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[Yanlin Gao](https://orcid.org/0000-0002-4587-5391), [Mina Maruyama](https://orcid.org/0000-0002-2872-5543), [Yasumitsu Miyata](https://orcid.org/0000-0002-9733-5119), [Susumu Okada](https://orcid.org/0000-0002-0783-3596)

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[Energetics and bistable morphologies of transition-metal dichalcogenide nanoscrolls](https://mdr.nims.go.jp/datasets/6d5a612b-6b0d-4aa2-8a91-441233f2db50)

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Energetics and bistable morphologies of transition-metal dichalcogenide nanoscrollsJapanese Journal ofApplied Physics      REGULAR PAPER • OPEN ACCESSEnergetics and bistable morphologies of transition-metal dichalcogenide nanoscrollsTo cite this article: Yanlin Gao et al 2026 Jpn. J. Appl. Phys. 65 055001 View the article online for updates and enhancements.You may also likeTwists and turns: stacking and structure-dependent optical response in MoS2nanoscrollsSagnik Chatterjee, Tamaghna Chowdhury,Pablo Díaz-Núñez et al.-Tunable bending stiffness of MoSe2/WSe2heterobilayers from flexural wrinklingYufeng Guo, Jiapeng Qiu and Wanlin Guo-Effect of misfit strain on the buckling ofgraphene/MoS2 van der WaalsheterostructuresRun-Sen Zhang and Jin-Wu Jiang-This content was downloaded from IP address 144.213.253.16 on 09/06/2026 at 00:52https://doi.org/10.35848/1347-4065/ae42a8/article/10.1088/2053-1583/ade9d8/article/10.1088/2053-1583/ade9d8/article/10.1088/2053-1583/ade9d8/article/10.1088/1361-6528/aa678d/article/10.1088/1361-6528/aa678d/article/10.1088/1361-6528/aa678d/article/10.1088/1361-6528/ac1f55/article/10.1088/1361-6528/ac1f55/article/10.1088/1361-6528/ac1f55/article/10.1088/1361-6528/ac1f55/article/10.1088/1361-6528/ac1f55aaaEnergetics and bistable morphologies of transition-metal dichalcogenidenanoscrollsYanlin Gao1,2* , Mina Maruyama1,2* , Yasumitsu Miyata3* , and Susumu Okada1,2*1Department of Physics, Graduate School of Science and Technology, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571, Japan2Tsukuba Institute for Advanced Research (TIAR), University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan3Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan*E-mail: ylgao@comas-tsukuba.jp; mmaruyama@comas-tsukuba.jp; MIYATA.Yasumitsu@nims.go.jp; sokada@comas-tsukuba.jpReceived December 11, 2025; revised January 18, 2026; accepted February 4, 2026; published online March 2, 2026Using a continuous elastic model combined with intershell van der Waals interaction, we investigated the energetics of nanoscrolls formed fromthe transition-metal dichalcogenides (TMDs) MoS2, MoSe2, WS2, WSe2, MoSSe, and WSSe. We found that, for TMD nanoscrolls with short rolledlengths, the strain effect competes with van der Waals effects to determine the geometries of the nanoscrolls. By contrast, for long rolled lengths,van der Waals effects dominate, leading to a high stability of the scrolled conformation for all TMDs. For Janus TMD nanoscrolls with short rolledlength, the combination of curvature induced by the intrinsic strain and van der Waals interactions leads to bistable morphologies, characterizedby scroll and arch conformations. These conformations can be switched by external conditions. © 2026 The Author(s). Published on behalf of TheJapan Society of Applied Physics by IOP Publishing Ltd1. IntroductionThe tight in-plane covalent bonding network and electroni-cally saturated surfaces of atomic-layer materials make themattractive building blocks for various compounds, in whichthey can be freely stacked without the constraints imposed bychemical bonds in conventional condensed matter.1–4) Suchcomplexes have unique physical properties, which exceedthose of the superposition of the constituent atomic layersbecause of their substantial wavefunction overlap, eventhough they are only weakly bound.3,4) In addition, atomic-layer materials can exhibit morphological variation dependingon the boundary conditions imposed on them. Nanotubes,5–12)nanoscrolls,13–19) and nanoribbons20,21) are representativeexamples of such nanomorphologies derived from atomic-layer materials by imposing open and periodic one-dimen-sional boundary conditions along the circumference. Theseboundary conditions lead to unconventional physical proper-ties in the morphological derivatives, depending on their sizeand shape. Carbon nanotubes are either metals or semicon-ductors, depending on the atomic arrangement along theircircumference, which corresponds to the quantizationcondition.6) Graphene nanoribbons with zigzag edges possessa peculiar edge-localized state arising from quantum inter-ference of wavefunctions around edge atomic sites.20,21)Among the one-dimensional morphologies of atomic-layermaterials, nanoscrolls have a unique structure, which ischaracterized by a continuously varying curvature from theinnermost to the outermost shells, as well as intershellinteractions and edge effects.13–18,22–26) In particular, thecurvature effect determines the electronic properties ofnanoscrolls, because the electronic structures of atomic-layermaterials are sensitive to curvature.27–31) Graphene nanosc-rolls and Janus WSSe nanoscrolls exhibit remarkablestability and a unique electronic structure along theircircumference.25,26) For example, WSSe nanoscrolls aresemiconductors that show band bending along the scroll,resulting in type-II band-edge alignment between the innerand outer shells of the scroll.26) This band-edge bending isattributed to the radial dipole moment arising from thecurvature and asymmetric chalcogen arrangement acrossthe shell. The electronic structure of graphene nanoscrollsalso exhibits a strong position dependence that is sensitive tothe nanoscroll shape. This dependence is due to electrostaticpotential modulation and intershell orbital hybridizationexerted by the multishell structure.25) The aforementionedtheoretical works imply that the electronic structure ofnanoscrolls can be tuned by controlling their conformationand constituent elements.Although the energetics and electronic properties ofnanoscrolls with small diameters have been investigated,little is known about nanoscrolls with large diameters andmultiple intershell stackings.23–26) In this work, we aim toinvestigate the energetics of transition-metal dichalcogenide(TMD) nanoscrolls for providing qualitative and compre-hensive knowledge about scroll geometries using a contin-uous elastic model combined with intershell van der Waalsinteractions, in which all parameters were determined usingdensity functional theory (DFT). We considered MoS2,MoSe2, WS2, and WSe2 nanoscrolls for conventionalTMDs and MoSSe and WSSe nanoscrolls as Janus TMDs,whose rolled length (L) is varied, ranging from 10 to 100 nm.Our analyses demonstrated that strain and van der Waalseffects compete to determine the geometries of TMDnanoscrolls for the short rolled length, while van der Waalseffects dominate for the long rolled length. For Janus TMDswith the short rolled length, the combination of curvatureinduced by intrinsic strain and van der Waals interactionsleads to bistable morphologies, characterized by nanoscrolland nanoarch structures.2. Calculation methodsTo construct the elastic model that describes the curvatureeffect of TMDs, we investigated the total energy of TMDnanotubes using DFT32,33) implemented in the programpackage Simulation Tool for Atom TEchnology.34,35) WeContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution ofthis work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.055001-1© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJapanese Journal of Applied Physics 65, 055001 (2026) REGULAR PAPERhttps://doi.org/10.35848/1347-4065/ae42a8https://crossmark.crossref.org/dialog/?doi=10.35848/1347-4065/ae42a8&domain=pdf&date_stamp=2026-03-02https://orcid.org/0000-0002-4587-5391https://orcid.org/0000-0002-2872-5543https://orcid.org/0000-0002-9733-5119https://orcid.org/0000-0002-0783-3596mailto:ylgao@comas-tsukuba.jpmailto:mmaruyama@comas-tsukuba.jpmailto:MIYATA.Yasumitsu@nims.go.jpmailto:sokada@comas-tsukuba.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1347-4065/ae42a8considered armchair MoS2, MoSe2, WS2, WSe2, MoSSe, andWSSe nanotubes. The exchange-correlation energy amongthe interacting electrons was expressed using the generalizedgradient approximation (GGA) with the functional form ofthe Perdew–Burke–Ernzerhof functional.36,37) Ultrasoftpseudopotentials generated using the Vanderbilt schemewere used to describe electron–ion interactions.38) Thevalence wavefunctions and deficit charge density wereexpanded in terms of the plane-wave basis set with cutoffenergies of 25 and 225 Ry, respectively. Integration over theone-dimensional Brillouin zone was carried out usingequidistant k-point sampling in which 5 k-points were takenalong the TMD nanotube axis. This allowed us to conductcalculations on TMD nanotubes with diameters up toapproximately 5 nm. The atomic structures of these nano-tubes were optimized until the force acting on each atom wasless than 5 mRyÅ−1. The lattice parameter along the tubeaxis was fixed to the optimized lateral lattice parameters ofthe isolated monolayer TMD sheets.Figure 1 shows the total energies per atom of MoS2,MoSe2, WS2, WSe2, MoSSe, and WSSe nanotubes withrespect to the corresponding isolated sheets as a function ofthe inverse of the radius. The total energy of the tubularmaterials is inversely proportional to the square of the radius.Thus, the energies were fitted using the quadruple poly-nomial of the inverse of the radius:( ) ( )= +rDrBr1s 2[where D and B are coefficients depending on the tubespecies. Evaluated coefficients are listed in Table I.Equation (1) corresponds to the energy cost to bend theTMD with curvature radius r. TMD nanoscrolls are modeledby the contentious elastic model shown in Fig. 2 in which thestructure is characterized by the innermost shell radius r0,TMD thickness Δ, intershell spacing d, and scroll angle θwhich assigne the particular position on nanoscroll. The localcurvature radius r(θ) of the nanoscroll is defined as(a) (b)(c) (d)(e) (f)Fig. 1. Total energy per atom of MoS2, MoSe2, WS2, WSe2, MoSSe, and WSSe nanotubes as a function of the inverse of their radius, r. The energieswere measured relative to those of the corresponding isolated sheets.055001-2© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 65, 055001 (2026) Y. Gao et al.( ) ( )= ++r rd2. 20In this work, we assumed Δ = 0.3 nm and d = 0.3 nm,which are approximate values for TMD monolayers andbilayers.39) Using a typical interlayer van der Waals inter-action εv = 0.02 eV/atom under d = 0.3 nm, the total energyof the TMD nanoscrolls was evaluated as( ) { ( ) } ( )= +E L r dl r, 3Ls v00where L is the rolled length of TMD nanoscrolls corre-sponding to the width of flat TMD nanoribbons. UsingEq. (2), the total energy of the TMD nanosrolls can beexpressed as( )( )=+++ +++E L r dDrBrd,24dv00 0 20where the angle α is the total rotational angle correspondingto the rolled length L(= d r0).3. Results and discussion3.1. MX2 (M = Mo, W and X = S, Se) nanoscrollsFigure 3 shows the total energy of MoS2, MoSe2, WS2, andWSe2 nanoscrolls as a function of the rolled length L and theinnermost radius r0. Conventional TMDs prefer a flat con-formation in their isolated form because of the symmetricchalcogen arrangement around the transition-metal atomlayer. The total energy increases with increasing curvature,which corresponds to the increase of strain, irrespective of theribbon width or rolled length L. For ribbons with a narrowwidth or scrolls with short rolled length L < 20 nm, the totalenergy increases monotonically with increasing curvature,even though they possess a scroll conformation. In this region,the energy gain by the intershell van der Waals interaction isinsufficient to overcome the energy cost associated with themechanical strain induced by the large curvature. Upon furtherincreasing the rolled length L to approximately 20 nm, a cuspemerges, which turns into a local minimum at approximatelyr0 = 2 nm. For rolled lengths L= 45.7, 47.5, 44.6, and41.8 nm for MoS2, MoSe2, WS2, and WSe2, respectively,the energy of the scrolled structure is lower than that of theirflat conformation, indicating that the scrolled conformation isthe possible ground state for the one-dimensional TMDnanostructure owing to the substantial van der Waals inter-shell interaction. The evaluated innermost shell radii r0at the critical rolled length L were 4.4, 4.5, 4.2, and 3.9 nmfor MoS2, MoSe2, WS2, and WSe2, respectively. The inner-most radii depend on the rolled length L. The radii were5.4, 5.6, 5.3, and 5.0 nm for MoS2, MoSe2, WS2, and WSe2,respectively, for the rolled length L = 100 nm. We attributethe increase in the innermost-shell radius r0 to increased shelloverlap at long rolled length, leading to a substantial energygain from van der Waals interactions. Thus, the delicatebalance between the strain energy and the inter-shell van derWaals interaction determines the conformation of the one-dimensional nanostructure of TMDs under appropriate ex-ternal conditions. We conclude that the nanoscrolls representtheir possible ground-state conformation of one-dimensionalstructures derived from atomic-layer materials with sufficientintershell overlap. It is plausible that the multiply-foldedconformation is another possible ground-state configurationfor one-dimensional structures derived from atomic-layermaterials with sufficient intershell overlap.40)The geometric structure of MoS2 nanoscrolls is depicted inFig. 4. The TMD has a characteristic morphology corre-sponding to different energy landscapes. Under the localminimum, the TMD has a scrolled structure with substantialintershell overlap [Fig. 4(a)]. By contrast, at the energybarrier, it assumes a scroll conformation with small shelloverlap corresponding [Fig. 4(b)]. Furthermore, the totalenergy of TMD nanoscrolls substantially decreases withincreasing number of shells for long rolled length L[Fig. 4(c)]. Thus, the energetics and conformations ofTMD nanoscrolls are determined by the delicate balancebetween the strain energy derived from curvature and theintershell van der Waals interaction.Table I. The coefficients D and B of the quadruple polynomial fitted to the total energies of MoS2, MoSe2, WS2, WSe2, MoSSe, and WSSe nanotubes.MoS2 MoSe2 WS2 WSe2 MoSSe WSSeD (eV nm2) 0.1393 0.1663 0.1586 0.2014 0.1462 0.1790B (eV nm) — — — — −0.0648 −0.0789Fig. 2. A structural model of the TMD nanoscroll, where the nanoscrollis denoted by a gray curve. The r0 is the innermost shell radius of thescroll, and θ is the scroll angle specifying the position on the scroll. Eachshell is separated by the sum of the intershell spacing d and the TMDthickness Δ.055001-3© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 65, 055001 (2026) Y. Gao et al.3.2. Janus MSSe (M = Mo, W) nanoscrollsFigure 5 shows the total energy of MoSSe and WSSenanoscrolls as a function of the rolled length L and theinnermost radius r0. The stable conformations of MoSSe andWSSe ribbons and sheets exhibit curvature because of theintrinsic tensile and compressive strains derived from thestructural asymmetry of the chalcogene layers. The curvatureradius in the stable conformation was calculated to be 4.4 nmfor MoSSe and WSSe, irrespective of the rolled length. Anew structure in the energy landscape appears near theinnermost radius r0 = 2 nm at the rolled lengths L = 15 nmand 16 nm for MoSSe and WSSe, respectively, and aminimum appears near r0 = 2.2 nm, upon further increasingthe rolled length L. The minima near r0 = 2 nm aremetastable up to the rolled length L = 20 nm and are deeperthan those corresponding to the intrinsic curvature. Theseminima correspond to the scrolled conformation of the JanusTMD, where van der Waals interactions are comparable to ordominate the strain energy, thereby stabilizing the scrolledconformation. In particular, wide Janus TMD sheets prefer ascrolled conformation, despite the large energy cost asso-ciated with the large curvature in their innermost shell. Wenote that Janus TMD nanoscrolls with the rolled length Lfrom 16 to 25 nm exhibit bistability corresponding toscrolled and arch conformations, which can be controlledby adjusting the external conditions.Finally, we discuss the conformations of bistable phases ofone-dimensional Janus TMDs. As described above, JanusTMDs with a moderate rolled length L from 15 to 40 nmexhibit bistability in their energy landscape, with two distinctlocal minima. Figure 6 shows the geometric structures of aJanus MoSSe nanoscroll [Fig. 6(a)] and nanoarch [Fig. 6(b)]with the rolled length L = 25 nm, which corresponds to localminima at r0 = 2 and 4 nm, respectively. In the nanoscroll,the large curvature increases the strain energy, whereas theintershell overlap leads to an energy gain from van der Waalsinteractions, which are dominant in determining the scrollconformation. By contrast, in the nanoarch, the moderatecurvature with a radius of 4 nm releases the intrinsic tensileand compressive strains in the Janus MoSSe, stabilizing thearch conformation. The energy barrier between these twoconformations is about 0.25 eV per scroll unit and dependson the scroll and arch lengths (Fig. 7). Furthermore, therelative stability of the two conformations is sensitive to theFig. 3. Contour plots of the total energy per nanoscroll unit of (a) MoS2, (b) MoSe2, (c) WS2, and (d) WSe2 nanoscrolls as a function of the rolledlength L and the innermost radius r0 of TMD nanoscrolls. The energy was measured from the flat conformation for each rolled length.055001-4© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 65, 055001 (2026) Y. Gao et al.rolled length L (Fig. 7): the nanoarch is more stable than thenanoscroll for short rolled length L, whereas the nanoscroll ismore stable for long rolled length L. Thus, a structural phasetransition is expected to occur between the two conforma-tions under appropriate external conditions, enabling JanusTMD nanoscrolls and nanoarchs to serve as functional unitsfor mechanical switching in nanodevices.4. ConclusionsWe investigated the energetics of TMD nanoscrolls using acontinuous elastic model combined with inter-shell van derWaals interactions, in which all parameters were determinedusing DFT. The strain energy as a function of the curvatureradius was evaluated from total energy calculations on thearmchair MoS2, MoSe2, WS2, WSe2, MoSSe, and WSSenanotubes using DFT with GGA. The van der Waalsinteraction was set to a representative value of 0.02 eV/atom at the optimum interlayer spacing of TMD bilayers. Wecalculated the total energies of MoS2, MoSe2, WS2, WSe2,MoSSe, and WSSe nanoscrolls for rolled lengths from 10 to100 nm and for different innermost shell radii. Our calcula-tions demonstrated that for short rolled lengths, strain andvan der Waals effects compete to determine the nanoscrollgeometry, whereas for long rolled lengths, van der Waalseffects dominate. For Janus TMDs with short rolled length,the curvature induced by intrinsic strain and van der Waalsinteractions cooperatively leads to bistable morphologies,characterized by scroll and arch conformations. Therefore,Janus nanoscrolls could serve as building blocks for nanos-cale mechanically switchable devices.Fig. 4. Cross-sectional shape of MoS2 with: (a) r0 = 4 nm and L = 40 nm at position A in Figs. 2(a), 2(b) r0 = 6 nm and L = 40 nm at position B inFig. 2(a), and 2(c) r0 = 4.5 nm and L = 80 nm at position C in Fig. 2(a). For simplicity, the atomic positions of Mo atoms are shown.Fig. 5. Contour plots of the total energy per nanoscroll unit of (a) MoSSe and (b) WSSe nanoscrolls as a function of the rolled length L and theinnermost radius r0. 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Introduction 2. Calculation methods 3. Results and discussion 3.1. MX2 (M = Mo, W and X = S, Se) nanoscrolls 3.2. Janus MSSe (M = Mo, W) nanoscrolls 4. Conclusions Acknowledgments A6