# Fileset

[s42005-018-0106-4.pdf](https://mdr.nims.go.jp/filesets/100d152d-5123-41c4-a56c-d76383de5c26/download)

## Creator

E. Mania, A. R. Cadore, [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), [K. Watanabe](https://orcid.org/0000-0003-3701-8119), L. C. Campos

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Topological valley transport at the curved boundary of a folded bilayer graphene](https://mdr.nims.go.jp/datasets/086f55a9-4320-44ab-84f3-edcbcc970c01)

## Fulltext

Topological valley transport at the curved boundary of a folded bilayer grapheneARTICLETopological valley transport at the curved boundaryof a folded bilayer grapheneE. Mania1,2, A.R. Cadore 1, T. Taniguchi3, K. Watanabe 3 & L.C. Campos 1The development of valleytronics demands long-range electronic transport with preservedvalley index, a degree of freedom similar to electron spin. A promising structure for this end isa topological one-dimensional channel formed in a bilayer graphene, called a domain wall. Inthese channels, the valley-index defines the propagation direction of the charge carriers, andthe chiral edge states are robust over many kinds of disorder. However, the fabrication ofdomain walls are challenging, requiring the design of complex multi-gate structures or pro-duction on rough substrates, showing a limited mean free path. Here, we report on a high-quality domain wall formed at the curved boundary of a folded bilayer graphene. Ourexperiments reveal long-range ballistic transport at such topological channels with the two-terminal resistance close to the ballistic resistance R= e2/4h at zero-magnetic field and thefour-terminal resistance near to zero. At the bulk, we measure a tunable band gap.https://doi.org/10.1038/s42005-018-0106-4 OPEN1 Physics Department, Federal University of Minas Gerais, Belo Horizonte 30123-970, Brazil. 2 Physics Department, State University of Feira de Santana, Feirade Santana 44036-900, Brazil. 3 National Institute for Materials Science, Namiki 305-0044, Japan. Correspondence and requests for materials should beaddressed to L.C.C. (email: lccampos@fisica.ufmg.br)COMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphys 11234567890():,;http://orcid.org/0000-0003-1081-0915http://orcid.org/0000-0003-1081-0915http://orcid.org/0000-0003-1081-0915http://orcid.org/0000-0003-1081-0915http://orcid.org/0000-0003-1081-0915http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0001-6792-7554http://orcid.org/0000-0001-6792-7554http://orcid.org/0000-0001-6792-7554http://orcid.org/0000-0001-6792-7554http://orcid.org/0000-0001-6792-7554mailto:lccampos@fisica.ufmg.brwww.nature.com/commsphyswww.nature.com/commsphysE lectric charge and spin are intrinsic quantum properties ofelectrons and, so far, are the basis of electronics. Likewise,charge carriers in two-dimensional (2D) hexagonal crystalshave an additional electronic degree of freedom, the valley-index,associated to degenerate bands at the inequivalent K and K’points in the Brillouin zone (BZ). The valleytronic field proposesthe creation of a new class of dissipationless electronic devicesbased on the manipulation of the valley-indices like valley filtersand valley valves1–4. One interesting 2D crystal with useful fea-tures for valleytronics is bilayer graphene (BLG). The material is atunable semiconductor and contains low lattice defects that pre-vents inter-valley scattering. Moreover, it holds topologicalproperties when its inversion symmetry is broken by the appli-cation of transverse electric field. In this condition, a topologicalinvariant is defined, the integer index called Chern number, withimportant implications on the quantum properties of BLG. Forinstance, it gives rise to the observation of the valley Hall Effect ingraphene5–7, which is a topological phase where gapless edgestates labeled by opposite valley-indices counter-propagate at theboundaries of the insulating bulk8. One important aspect ofthe Chern number in BLG is that its sign depends either on thevalley-index as well as on the sign of the band gap (interlayerenergy difference), which can be changed by inverting the electricfield direction or by inverting the stacking order of thematerial1,8–12. Such control of the band gap of BLG allows thedesign of topological one-dimensional (1D) interfaces betweenregions with opposite Chern numbers—a domain wall (DW)—where strongly confined edge states, called kink states, arepredicted1,9–12. The kink states have several useful features forvalleytronics. There are two spin-degenerate kink states per valleyand they are chiral, meaning that the propagation direction in theDW is defined by the valley-index. Such chiral edge states arerobust for almost any kind of boundary configurations of thedomains (except perfect armchair) and the topological protectioninhibits backscattering from smooth disorder potentials10. Ifvalley-mixing is suppressed in the DW, such as by reducing theshort-range disorder like edge defects and substrate corrugation, adissipationless electrical conduction with conserved valley-indexis expected.To date, there are two routes to investigate kink states in BLGflakes. One exploits DWs formed along stacking faults (AB-BAboundaries). However, so far, such DWs have been only pro-duced in BLG placed on top of rough silicon dioxide (SiO2)substrates13,14 showing limited mean free path. The other pos-sible way is by designing complex gate-controlled topologicalchannels, which requires a very precise alignment of the bottomand top gates15,16. Here, we observe strong evidence of kink statesin high-quality DW formed at the curved boundary of a foldedbilayer graphene (folded-BLG). Such compact geometry providesseveral advantages: the DW is atomically narrow, a variety oftechniques enable the controlled production of such foldedstructures17,18 and this architecture simplify the fabrication ofvalley-filters and valley-valves using fewer metallic gates. More-over, we show that the topologically protected electronic trans-port is robust up to room temperature and shows a mean freepath (MFP) up to the length of 20 μm at low temperatures, whichis one of the longest MFP ever reported in a DW.ResultsDevice preparation. To introduce our valleytronic device, in theFig. 1a we show a cartoon with some typical components of thedevice such as the folded-BLG, the metallic gates, and the dielec-trics. The folded-BLG is encapsulated in between two hexagonalboron nitride (hBN) crystals. The bottom hBN is placed on top of aSiO2/Si++ wafer, such that the Si++ is a highly p-type doped siliconused as a backgate. The top hBN is covered by a metallic gatecomposed by Cr/Au. To illustrate our fabrication process, in theFig. 1b we show a typical heterostructure of a naturally folded-BLGon top of a flat hBN crystal, before patterning the metallic contacts(fabrication details are discussed in Methods, Supplementary Fig-ure 1 and Supplementary Figure 2). The dashed lines in this pictureindicate the position of such electric terminals: two of them standon the curved boundary and two of them are placed on the etchedbCurved boundaryEtchededgesSiO2hBNBilayergrapheneEK K′�=0K K′–�/2�/2–�/2�/2�–�cde aEhBNBackgateSiO2hBNTopgateKK′Fig. 1 Valleytronic device based on a folded bilayer graphene. a Components of the folded bilayer graphene (folded-BLG) valleytronic device. The folded-BLG is sandwiched by hexagonal boron nitride (hBN) crystals that separate the material from the metallic gates. Under a transverse electric field, the bulkbehaves likely semiconductor with band gap and a topological 1D conducting channel forms at the curved boundary, where the valley-index defines thedirection of propagation. b Optical image of a folded-BLG transferred on top of the bottom hBN flake. Dashed lines indicate the position of the electricterminals. Scale bar: 4 μm. c A false-color atomic force microscopy (AFM) image of device 1 before the transference of the top hBN. The AFMmeasurement reveals that the curved boundary is free from contamination of fabrication processes. Scale bar: 1 μm. d Electrostatic potential energy (Δ/2)of the bilayer graphene (BLG) layers, calculated relative to the center of each BLG. The layer energies reverse sign from the bottom BLG to the top BLG andvanish across the curved boundary, where the electric field is parallel to the layers. This variation of the electrostatic potential energy enables the formationof a domain wall at the curved boundary. e Illustration of the pair of kink states localized at inequivalent points K and K’ in the Brillouin zone of BLG, havingopposite group-velocities for different valleys. In the domain wall, these edge states propagate in opposite one-dimensional directions due their chiralnatureARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-018-0106-42 COMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphyswww.nature.com/commsphysedges. Figure 1c shows a false-color atomic force microscopy(AFM) topography measurement of device 1. Here, we presentdevice 1 after the cleaning process and before encapsulating with atop hBN crystal. From this measurement, we see the high qualityand cleanness of the device, which prevents short-range scatteringalong the 1D channel. These good conditions are provided either bythe flat surface of the hBN crystals as well as by the efficacy of themechanical cleaning method to remove contamination from thefabrication process.Kink states in a folded bilayer graphene. In the Fig. 1d, wepresent a scheme that describes the electrostatic conditionsimposed to the folded-BLG by application of gate potential. Thetransverse electric field breaks the inversion symmetry of eachBLG (bottom sheet and top sheet of the folded-BLG), which leadsto an energy band gap (Δ)19 defined as the layer energy differencebetween the top graphene layer and the bottom graphene layer ofBLG. At the bottom BLG sheet, the top graphene layer acquires arelative energy +Δ/2, calculated relative to the center of the sheet,and the bottom layer acquires a relative energy −Δ/2. Thiselectrostatic energy distribution inverts in the other BLG sheet ontop. The bottom graphene layer (former top layer) now acquires arelative energy −Δ/2 and the top layer (former bottom layer)acquires a relative energy +Δ/2. Then, the band gap inverts itssign from the bottom to top BLG and, consequently, a valley atthese different BLGs holds opposite Chern numbers. In thiscondition, the curved boundary of the folded-BLG transformsinto a DW. We use the model proposed by Martin et al.1 todemonstrate the emergence of kink states in such topologicalfolded structure (Supplementary Figure 3 and SupplementaryNote 1). In the Fig. 1e, we illustrate the pair of spin-degeneratekink states localized at the points K and K’ of the BZ, havingopposite group-velocities at different valleys. These chiral edgestates propagate in the curved boundary along a 1D directiondefined by the valley-index, as illustrated in Fig. 1a.Two-terminal measurements. One of the main achievements ofthis work is the measurement of a quantization of the two-terminalresistance (R) along the curved boundary near of the ballisticresistance R= 6.45 kΩ (or R= e2/4h) at B= 0 T and T= 1.2 K.Such result is a remarkable evidence of kink states, since the con-ductance of the 1D channel is governed by a ballistic transportregime related to a pair of chiral edge states spin-degenerated1,9,10.This result is presented in Fig. 2, which shows raw data of R as afunction of the backgate voltage (VBG) and the topgate voltage (VTG)measured at electric contacts placed along the etched edge (Fig. 2a)and along the curved boundary (Fig. 2b). Both measurementsexhibit a diagonal line that shows a strong dependence of resistancewith gate potentials. Along these diagonal lines, the electrostaticcondition defined by the gate potentials set zero charge in the BLGs,called the charge neutrality point (CNP). The resistance at suchdiagonal lines are defined as follows: for the electric measurementsrealized on the etched edge it will be called REE,CNP and for theelectric measurements realized on the curved boundary it will becalled RCB,CNP. A better comparison of REE,CNP and RCB,CNP ispresent in Fig. 2c, where we plot R as a function of the displacementfield D, obtained from the data showed in Fig. 2a, b. We convertedthe gate potentials to displacement field with the following formula:D= (CTGVTG–CBGVBG)/ε0, where CTG and CBG are, respectively, thecapacitances per unit of area and charge of the top capacitor andbottom capacitor, and ε0 is the vacuum permittivity. From datapresent in Fig. 2c we note that the monotonic increasing of REE,CNPwith D reflects a tunable band gap caused by the broken inversionsymmetry of BLGs20,21. In contrast, the RCB,CNP saturates near ofthe ballistic resistance R= h/4e2 for |D|>1.6 V nm−1. This saturationof the resistance reveals that the DW formed at the curved boundarybecomes electric isolated from the bulk of the folded-BLG and aballistic transport regime governs the carrier motion at this 1Dregion. The quantization of resistance close to the ballistic resistanceshow a robust valley transport, with backscattering strongly inhib-ited by the lack of short-range disorder along the channel.The strong suppression of backscattering in the DW formedalong the curved boundary leads to a long MFP. We use theLandauer-Büttiker formula22 R= R0(1+ L/LMFP) to calculate theMFP of the ballistic channel in our two devices. Here, LMFP is theMFP, R0= h/4e2 is the ballistic resistance and L is the length ofthe channels: L= 1 μm for device 1 and L= 1.75 μm for device 2(Supplementary Figure 4 and Supplementary Note 2). As theexperiment shows a resistance close to R= e2/4h, we neglectedany other residual resistances in this channel. The calculated MFPof the channels are: LMFP∼ 20 μm for device 1 and LMFP∼ 17 μmfor device 2. Such long MFP show that the DW formed at thefolded-BLG is comparable to the best topological channelscreated by gate-confinement15,16 and at least, two-orders higherthan the MFP reported in a DW of BLG on SiO213.T=1.2 KaEtched edge4–4 0–86860VBG (V)–86860VBG (V)3142ACurved boundaryEtchededge4–4 0VTG (V)VTG (V)T=1.2 KbCurved boundary3142A19.50.2h/4e20–2.3 2.30D (V/nm)c321R (h/4e2 )R (kΩ)R (kΩ) 19.50.2h/4e2R (kΩ)20100155REE,CNPRCB,CNPFig. 2 Two-terminal electronic measurements: Evidence of a topological valley transport in the curved boundary of the folded bilayer graphene (folded-BLG). a and b Two-terminal electrical measurements of resistance (R) vs VTG vs VBG in the etched edge (contacts 1–3) and curved boundary (contacts 1–2),respectively, at T= 1.2 K and B= 0 T. The insets show each particular measurement configuration. c R as a function of displacement field (D) from datashowed in the Fig. 2a, b. The resistance at the etched edge, REE,CNP, monotonically increases with D indicating a semiconducting regime with a band gap.For sufficient electric insulation of the bulk (achieved at high D) the resistance at the curved boundary, RCB,CNP, saturate close to the ballistic resistanceR= h/4e2, an evidence of kink states and the suppression of backscattering in this 1D conducting channelCOMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-018-0106-4 ARTICLECOMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphys 3www.nature.com/commsphyswww.nature.com/commsphysFour-terminal measurements. Further details about themechanisms of conduction in the folded-BLG are obtained byusing a four-terminal electronic configuration. In the Fig. 3, weshow the raw data of the longitudinal resistance (Rxx) as afunction of the VBG and VTG measured at contacts placed alongthe etched edge (Fig. 3a) and the curved boundary (Fig. 3b).Again, both measurements show distinct diagonal lines where theresistance strongly depends on the gate potential. These depen-dence are better visualized in Fig. 3c, where we plot only thelongitudinal resistances along the diagonal line as a function of D.Such resistances are called REE;CNPxx for the electric measurementsrealized at the etched edge and RCB;CNPxx for the electric mea-surements performed at the curved boundary. We note thatsimilarly to the two-terminal measurements, REE;CNPxx con-tinuously increase with the displacement field. It changes fromREE;CNPxx ∼1 kΩ up to REE;CNPxx ∼12 kΩ, an expected behavior relatedto the tunable semiconducting nature of the BLGs by the action ofthe transverse electric field. On the other hand, we measure adifferent trend at the curved boundary channel. We observe thatRCB;CNPxx decreases with D, changing from RCB;CNPxx ∼400Ω down toRCB;CNPxx ∼60Ω for high D. Such small longitudinal resistance is adistinct feature of a ballistic transport regime in a channel withquasi-absence of backscattering. It provides another importantevidence that a ballistic charge motion was achieved at the DW inthe curved boundary.Temperature dependence. Next, we investigate the effect of tem-perature on the electric conduction at the different regions of thefolded-BLG in a four-terminal configuration (Details about thetemperature dependence of two-terminal measurements are shownon Supplementary Figure 5 and Supplementary Note 3). In Fig. 3d, ewe show measurements of RXX as function of VTG, with the backgatevoltage fixed at VBG=−86 V, while we changed the temperature ofthe system from T= 1.2 K up to room temperature (T= 300 K). Atlow temperatures, the electric conduction in the curved boundary isgoverned by a ballistic transport regime, revealed by the measure-ment of a small longitudinal resistance. At same electrostatic con-dition the BLGs at the etched edge reveal a semiconducting regime.As showed in Fig. 3d, the elevation of temperature in the system letto a decreasing of RXX measured along the etched edge. Clearly, it isthe expected behavior of a semiconducting regime dominated bythermally activated processes21. A different feature is observed at thecurved boundary, as illustrated in Fig. 3e. The longitudinal resistanceof such region increases when temperature goes up. Such behaviorrevels that temperature promotes valley-mixing by phonon scatter-ing and enhances the scattering of edge states localized at the curvedboundary channel to BLG states that may conduct due to chargeinhomogeneity. These measurements on different temperatures givea third evidence that chiral edge states at the curved boundary let toa different electronic transport regime when compared to the otherregions of the folded-BLG.T=1.2 Kb 0.01 0.4Curved boundaryVxxI4 3124–4 0T=1.2 Ka Etched edge 11.70.06VxxI13424–4 0–86860VTG (V) VTG (V)VBG (V)–86860VBG (V)cD (V/nm)–2.3 0 2.3101102103104EE,CNPRxxRxxCB,CNPRxx (kΩ) Rxx (kΩ)Rxx (kΩ)VTG (V) VTG (V)Etched edgedVBG = –86 V VBG = –86 VT (K)1.2 30012840 1 3 42Rxx (kΩ)Rxx (kΩ)eT (K)1.2 3003002001000 1 3 42Curved boundaryFig. 3 Four-terminal electronic measurements and influence of temperature on the kink states. a and b Four-terminal raw data of the longitudinal resistanceRXX as a function of VTG and VBG in the etched edge and curved boundary, respectively. The insets show how the electronic measurements are performed.c RXX as a function of D when the bilayer graphenes are at the charge neutrality point (CNP). The resistances measured along the etched edge, REE;CNPxx , arerepresented by the red squares and the resistances measured at the curved boundary, RCB;CNPxx , are represented by the blue circles. REE;CNPxx increases by oneorder of magnitude, while under same electrostatic conditions RCB;CNPxx decreases down to a few tens of ohms, an expected behavior for the longitudinalresistance of a channel on the ballistic regime. d and e RXX in the etched edge and curved boundary, respectively, as a function of VTG for a fixed VBG=−86 V, when the temperature of the system changes from T= 1.2 K up to T= 300 K. Such measurements reveals that different transport mechanismsgoverns the electric conduction at the etched edge region and at the curved boundary channelARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-018-0106-44 COMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphyswww.nature.com/commsphysDiscussionWe perform a set of two-terminal, four-terminal measurements,and temperature dependence to investigate the mechanisms ofconduction at the curved boundary and at the bulk of a foldedbilayer graphene. We observed that under an external electricfield, the bulk becomes a semiconductor with tunable band gapwhile a topological domain wall forms at the curved boundary. Atsuch a one-dimensional channel, we have evidence of a dis-sipationless transport mechanism governed by topological edgestates—kink states—rather than ordinary ones. The two-terminalelectric resistance saturates near of the ballistic resistance R= h/4e2. It shows that both spin and valley are well-preserved quan-tum numbers. In addition, the four-terminal measurementsshow the resistance dropping down to a few tens of ohms, con-firming the ballistic nature of the electric conduction. On theother hand, the electrical measurements performed along the bulkshow that the resistance of two bilayer graphenes placed one ontop of the other continuously increases as a function of theelectric field, behaving quite similarly gate tunable semi-conductors like single bilayer graphene. Finally, from the elec-trical measurements as a function of temperature, we confirm thedifferent behavior of the bulk states and chiral states of the foldededge. The bulk shows electronic conduction governed by athermo-activated process typical of semiconductors while theresistance along the curved boundary shows temperaturedependence similar to metallic materials, showing that phononsenhance the scattering of conducting edge states.Our electrical measurements in one valleytronic device showstrong evidence of the different mechanisms of conduction alongthe curved boundary and conduction along the bulk. In order tofind more evidence of the topological nature of edge states on thecurved boundary, we fabricated a second valleytronic device. Atsuch device, we also observe the two-terminal electric resistancesaturating near of the ballistic resistance R= h/4e2 under highelectric fields. Such experiments performed at this second deviceprovide further evidence that the topological edge states lie at thecurved boundary of a folded bilayer graphene. Finally, we notethat the electric resistance of the gapped bulk is smaller thantypically resistances observed in single bilayer graphene undersimilar electric fields. As the bulk and the curved boundary arephysically connected, one expects that a small bulk resistancecould lead to more scattering of kink states to bulk states.However, our two-terminal resistances on both devices are veryclose to the ballistic resistance of R= h/4e2 at the curvedboundary. It confirms a strong suppression the scattering fromkink states to bulk states. We believe that future microscopicmeasurements could bring more explanation about the nature ofsuch strong protection of the edge conduction.In summary, our findings show the existence of topologicalchiral edge states in a domain wall formed at the curved boundaryof a folded bilayer graphene. We observe a strong suppression ofvalley scattering at this high-quality one-dimensional channelthat leads to a long-range ballistic conduction at zero-magneticfields. Such platform contains elements to promote the develop-ment of dissipationless valleytronic devices and provides a routeto investigate graphene-based superconducting effects23,24 as wellas Luttinger liquid interactions25.MethodsThe heterostructures of folded bilayer graphene (folded-BLG) sandwiched betweenhexagonal boron nitride (hBN) crystals are prepared with the following steps: wefirst employed the mechanical cleavage method to separate few layers of graphenefrom graphite flakes on top of a polymeric film of methyl methacrylate (MMA 495C4). Next, we selected self-folded BLG samples and we transferred such flakes totop of clean hBN crystals supported on a 285-nm thick SiO2/Si++, where Si++ is ahighly doped Si wafer used as a metallic backgate. The fabrication of devices isdivided into three main steps. First, we fabricated the electric terminals by usingconventional electron beam lithography and thermal metalization of Cr/Au (1 nm/40 nm). We also used electron beam lithography and etching processes with oxygenplasma to define and shape our devices. Next, we used a mechanical cleaningmethod with an atomic force microscopy (AFM) probe26 to remove any con-tamination of fabrication processes from the surface of the folded-BLG. We fin-ished the fabrication by covering the device with another hBN flake and patterninga metallic top-gate. The electronic measurements are realized inside a cryogensystem that enables the application of magnetic field up to B= 7 T. In our elec-tronic measurements we normally operated at T= 1.2 K and we performed themeasurements using a low-frequency (f= 17 Hz) Lock-in technique. In the two-terminal measurements we applied a constant bias (Vbias= 1 mV) between thecontacts and we measured it electric current. The conductance is calculated byusing the formula G= I/V. In the four-terminal measurements, a constant electriccurrent (I= 100 nA) is applied between two electric terminals and a longitudinalvoltage (VXX) is measured in between the other electric terminals on the oppositeside. The longitudinal resistance is calculated by using the Ohm’s law RXX=VXX/I.Data availabilityThe data that support the findings of this study are available from the corre-sponding author upon reasonable request.Received: 24 August 2018 Accepted: 21 November 2018References1. Martin, I., Blanter, Y. M. & Morpurgo, A. F. Topological confinement inbilayer graphene. Phys. Rev. Lett. 100, 1–4 (2008).2. Qiao, Z., Jung, J., Niu, Q. & MacDonald, A. H. Electronic highways in bilayergraphene. Nano Lett. 11, 3453–3459 (2011).3. Lee, M. K., Lue, N. Y., Wen, C. K. & Wu, G. Y. Valley-based field-effecttransistors in graphene. Phys. Rev. B 86, 10980121 (2012).4. Pan, H., Li, X., Zhang, F. & Yang, S. A. Perfect valley filter in a topologicaldomain wall. Phys. Rev. B 92, 041404 (2015).5. Gorbachev, R. V. et al. Detecting topological currents in graphenesuperlattices. Science 346, 448–451 (2014).6. Sui, M. et al. Gate-tunable topological valley transport in bilayer graphene.Nat. Phys. 11, 1027–1031 (2015).7. Shimazaki, Y. et al. Generation and detection of pure valley current byelectrically induced Berry curvature in bilayer graphene. Nat. Phys. 11,1032–1036 (2015).8. Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magneticmoment and topological transport. Phys. Rev. Lett. 99, 1–4 (2007).9. Yao, W., Yang, S. A. & Niu, Q. Edge states in graphene: from gapped flat-bandto gapless chiral modes. Phys. Rev. Lett. 102, 1–4 (2009).10. Jung, J., Zhang, F., Qiao, Z. & MacDonald, A. H. Valley-Hall kink and edgestates in multilayer graphene. Phys. Rev. B 84, 1–5 (2011).11. Zhang, F., MacDonald, A. H. & Mele, E. J. Valley Chern numbers andboundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110,10546–10551 (2013).12. Vaezi, A., Liang, Y., Ngai, D. H., Yang, L. & Kim, E. A. Topological edge statesat a tilt boundary in gated multilayer graphene. Phys. Rev. X 3, 1–9 (2013).13. Ju, L. et al. Topological valley transport at bilayer graphene domain walls.Nature 520, 650–655 (2015).14. Jiang, L. et al. Manipulation of domain-wall solitons in bi- and trilayergraphene. Nat. Nanotech. 13, 204–208 (2018).15. Li, J. et al. Gate-controlled topological conducting channels in bilayergraphene. Nat. Nanotech. 11, 1060–1065 (2016).16. Lee, J., Watanabe, K., Taniguchi, T. & Lee, H. J. Realisation of topologicalzero-energy mode in bilayer graphene in zero magnetic field. Sci. Rep. 7, 6466(2017).17. Li, L. X. et al. Tearing, folding and deformation of a carbon–carbon sp2-bonded network. Carbon N. Y. 44, 1544–1547 (2006).18. Annett, J. & Cross, G. L. W. Self-assembly of graphene ribbons byspontaneous self-tearing and peeling from a substrate. Nature 535, 271–275(2016).19. McCann, E. Asymmetry gap in the electronic band structure of bilayergraphene. Phys. Rev. B 74, 161403 (2006).20. Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayergraphene. Nature 459, 820–823 (2009).21. Taychatanapat, T. & Jarillo-Herrero, P. Electronic transport in dual-gated bilayergraphene at large displacement fields. Phys. Rev. Lett. 105, 166601 (2010).22. Datta, S. Electronic Transport in Mesoscopic Systems. (Cambridge UniversityPress, 1995).COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-018-0106-4 ARTICLECOMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphys 5www.nature.com/commsphyswww.nature.com/commsphys23. Schroer, A., Silvestrov, P. G. & Recher, P. Valley-based Cooper pair splittingvia topologically confined channels in bilayer graphene. Phys. Rev. B 92, 1–5(2015).24. Klinovaja, J., Ferreira, G. J. & Loss, D. Helical states in curved bilayergraphene. Phys. Rev. B 86, 1–4 (2012).25. Killi, M., Wei, T. C., Affleck, I. & Paramekanti, A. Tunable luttinger liquidphysics in biased bilayer graphene. Phys. Rev. Lett. 104, 216406 (2010).26. Goossens, A. M. et al. Mechanical cleaning of graphene. Appl. Phys. Lett. 100,073110 (2012).AcknowledgementsThe authors thank prof. Javier D. Sanchez-Yamagishi, prof. Hadar Steinberg andprof. Marcos H. D. Guimaraes for the fruitful discussions and the paper revision. Theauthors acknowledge the support of LabNS and LabNano for the Raman and AFMmeasurements. E.M., A.R.C. and L.C.C. acknowledge the support of the Brazilian agencies:Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq/MCTI), Coor-denacao de Aperfeicoamento de Pessoal de Nivel Superior (Capes), Fundacao de Amparoa Pesquisa do Estado de Minas Gerais (FAPEMIG). K.W. and T.T. acknowledge supportfrom the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST(JPMJCR15F3), JST.Author contributionsL.C.C. conceived the main idea of the work. E.M. and A.R.C. fabricated the devices. K.W.and T.T. supplied the high-quality hBN flakes. E.M. and L.C.C. planned, realize themeasurements, analyzed the data and wrote the manuscript.Additional informationSupplementary information accompanies this paper at https://doi.org/10.1038/s42005-018-0106-4.Competing interests: The authors declare no competing interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directly fromthe copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2019ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-018-0106-46 COMMUNICATIONS PHYSICS |             (2019) 2:6 | https://doi.org/10.1038/s42005-018-0106-4 | www.nature.com/commsphyshttps://doi.org/10.1038/s42005-018-0106-4https://doi.org/10.1038/s42005-018-0106-4http://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/commsphys Topological valley transport at the curved boundary of a folded bilayer graphene Results Device preparation Kink states in a folded bilayer graphene Two-terminal measurements Four-terminal measurements Temperature dependence Discussion Methods References References Acknowledgements Author contributions Competing interests Supplementary information ACKNOWLEDGEMENTS