# Fileset

[d2nr06616e.pdf](https://mdr.nims.go.jp/filesets/c3b584ec-b3b5-4a45-b184-a498311851fb/download)

## Creator

Shaochun Zhang, Mina Maruyama, Susumu Okada, Mengsong Xue, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Kazuki Hashimoto, Yasumitsu Miyata, Ruben Canton-Vitoria, [Ryo Kitaura](https://orcid.org/0000-0001-8108-109X)

## Rights



## Other metadata

[Observation of the photovoltaic effect in a van der Waals heterostructure](https://mdr.nims.go.jp/datasets/82c3bbfd-ec8b-4360-8c7a-1a5c0718a202)

## Fulltext

Observation of the photovoltaic effect in a van der Waals heterostructureNanoscalePAPERCite this: Nanoscale, 2023, 15, 5948Received 26th November 2022,Accepted 20th February 2023DOI: 10.1039/d2nr06616ersc.li/nanoscaleObservation of the photovoltaic effect in a van derWaals heterostructure†Shaochun Zhang,a Mina Maruyama,b Susumu Okada,b Mengsong Xue,aKenji Watanabe, d Takashi Taniguchi,c Kazuki Hashimoto,e Yasumitsu Miyata,eRuben Canton-Vitoriaa and Ryo Kitaura *a,cvan der Waals (vdW) heterostructures, which can be assembled with various two-dimensional materials,provide a versatile platform for exploring emergent phenomena. Here, we report an observation of thephotovoltaic effect in a WS2/MoS2 vdW heterostructure. Light excitation of WS2/MoS2 at a wavelength of633 nm yields a photocurrent without applying bias voltages, and the excitation power dependence ofthe photocurrent shows characteristic crossover from a linear to square root dependence. Photocurrentmapping has clearly shown that the observed photovoltaic effect arises from the WS2/MoS2 region, notfrom Schottky junctions at electrode contacts. Kelvin probe microscopy observations show no slope inthe electrostatic potential, excluding the possibility that the photocurrent originates from an unintention-ally formed built-in potential.IntroductionArtificial van der Waals stackings (vdWSs)1–3 provide a generalplatform to explore emergent phenomena. Unlike fabricatingconventional heterostructures based on three-dimensionalmaterials, stacking different two-dimensional (2D) materialscan realize diverse vdWSs regardless of the lattice mismatch.The interlayer interactions in vdWSs can cause synergisticeffects in the electronic and optical properties, which areabsent in the individual components alone. For example,twisted bilayer graphene with a twist angle of ∼1.1°, the so-called magic angle,4 exhibits unconventional superconduc-tivity due to the flat bands arising from the interlayer moirépotential. Also, vdWSs composed of transition metal dichalco-genides (TMDs) host long-lived interlayer excitons,5 where elec-trons and holes reside in different layers. Furthermore, whenTMD-based vdWSs possess a certain stacking angle, moiréexcitons emerge6 and work as arrayed quantum emitters.7These emergent properties have attracted significant attention,and further discovery is yet to come.Meanwhile, the photovoltaic effect (PVE), which emerges innoncentrosymmetric materials, has ignited the search for newPVE materials. Typically, PVE appears in inhomogeneous semi-conductors with p–n junctions,8 where the spontaneouslyformed built-in potential generates a photovoltage in responseto light irradiation. In contrast, the bulk photovoltaic effect(BPVE),9 which appears in noncentrosymmetric materials,10does not require a built-in potential. Theoretical studies haveproposed the origin of BPVE:11 (1) the shift of the electroncloud in real space upon light excitation (shift current) and (2)the asymmetry of the velocity of electron wavepackets (ballisticcurrent). As these mechanisms differ distinctly from PVEbased on p–n junctions, BPVE is free from the Shockley–Queisser (SQ) limit.12 The possibility of PVE materials beyondthe SQ limit and their fundamental mechanisms have beenattracting much attention.vdWSs provide a diverse platform to search for new systemswith emergent properties, including non-zero BPVE. Althoughinversion symmetry breaking is required for BPVE to emerge,this requirement alone is insufficient. For example, the three-fold rotational (C3) symmetry of monolayer TMDs cancels outthe in-plane photovoltage, resulting in zero BPVE. By contrast,significant BPVE appears in WS2 nanotubes13 and WSe2/blackphosphorus (BP),14 where the C3 symmetry is broken byrolling-up and BP stacking, respectively. These examples showthat lowering the spatial symmetry can cause BPVE, and stack-ing two independent layers to form vdWSs is a promising wayto fabricate new BPVE materials.†Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2nr06616eaDepartment of Chemistry, Nagoya University, Nagoya, Aichi 464-8602, Japan.E-mail: KITAURA.Ryo@nims.go.jp, r.kitaura@nagoya-u.jpbDepartment of Physics, Graduate School of Pure and Applied Sciences, University ofTsukuba, 1-1-1 Tennodai, Tsukuba 305-8571, JapancInternational Center for Materials Nanoarchitectonics, National Institute forMaterials Science, 1-1 Namiki, Tsukuba 305-0044, JapandResearch Center for Functional Materials, National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, JapaneDepartment of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397,Japan5948 | Nanoscale, 2023, 15, 5948–5953 This journal is © The Royal Society of Chemistry 2023Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article OnlineView Journal  | View Issuehttp://rsc.li/nanoscalehttp://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0001-8108-109Xhttps://doi.org/10.1039/d2nr06616ehttps://doi.org/10.1039/d2nr06616ehttps://doi.org/10.1039/d2nr06616ehttp://crossmark.crossref.org/dialog/?doi=10.1039/d2nr06616e&domain=pdf&date_stamp=2023-03-20http://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616ehttps://pubs.rsc.org/en/journals/journal/NRhttps://pubs.rsc.org/en/journals/journal/NR?issueid=NR015012Here we report the emergence of PVE in WS2/MoS2 vdWheterostructures. Although both WS2 and MoS2 have C3 sym-metry and sets of mirror planes (Fig. 1A), the symmetry canprobably be altered at the WS2 and MoS2 interface due to theinterlayer interaction. Photocurrent mapping measurementshave demonstrated that a photocurrent up to 28 nA appearswithout applying bias voltages under 996 µW light excitation;the photocurrent is almost zero when the excitation laser sportis placed outside the stacked region. The observed photo-current is comparable to the recently reported PVE response inWS2 nanotubes13 and strained MoS2.11 Kelvin probemicroscopy observations did not show any drop and/or slopein potential, ruling out the photocurrent originating from theunintentional built-in potential. The excitation power depen-dence of the photocurrent shows a linear relationship in thelow excitation power region and a square root relationship inthe high power region. This work suggests that simply stackingtwo different layered structures can lead to observing PVE,which is consistent with BPVE.Results and discussionAccording to the procedure reported in previous work, multi-layer WS2 and MoS2 flakes were mechanically exfoliated onSiO2/Si (270 nm) substrates and transferred to form vdWSs bythe dry method with polymer stamps.15 Raman spectraobtained with 532 nm excitation show the E12g and A1g peaks ofWS2 and MoS2, located at 354 cm−1,421.5 cm−1 and 384 cm−1,408.5 cm−1 respectively,16 consistent with the multilayer struc-ture (see ESI, Fig. S1†). Also, the atomic force microscopy(AFM) image and height profile show that MoS2 is 6-layer andWS2 is 5-layer (see ESI, Fig. S2†). As for the stacking angle ofvdWSs, we estimated the crystal orientation of each flakebased on the edge direction: linear edges with an angle of 60or 120 degrees corresponding to the zigzag edge.17 Onceknowing the crystal orientation, we can control the stackingangle in WS2/MoS2. In this study, we use a stacking angle of 90and 60 degrees; hereafter the results of 90 degrees aredescribed in detail (for 60 degrees, please see the ESI†). Aftermaking vdWSs, we made electrical contact with bismuth (Bi)to reduce the Schottky barrier at each contact;18 a smallSchottky barrier is essential to have low contact resistance,leading to a larger short-circuit current. It should be notedthat the two Bi electrodes contact only with the MoS2 part, notthe WS2/MoS2 stacking region, as shown in Fig. 1B and C.To study the spatial distribution of the photocurrent inWS2/MoS2 systemically, we applied scanning photocurrentmicroscopy, where an excitation laser spot is scanned acrossthe surface of the device to measure the position dependenceof the photocurrent. Fig. 2A and B (also Fig. S3A and B†) showone-dimensional and two-dimensional photocurrent mappingmeasured without applying a bias voltage (short-circuitcurrent), respectively. The short-circuit current gives an oppo-site sign at the two electrodes, consistent with the currentdriven by the built-in potential arising from the Schottkybarriers19,20 at the contacts (or the photothermoelectriceffect21,22). Also, we observed a short-circuit photocurrent withopposite signs on both edges of the WS2/MoS2 region. Thephotocurrent on both edges probably arises from the bandbending at the lateral interface between MoS2 and WS2/MoS2.23 The orbital hybridization between WS2 and MoS2changes the electronic bands of MoS2 only in the WS2/MoS2region, resulting in band bending at the interface. Similarphotocurrent signals were also observed in other hetero-structures, such as graphene/MoS224 (Fig. S3C and D†).In addition to the edges, the non-zero photocurrent alsoappears over the whole WS2/MoS2 region. Importantly, thephotocurrent is almost zero when the excitation laser spot isplaced on the MoS2 part, demonstrating that the photocurrentoriginates from the WS2/MoS2 stacking structure. To furtherinvestigate the PVE observed at WS2/MoS2, the current–voltage(I–V) characteristics at room temperature were measured under9.96 × 102 µW excitation with a wavelength of 633 nm. Asshown in Fig. 2C, the I–V curve is linear over −0.5 to 0.5 Vwithout any rectification behavior, which is usually seen in p–n junctions.25 The photocurrent observed without applying avoltage is 28 nA (6 × 101 A cm−2 with excitation of ∼104 Wcm−2), which is considerably larger than photoresponsesreported in inorganic ferroelectrics (such as BiFeO3 andFig. 1 (A) Schematic illustration of the structure of monolayer MoS2 or WS2. Purple and yellow spheres correspond to metal and sulfur atoms,respectively. The red lines and the open circle represent mirror planes and the C3 axe, respectively. (B) and (C) are a schematic representation and anoptical image of the WS2/MoS2 device, respectively.Nanoscale PaperThis journal is © The Royal Society of Chemistry 2023 Nanoscale, 2023, 15, 5948–5953 | 5949Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616eBiTiO3)26–30 and comparable to the recently reported photore-sponses in low-dimensional systems, such as WS2 nanotubes13and strained MoS2.11 In contrast to the I–V curve under photo-excitation, the dark I–V curve in Fig. 2C shows almost zerothroughout the voltage range tested, demonstrating that theobserved current originates from photoexcitation. Fig. 2Dshows the photocurrent response when the laser excitation isrepeatedly turned on and off. As seen in Fig. 2D, the photo-current returns to similar values each time the laser is turnedon, indicating that the PVE in WS2/MoS2 is robust both inquality and quantity; the zero-photocurrent observed withoutlight excitation is consistent with the zero-current shown inthe dark I–V curve shown in Fig. 2C.Fig. 2E shows a log–log plot of an excitation power depen-dence of the photocurrent measured with the excitation wave-length of 633 nm, showing the characteristic crossover from alinear to square-root dependence31 at around 103 µW cm−2. Asimilar crossover from a linear to square-root dependence hasalso been observed in WS2 nanotubes13 and WSe2/BP,14 wherethe non-zero short-circuit current originates from the shiftcurrent. To further address the mechanism of the photo-current, we analysed the excitation wavelength dependence ofthe photocurrent. As seen in Fig. 2F, the wavelength depen-dence has several peaks in the range of 1.85–2.05 eV, whichcorrespond to the exciton resonances of MoS2, indicating thatexciton resonances can enhance the photovoltaic response; thephotocurrent enhancement at exciton resonances has beenpredicted.32 When the photon energy increases and reachesca. 1.8 eV, the optical gap of MoS2, the photovoltaic responseis enhanced due to the increase of joint density of states andreaches the maximum around the optical transition betweenbands around K (K′) points. As the excitation photon energyfurther increases, the photovoltaic response is eventually sup-pressed, probably because of the reduction of the shiftvector.14Kelvin Probe Force Microscopy (KPFM) has provided criticalinformation to exclude the possibility that the observed photo-current arises from the unintentionally-formed built-in poten-tial. Note that an out-of-plane built-in potential, which cannotbe observed with KPFM, is probably present due to the type-IIband alignment, but this built-in potential should not contrib-ute to the lateral photocurrent observed (see also discussion inthe ESI†). Fig. 3A and B illustrate a KPFM image and a lineprofile along the red dashed line in the image, respectively. Asseen in Fig. 3B, there is no potential drop over the wholesurface of the WS2/MoS2 region, clearly demonstrating that theobserved photocurrent does not arise from the built-in poten-tial; the open-circuit voltage shown in Fig. 2C means that anin-plane built-in potential of the order of 102 mV should existif the built-in potential is the origin of the photocurrent. Notethat shunt resistances alter open-circuit voltages, but it is safeto say that the actual open-circuit voltage is at least 102 meVorder. The absence of a built-in potential is reasonablebecause we made the WS2/MoS2 structure using intrinsic WS2and MoS2 without additional doping for p–n junctions. Theslight change in potential comes from edges and wrinkles,and the potential remains almost uniform in the WS2/MoS2region, excluding the possibility that the photocurrent orig-inates from an electric field from surface charge. These KPFMobservations mean that no electric field is unintentionallyformed in our current device. Polarization direction depen-dence (Fig. S4†) shows a small direction dependence of thephotocurrent, depending on the devices used.To further explore the origin of the observed photocurrent,we have performed ab initio density functional theory (DFT)calculations of MoS2/WS2 heterostructures. We used hetero-Fig. 2 (A) A photocurrent map of the WS2/MoS2 device. (B) A photocurrent profile along the dotted line shown in (A). The black dotted lines rep-resent the edges of the WS2. (C) I–V characteristic of the WS2/MoS2 device measured with (red) and without (blue) an excitation wavelength of633 nm. (D) Time dependence of the photocurrent recorded during on–off cycles of an incident laser. (E) Excitation power (P) dependence of thephotocurrent (I). (F) Photon energy dependence of the photocurrent. All measurements were performed at room temperature, respectively.Paper Nanoscale5950 | Nanoscale, 2023, 15, 5948–5953 This journal is © The Royal Society of Chemistry 2023Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616estructures consisting of monolayer WS2 and MoS2 to modelthe interface between WS2 and MoS2 in the device; MoS2/WS2heterostructures with different twist angles (0 and 38 degrees)and translational shifts were used. For visualizing the sym-metry at the MoS2/WS2 interface, the differences in the calcu-lated electrostatic potential between WS2/MoS2 hetero-structures and isolated components are shown in Fig. 3 andFig. S5.† As clearly seen in the contour plots, the electrostaticpotential at the WS2/MoS2 interface retains the C3 rotationalsymmetry when the upper MoS2 and lower WS2 layers sharethe C3 axis. In contrast, the C3 rotational symmetry is brokenwhen the C3 axis of each layer does not coincide. For example,in the case of the twist angle of 38 degrees, the C3 rotationalsymmetry disappears after a translational shift of 0.1 nm, asillustrated in Fig. 3D. This interaction-induced symmetry-breaking is similar to A/B sublattice symmetry breaking in gra-phene epitaxially grown on SiC.33 In this case, couplingbetween graphene and a SiC substrate can break the sublatticesymmetry, resulting in a bandgap opening.In the sample preparations, we manually transfer WS2flakes onto MoS2 flakes to form WS2/MoS2, and in this case,each C3 axis probably does not match completely. As a result,the C3 symmetry breaking probably occurs at the interface.Rotational symmetry breaking by stacking has also beenreported in WSe2/BP, where the interface does not possess anyrotational symmetry due to distinct rotational and mirror sym-metries of WSe2 and BP; two-fold and three-fold rotationalsymmetries of BP and WSe2 are incompatible with anyrotational symmetry. On the other hand, the present MoS2/WS2 case suggests that the resulting heterostructure can breakthe C3 rotational symmetry, particularly at the interface, evenwhen both components have C3 rotational symmetry. Thisinterlayer interaction mechanism is not expected to requirerigorous twist-angle and layer-number control, different fromthe superconductivity in twisted-bilayer graphenes,4 andindeed, we observed similar photoresponses in another WS2/MoS2 with a different twist angle and thickness (Fig. S3†).As discussed above, the interlayer interaction may liftrotational symmetry. In TMD-based vdWSs, however, moirélattice with C3 rotational symmetry can play an important role.In this case, the photocurrents can cancel each other out.However, the moiré periodicity is probably insufficient tocancel out the generated photocurrents, and residual currentsare probably detected.34 Another possibility is that the elec-tron–electron interaction could break symmetry spon-taneously. For example, the strong interaction in twisteddouble bilayer graphene35 (TDBG) possesses an electronicnematic phase, where the C3 symmetry is broken. In thisexample, the moiré flat band plays a role and might not bedominant in misaligned WS2/MoS2 investigated in this study.The final possibility is that unintentionally introduced strainduring the sample preparation breaks the C3 rotational sym-metry. The process-induced strain is, however, expected to beintroduced throughout the sample. In this case, both WS2/MoS2 and MoS2-only regions should show a similar photo-current, inconsistent with the photocurrent that appears onlyin the WS2/MoS2 region (Fig. 2A). We, therefore, think that theprocess-induced strain might also not be dominant in samplesinvestigated in this study.SummaryThe non-zero photocurrent was observed at zero bias voltagein WS2/MoS2 under photoexcitation with a wavelength of633 nm. I–V curves under photoexcitation were linear, and theexcitation power dependence showed a crossover from a linearto square root dependence. No noticeable potential drop orFig. 3 (A) Kelvin Probe Force Microscopy (KPFM) image of the WS2/MoS2 device. The image was obtained at room temperature. (B) A line profilealong the red dotted line shown in (A). (C) and (D) 2D electrostatic potential profiles of AB stack WS2/MoS2 and staggered WS2/MoS2 and the corres-ponding structure models. The 2D profiles show electrostatic potential in the middle of the bilayer structures, representing the electrostatic potentialdifference between WS2/MoS2 and each component (independent monolayer MoS2 and WS2).Nanoscale PaperThis journal is © The Royal Society of Chemistry 2023 Nanoscale, 2023, 15, 5948–5953 | 5951Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616eslope was observed in the KPFM images, which rules out theexistence of unintentionally formed potential drops andslopes. DFT-based theoretical investigations suggest thatspatial symmetry can be lowered due to the interlayer inter-action in WS2/MoS2. These experimental results and theore-tical considerations are consistent with BPVE. Although theorigin of the PVEs observed in this study needs to be furtherexplored, it provides an approach for finding materials thatexhibit PVE.ExperimentalSample preparationWe prepared WS2 and MoS2 flakes by the standard mechanicalexfoliation method. After selecting suitable WS2 and MoS2flakes, WS2/MoS2 was prepared on 270 nm SiO2/Si by thepolymer-based dry transfer technique. The prepared WS2/MoS2sample was rinsed with acetone for one hour and annealedunder a H2/Ar flow to clean organic residues and make contactbetween WS2 and MoS2 better. Finally, we made electrical con-tacts by the standard microfabrication technique, includingpattern drawing with electron beam lithography, developmentof the electrode pattern, metal deposition (Au 50 nm/Bi10 nm), and the lift-off process.Ab initio calculationsThe geometrical and electronic structures were investigatedusing the STATE package based on DFT. A generalized gradientapproximation using the Perdew–Burke–Ernzerhof functionalform was employed to describe the exchange–correlationpotential energy. Electron–ion interactions were treated interms of ultrasoft pseudopotentials. The valence wave functionand deficit charge density were expanded by plane-wave basissets with cutoff energies of 25 Ry and 225 Ry, respectively.Atomic coordinates were optimized until the forces acting oneach atom were less than 5 mRy A−1 under the lattice para-meter corresponding to the experimental value.MeasurementsAll photocurrent measurements were carried out undervacuum conditions in an optical cryostat (KONTI-Cryostat-Micro, CryoVac). Helium–neon CW laser (Thorlabs, HNL050L,λ = 633 nm) was used to excite samples in photocurrentmeasurements, including measurements of photocurrentmapping, power dependence, I–V characteristic, and polariz-ation dependence. For wavelength dependence measurements,a broadband super-continuum pulsed laser (SuperK EXTREMENKT Photonic, 40 MHz) with a monochromator (PrincetonInstruments, SP2150) was used. The laser beam was focusedon a sample by a 50× objective lens with a correction ring(Nikon, CFI L Plan EPI CR, NA = 0.7). The photocurrent wasdetected with a lock-in amplifier (Model SR830 DSP) andoptical chopper (Thorlabs, MC1F10). KPFM measurement wasperformed using an atomic force microscope (NX10, ParkSystems).Conflicts of interestThere are no conflicts to declare.AcknowledgementsThis work was supported by JSPS KAKENHI Grant NumbersJP22H05458, JP21K18930, JP20H02566, JP20H05664,JP21H05232, JP21H05234 and JP22H00283, and JST CRESTGrant Number JPMJCR16F3 and JPMJCR19H4, FOREST(JPMJFR213X), and JST PRESTO Grant NumberJPMJPR20A2. K. W. and T. T. acknowledge the support fromJSPS KAKENHI Grant Numbers 19H05790, 20H00354, and21H05233. The authors are grateful to Satoru Konabe (HoseiUniv.) for fruitful discussions.References1 K. S. Novoselov, A. Mishchenko, A. Carvalho andA. H. Castro Neto, Science, 2016, 353, aac9439.2 A. K. Geim and I. V. Grigorieva, Nature, 2013, 499, 419–425.3 Y. Liu, N. O. Weiss, X. Duan, H.-C. Cheng, Y. Huang andX. Duan, Nat. Rev. Mater., 2016, 1, 16042.4 Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi,E. Kaxiras and P. Jarillo-Herrero, Nature, 2018, 556, 43–50.5 Y. Jiang, S. Chen, W. Zheng, B. Zheng and A. Pan, Light: Sci.Appl., 2021, 10, 72.6 S. Brem, C. Linderälv, P. Erhart and E. Malic, Nano Lett.,2020, 20, 8534–8540.7 J. Dang, S. Sun, X. Xie, Y. Yu, K. Peng, C. Qian, S. Wu,F. Song, J. Yang, S. Xiao, L. Yang, Y. Wang, M. A. Rafiq,C. Wang and X. Xu, npj 2D Mater. Appl., 2020, 4, 2.8 A.-J. Cho, M.-K. Song, D.-W. Kang and J.-Y. Kwon, ACS Appl.Mater. Interfaces, 2018, 10, 35972–35977.9 A. M. Cook, B. M. Fregoso, F. de Juan, S. Coh andJ. E. Moore, Nat. Commun., 2017, 8, 14176.10 B. Sturman and V. Fridkin, The Photovoltaic andPhotorefractive Effects in Noncentrosymmetric Materials,1992.11 J. Jiang, Z. Chen, Y. Hu, Y. Xiang, L. Zhang, Y. Wang,G.-C. Wang and J. Shi, Nat. Nanotechnol., 2021, 16, 894–901.12 W. Shockley, Bell Syst. Tech. J., 1949, 28, 435–489.13 Y. J. Zhang, T. Ideue, M. Onga, F. Qin, R. Suzuki, A. Zak,R. Tenne, J. H. Smet and Y. Iwasa, Nature, 2019, 570, 349–353.14 T. Akamatsu, T. Ideue, L. Zhou, Y. Dong, S. Kitamura,M. Yoshii, D. Yang, M. Onga, Y. Nakagawa, K. Watanabe,T. Taniguchi, J. Laurienzo, J. Huang, Z. Ye, T. Morimoto,H. Yuan and Y. Iwasa, Science, 2021, 372, 68–72.15 T. Hotta, A. Ueda, S. Higuchi, M. Okada, T. Shimizu,T. Kubo, K. Ueno, T. Taniguchi, K. Watanabe andR. Kitaura, ACS Nano, 2021, 15, 1370–1377.Paper Nanoscale5952 | Nanoscale, 2023, 15, 5948–5953 This journal is © The Royal Society of Chemistry 2023Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616e16 K. H. Shin, M.-K. Seo, S. Pak, A.-R. Jang and J. I. Sohn,Nanomaterials, 2022, 12, 1393.17 Y. Guo, C. Liu, Q. Yin, C. Wei, S. Lin, T. B. Hoffman,Y. Zhao, J. H. Edgar, Q. Chen, S. P. Lau, J. Dai, H. Yao,H. S. P. Wong and Y. Chai, ACS Nano, 2016, 10, 8980–8988.18 P.-C. Shen, C. Su, Y. Lin, A.-S. Chou, C.-C. Cheng,J.-H. Park, M.-H. Chiu, A.-Y. Lu, H.-L. Tang, M. M. Tavakoli,G. Pitner, X. Ji, Z. Cai, N. Mao, J. Wang, V. Tung, J. Li,J. Bokor, A. Zettl, C.-I. Wu, T. Palacios, L.-J. Li and J. Kong,Nature, 2021, 593, 211–217.19 Q. Ma, S.-Y. Xu, C.-K. Chan, C.-L. Zhang, G. Chang, Y. Lin,W. Xie, T. Palacios, H. Lin, S. Jia, P. A. Lee, P. Jarillo-Herrero and N. Gedik, Nat. Phys., 2017, 13, 842–847.20 H. Yuan, X. Wang, B. Lian, H. Zhang, X. Fang, B. Shen,G. Xu, Y. Xu, S. C. Zhang, H. Y. Hwang and Y. Cui, Nat.Nanotechnol., 2014, 9, 851–857.21 M. Buscema, M. Barkelid, V. Zwiller, H. S. J. van der Zant,G. A. Steele and A. Castellanos-Gomez, Nano Lett., 2013, 13,358–363.22 M. Freitag, T. Low, F. Xia and P. Avouris, Nat. Photonics,2013, 7, 53–59.23 Y. Ou, Z. Kang, Q. Liao, Z. Zhang and Y. Zhang, Nano Res.,2020, 13, 701–708.24 D. Pierucci, H. Henck, J. Avila, A. Balan, C. H. Naylor,G. Patriarche, Y. J. Dappe, M. G. Silly, F. Sirotti,A. T. C. Johnson, M. C. Asensio and A. Ouerghi, Nano Lett.,2016, 16, 4054–4061.25 K. Nassiri Nazif, A. Kumar, J. Hong, N. Lee, R. Islam,C. J. McClellan, O. Karni, J. van de Groep, T. F. Heinz,E. Pop, M. L. Brongersma and K. C. Saraswat, Nano Lett.,2021, 21, 3443–3450.26 M. Ichiki, R. Maeda, Y. Morikawa, Y. Mabune, T. Nakadaand K. Nonaka, Appl. Phys. Lett., 2004, 84, 395–397.27 A. Zenkevich, Y. Matveyev, K. Maksimova, R. Gaynutdinov,A. Tolstikhina and V. Fridkin, Phys. Rev. B: Condens. MatterMater. Phys., 2014, 90, 161409.28 H. Matsuo, Y. Noguchi and M. Miyayama, Nat. Commun.,2017, 8, 207.29 T. Choi, S. Lee, Y. J. Choi, V. Kiryukhin and S.-W. Cheong,Science, 2009, 324, 63–66.30 I. Grinberg, D. V. West, M. Torres, G. Gou, D. M. Stein,L. Wu, G. Chen, E. M. Gallo, A. R. Akbashev, P. K. Davies,J. E. Spanier and A. M. Rappe, Nature, 2013, 503, 509–512.31 T. Morimoto and N. Nagaosa, Sci. Adv., 2016, 2, e1501524.32 T. Morimoto and N. Nagaosa, Phys. Rev. B, 2016, 94,035117.33 X. Peng and R. Ahuja, Nano Lett., 2008, 8, 4464–4468.34 D. Halbertal, N. R. Finney, S. S. Sunku, A. Kerelsky,C. Rubio-Verdú, S. Shabani, L. Xian, S. Carr, S. Chen,C. Zhang, L. Wang, D. Gonzalez-Acevedo, A. S. McLeod,D. Rhodes, K. Watanabe, T. Taniguchi, E. Kaxiras,C. R. Dean, J. C. Hone, A. N. Pasupathy, D. M. Kennes,A. Rubio and D. N. Basov, Nat. Commun., 2021, 12, 242.35 C. Rubio-Verdú, S. Turkel, Y. Song, L. Klebl, R. Samajdar,M. S. Scheurer, J. W. F. Venderbos, K. Watanabe,T. Taniguchi, H. Ochoa, L. Xian, D. M. Kennes,R. M. Fernandes, Á. Rubio and A. N. Pasupathy, Nat. Phys.,2022, 18, 196–202.Nanoscale PaperThis journal is © The Royal Society of Chemistry 2023 Nanoscale, 2023, 15, 5948–5953 | 5953Open Access Article. Published on 20 February 2023. Downloaded on 3/25/2023 6:46:55 AM.  This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.View Article Onlinehttp://creativecommons.org/licenses/by-nc/3.0/http://creativecommons.org/licenses/by-nc/3.0/https://doi.org/10.1039/d2nr06616e Button 1: