research published by Wiley-VCH GmbH 27511200, 2024, 1, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/apxr.202300064 by National Institute For, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advphysicsres.comwww.advancedsciencenews.com www.advphysicsres.comFigure 3. Heat map of the (a) RL and (b) RNL as a function of top-gate and bottom-gate. c) RL and RNL measured as a function of top-gate voltage withback-gate fixed at different values. All the measurements are performed at 10 K.Figure 4. 1∕𝜌maxL as a function of 1/T plot for different VBG showing thetemperature dependence of 𝜌maxL . The dotted line indicates the fitting toEquation (3) in the high-temperature regime from which the bandgap ofthe heterostructure at different VBG is extracted.tions. Next, we look at the Berry curvature calculated for the het-erostructure. Berry curvature for an electronic band is defined as𝛀n(k) = i ℏ2m2∑n≠n′⟨un,k|p̂|un′ ,k⟩ × ⟨un′ ,k|p̂|un,k⟩(𝜀n − 𝜀n′ )2(4)Table 1. Bandgap extracted from the 1∕𝜌maxL versus 1/T plot for differentVBG. E⊥ is the electric field corresponding to each VBG at 𝜌maxL .VBG (V) E⊥ (V/nm) Band gap (meV) RmaxNL (Ω)-20 -0.44 45.5 160-10 -0.30 35.3 940 -0.14 24.8 6410 0.00 17.5 34where |un,k⟩ is the periodic part of the Bloch function, p̂ is themomentum operator, 𝜖n is the energy of the nth band and 𝜀n′represents the energy of all other bands. The total Berry curva-ture is the sum of the individual occupied band’s Berry curvature(𝛀(k) =∑n fn𝛀n(k)). The Wannier interpolation scheme dictatesthat a pair of bands that are either occupied or unoccupied havea negligible contribution to the total Berry curvature.[29] The ma-jor contribution to the total Berry curvature comes from a pair ofbands where one is occupied and another unoccupied, such asthe low energy bands in the hBN/bilayer graphene heterostruc-ture. In addition, the denominator of Equation (4) suggests thatthe Berry curvature value varies as the square of the energy dif-ference between two adjacent bands. Thus in our case, the Berrycurvature changes with the electric field as the band gap changes.The heterostructure has an intrinsic non-zero Berry curvature, asshown in Figure 5h. A negative electric field reduces the magni-tude of the Berry curvature as it widens the gap between the lowAdv. Physics Res. 2024, 3, 2300064 2300064 (4 of 6) © 2023 The Authors. Advanced Physics Research published by Wiley-VCH GmbH 27511200, 2024, 1, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/apxr.202300064 by National Institute For, Wiley Online Library on [31/07/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensehttp://www.advancedsciencenews.comhttp://www.advphysicsres.comwww.advancedsciencenews.com www.advphysicsres.comFigure 5. Electronic band structure calculated for the hBN/bilayer graphene heterostructure at electric fields of magnitude a) -0.5 Vnm-1, b) -0.25 Vnm-1,c) 0 Vnm-1, d) 0.5 Vnm-1, and e) 1.25 Vnm-1. The path of the band structure calculation is M → K → Γ. Berry curvature calculated at K high symmetrypoint for the heterostructure at electric fields of magnitude f) -0.5 Vnm-1, g) -0.25 Vnm-1, h) 0 Vnm-1, i) 0.5 Vnm-1, and j) 1.25 Vnm-1. The path of theBerry curvature calculation is the same as the band structure calculation.energy bands (Figure 5f,g). On the other hand, a small positiveelectric field (0.5 Vnm-1) enhances the magnitude of the Berrycurvature due to the narrow bandgap (Figure 5i). However, twokey differences could be observed at a higher positive electric field(Figure 5j). One, the magnitude of the Berry curvature reducesowing to the widening of the bandgap. The second is the changein the polarity of the Berry curvature, which implies that the po-larity of the layer asymmetry switches direction at higher positiveelectric fields.3. ConclusionIn conclusion, we have observed Berry curvature induced VHE innon-encapsulated hBN/bilayer graphene heterostructure, wherethe hBN and bilayer graphene are aligned with a near-zero twistangle. Aligning bilayer graphene with hBN gives rise to a globalbandgap and a finite Berry curvature at the CNP, resulting inVHE. The VHE is detected as a non-local resistance near theCNP. The cubic relation observed between RNL and 𝜌 validatesthat the measured RNL indeed originates from the VHE. Themeasured RNL could be manipulated with the application of adisplacement field across the layers, which is attributed to thechange in the electronic band structure and the asymmetry ofthe bilayer graphene under a displacement field. The intrinsicbandgap of the heterostructure and its evolution under the dis-placement field is confirmed from the temperature-dependent RLmeasurement in the high-temperature regime. The experimentalobservations were substantiated with ab initio calculations thatshowed that the heterostructure has an intrinsic bandgap and anon-zero Berry curvature, both of which could be controlled by aperpendicular electric field.Supporting InformationSupporting Information is available from the Wiley Online Library or fromthe author.AcknowledgementsT.S. and A.K. contributed equally to this work. Part of this research was sup-ported by Toshiba electronic devices and storage corporation’s academicencouragement program.Conflict of InterestThe authors declare no conflict of interest.Data Availability StatementThe data that support the findings of this study are available from the cor-responding author upon reasonable request.Keywordsbilayer graphene, hBN, valleytronicsReceived: June 5, 2023Revised: July 28, 2023Published online: August 31, 2023[1] J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W.Yao, X. Xu, Nat. Rev. Mater. 2016, 1, 16055.Adv. Physics Res. 2024, 3, 2300064 2300064 (5 of 6) © 2023 The Authors. Advanced Physics Research published by Wiley-VCH GmbH 27511200, 2024, 1, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/apxr.202300064 by National Institute For, Wiley Online Library on [31/07/2025]. 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