Abstract
As the dimensions of a material shrink from an extended bulk solid to a nanoscale structure, size and quantum confinement effects become dominant, altering the properties of the material. Materials with nanoscale curved geometries, such as rolled-up nanomembranes and zigzag-shaped nanowires, have recently been found to exhibit a number of intriguing electronic and magnetic properties due to shape-driven modifications of charge motion or confinement effects. Local strain generated by curvature can also lead to changes in material properties due to electromechanical coupling. Here we review the development of electronic materials with nanoscale curved geometries. We examine the origin of shape-, confinement- and strain-induced effects and explore how to exploit these in electronic, spintronic and superconducting devices. We also consider the methods required to synthesize and characterize curvilinear nanostructures, and highlight key areas for the future development of curved electronics.
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References
Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).
Albrecht, M. et al. Magnetic multilayers on nanospheres. Nat. Mater. 4, 203–206 (2005).
Lavrijsen, R. et al. Magnetic ratchet for three-dimensional spintronic memory and logic. Nature 493, 647–650 (2013).
Becker, C. et al. Self-assembly of highly sensitive 3D magnetic field vector angular encoders. Sci. Adv. 5, eaay7459 (2019).
Karnaushenko, D. et al. Self-assembled on-chip-integrated giant magneto-impedance sensorics. Adv. Mater. 27, 6582–6589 (2015).
Steinhögl, W., Schindler, G., Steinlesberger, G. & Engelhardt, M. Size-dependent resistivity of metallic wires in the mesoscopic range. Phys. Rev. B 66, 075414 (2002).
Jedema, F. J., Filip, A. T. & van Wees, B. J. Electrical spin injection and accumulation at room temperature in an all-metal mesoscopic spin valve. Nature 410, 345–348 (2001).
Valenzuela, S. O. & Tinkham, M. Spin-polarized tunneling in room-temperature mesoscopic spin valves. Appl. Phys. Lett. 85, 5914–5916 (2004).
Kimura, T. & Otani, Y. Large spin accumulation in a permalloy-silver lateral spin valve. Phys. Rev. Lett. 99, 196604 (2007).
Žutić, I., Fabian, J. & Das Sarma, S. Spintronics: fundamentals and applications. Rev. Mod. Phys. 76, 323–410 (2004).
Kimura, T., Sato, T. & Otani, Y. Temperature evolution of spin relaxation in a NiFe/Cu lateral spin valve. Phys. Rev. Lett. 100, 066602 (2008).
Das, K. S. et al. Independent geometrical control of spin and charge resistances in curved spintronics. Nano Lett. 19, 6839–6844 (2019).
Schade, N. B., Schuster, D. I. & Nagel, S. R. A nonlinear, geometric Hall effect without magnetic field. Proc. Natl Acad. Sci. USA 116, 24475–24479 (2019).
Dresselhaus, M. S., Dresselhaus, G. & Avouris, P. Carbon Nanotubes: Synthesis, Structure, Properties and Applications 1st edn (Springer, 2001).
Bhandari, S. et al. Imaging cyclotron orbits of electrons in graphene. Nano Lett. 16, 1690–1694 (2016).
Chang, C.-H. & Ortix, C. Theoretical prediction of a giant anisotropic magnetoresistance in carbon nanoscrolls. Nano Lett. 17, 3076–3080 (2017).
Song, S. N., Wang, X. K., Chang, R. P. H. & Ketterson, J. B. Electronic properties of graphite nanotubules from galvanomagnetic effects. Phys. Rev. Lett. 72, 697–700 (1994).
Kasumov, A. Y., Khodos, I. I., Ajayan, P. M. & Colliex, C. Electrical resistance of a single carbon nanotube. Europhys. Lett. 34, 429 (1996).
Cresti, A., Fogler, M. M., Guinea, F., Castro Neto, A. H. & Roche, S. Quenching of the quantum Hall effect in graphene with scrolled edges. Phys. Rev. Lett. 108, 166602 (2012).
Müller, J. E. Effect of a nonuniform magnetic field on a two-dimensional electron gas in the ballistic regime. Phys. Rev. Lett. 68, 385–388 (1992).
Zhao, B. et al. High-order superlattices by rolling up van der Waals heterostructures. Nature 591, 385–390 (2021).
Viculis, L. M., Mack, J. J. & Kaner, R. B. A chemical route to carbon nanoscrolls. Science 299, 1361 (2003).
Xie, X. et al. Controlled fabrication of high-quality carbon nanoscrolls from monolayer graphene. Nano Lett. 9, 2565–2570 (2009).
Lauhon, L. J., Gudiksen, M. S., Wang, D. & Lieber, C. M. Epitaxial core–shell and core–multishell nanowire heterostructures. Nature 420, 57–61 (2002).
Rieger, T., Luysberg, M., Schäpers, T., Grützmacher, D. & Lepsa, M. I. Molecular beam epitaxy growth of GaAs/InAs core-shell nanowires and fabrication of InAs nanotubes. Nano Lett. 12, 5559–5564 (2012).
Rosdahl, T. O., Manolescu, A. & Gudmundsson, V. Signature of snaking states in the conductance of core-shell nanowires. Nano Lett. 15, 254–258 (2015).
Rickhaus, P. et al. Snake trajectories in ultraclean graphene p–n junctions. Nat. Commun. 6, 6470 (2015).
Taychatanapat, T. et al. Conductance oscillations induced by ballistic snake states in a graphene heterojunction. Nat. Commun. 6, 6093 (2015).
Ferrari, G., Goldoni, G., Bertoni, A., Cuoghi, G. & Molinari, E. Magnetic states in prismatic core multishell nanowires. Nano Lett. 9, 1631–1635 (2009).
Bardarson, J. H. & Moore, J. E. Quantum interference and Aharonov Bohm oscillations in topological insulators. Rep. Prog. Phys. 76, 056501 (2013).
Dufouleur, J. et al. Quasiballistic transport of Dirac fermions in a Bi2Se3 nanowire. Phys. Rev. Lett. 110, 186806 (2013).
Ziegler, J. et al. Probing spin helical surface states in topological HgTe nanowires. Phys. Rev. B 97, 035157 (2018).
Kozlovsky, R., Graf, A., Kochan, D., Richter, K. & Gorini, C. Magnetoconductance, quantum Hall effect, and Coulomb blockade in topological insulator nanocones. Phys. Rev. Lett. 124, 126804 (2020).
Nagasawa, F., Frustaglia, D., Saarikoski, H., Richter, K. & Nitta, J. Control of the spin geometric phase in semiconductor quantum rings. Nat. Commun. 4, 2526 (2013).
Ying, Z.-J., Gentile, P., Ortix, C. & Cuoco, M. Designing electron spin textures and spin interferometers by shape deformations. Phys. Rev. B 94, 081406 (2016).
Nitta, J., Meijer, F. E. & Takayanagi, H. Spin-interference device. Appl. Phys. Lett. 75, 695–697 (1999).
König, M. et al. Direct observation of the Aharonov-Casher phase. Phys. Rev. Lett. 96, 076804 (2006).
Frustaglia, D. & Richter, K. Spin interference effects in ring conductors subject to Rashba coupling. Phys. Rev. B 69, 235310 (2004).
Nagasawa, F., Takagi, J., Kunihashi, Y., Kohda, M. & Nitta, J. Experimental demonstration of spin geometric phase: radius dependence of time-reversal Aharonov-Casher oscillations. Phys. Rev. Lett. 108, 086801 (2012).
Wang, M. et al. Geometry-assisted topological transitions in spin interferometry. Phys. Rev. Lett. 123, 266804 (2019).
Gentile, P., Cuoco, M. & Ortix, C. Edge states and topological insulating phases generated by curving a nanowire with Rashba spin-orbit coupling. Phys. Rev. Lett. 115, 256801 (2015).
Zak, J. Symmetry criterion for surface states in solids. Phys. Rev. B 32, 2218–2226 (1985).
Pandey, S., Scopigno, N., Gentile, P., Cuoco, M. & Ortix, C. Topological quantum pump in serpentine-shaped semiconducting narrow channels. Phys. Rev. B 97, 241103 (2018).
Thouless, D. J. Quantization of particle transport. Phys. Rev. B 27, 6083–6087 (1983).
Niu, Q. Towards a quantum pump of electric charges. Phys. Rev. Lett. 64, 1812–1815 (1990).
Pylypovskyi, O. V. et al. Rashba torque driven domain wall motion in magnetic helices. Sci. Rep. 6, 23316 (2016).
Yershov, K. V., Kravchuk, V. P., Sheka, D. D. & Gaididei, Y. Curvature and torsion effects in spin-current driven domain wall motion. Phys. Rev. B 93, 094418 (2016).
Gaididei, Y., Kravchuk, V. P. & Sheka, D. D. Curvature effects in thin magnetic shells. Phys. Rev. Lett. 112, 257203 (2014).
Sheka, D. D., Kravchuk, V. P., Yershov, K. V. & Gaididei, Y. Torsion-induced effects in magnetic nanowires. Phys. Rev. B 92, 054417 (2015).
Bogdanov, A. & Hubert, A. Thermodynamically stable magnetic vortex states in magnetic crystals. J. Magn. Magn. Mater. 138, 255–269 (1994).
Yershov, K. V., Kravchuk, V. P., Sheka, D. D. & Rössler, U. K. Curvature effects on phase transitions in chiral magnets. SciPost Phys. 9, 43 (2020).
Huo, X. & Liu, Y. The stability of a skyrmion in a nanotube. N. J. Phys. 21, 093024 (2019).
Yan, M., Andreas, C., Kakay, A., Garcia-Sanchez, F. & Hertel, R. Chiral symmetry breaking and pair-creation mediated Walker breakdown in magnetic nanotubes. Appl. Phys. Lett. 100, 252401 (2012).
Schryer, N. L. & Walker, L. R. The motion of 180° domain walls in uniform d.c. magnetic fields. J. Appl. Phys. 45, 5406–5421 (1974).
Otálora, J. A., Yan, M., Schultheiss, H., Hertel, R. & Kákay, A. Curvature-induced asymmetric spin-wave dispersion. Phys. Rev. Lett. 117, 227203 (2016).
Körber, L. et al. Symmetry- and curvature effects on spin waves in vortex-state hexagonal nanotubes. Phys. Rev. B 104, 184429 (2021).
Linder, M. & Robinson, J. W. A. Superconducting spintronics. Nat. Phys. 11, 307–315 (2015).
Sigrist, M. & Ueda, K. Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, 239–311 (1991).
Bergeret, F. S., Volkov, A. F. & Efetov, K. B. Long-range proximity effects in superconductor-ferromagnet structures. Phys. Rev. Lett. 86, 4096–4099 (2001).
Eschrig, M. & Löfwander, T. Triplet supercurrents in clean and disordered half-metallic ferromagnets. Nat. Phys. 4, 138–143 (2008).
Robinson, J. W. A., Witt, J. D. S. & Blamire, M. Controlled injection of spin-triplet supercurrents into a strong ferromagnet. Science 329, 59–61 (2010).
Bergeret, F. S. & Tokatly, I. V. Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures. Phys. Rev. B 89, 134517 (2014).
Gorkov, L. P. & Rashba, E. I. Superconducting 2D system with lifted spin degeneracy: mixed singlet-triplet state. Phys. Rev. Lett. 87, 037004 (2001).
Frigeri, P. A., Agterberg, D. F., Koga, A. & Sigrist, M. Superconductivity without inversion symmetry: MnSi versus CePt3Si. Phys. Rev. Lett. 92, 097001 (2004).
Ying, Z.-J., Cuoco, M., Ortix, C. & Gentile, P. Tuning pairing amplitude and spin-triplet texture by curving superconducting nanostructures. Phys. Rev. B 96, 100506 (2017).
Francica, G., Cuoco, M. & Gentile, P. Topological superconducting phases and Josephson effect in curved superconductors with time reversal invariance. Phys. Rev. B 96, 100506 (2017).
Mei, Y. et al. Optical properties of a wrinkled nanomembrane with embedded quantum well. Nano Lett. 7, 1676–1679 (2007).
Zubko, P., Catalan, G. & Tagantsev, A. K. Flexoelectric effect in solids. Annu. Rev. Mater. Res. 43, 387–421 (2013).
Van de Walle, C. G. Band lineups and deformation potentials in the model-solid theory. Phys. Rev. B 39, 1871–1883 (1989).
Ortix, C., Kiravittaya, S., Schmidt, O. G. & van den Brink, J. Curvature-induced geometric potential in strain-driven nanostructures. Phys. Rev. B 84, 045438 (2011).
Ortix, C. & van den Brink, J. Effect of curvature on the electronic structure and bound-state formation in rolled-up nanotubes. Phys. Rev. B 81, 165419 (2010).
Aoki, H., Koshino, M., Takeda, D., Morise, H. & Kuroki, K. Electronic structure of periodic curved surfaces: topological band structure. Phys. Rev. B 65, 035102 (2001).
Pandey, S. & Ortix, C. Topological end states due to inhomogeneous strains in wrinkled semiconducting ribbons. Phys. Rev. B 93, 195420 (2016).
de Juan, F., Cortijo, A. & Vozmediano, M. A. H. Charge inhomogeneities due to smooth ripples in graphene sheets. Phys. Rev. B 76, 165409 (2007).
Meyer, J. C. et al. The structure of suspended graphene sheets. Nature 446, 60–63 (2007).
Martin, J. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nat. Phys. 4, 144–148 (2008).
de Juan, F., Sturla, M. & Vozmediano, M. A. H. Space dependent Fermi velocity in strained graphene. Phys. Rev. Lett. 108, 227205 (2012).
Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30–33 (2010).
Levy, N. et al. Strain-induced pseudo–magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).
Jiang, Y. et al. Visualizing strain-induced pseudomagnetic fields in graphene through an hBN magnifying glass. Nano Lett. 17, 2839–2843 (2017).
Couto, N. J. G. et al. Random strain fluctuations as dominant disorder source for high-quality on-substrate graphene devices. Phys. Rev. X 4, 041019 (2014).
Rizzo, D. J. et al. Nanometer-scale lateral p-n junctions in graphene/α-RuCl3 heterostructures. Nano Lett. 22, 1946–1953 (2022).
Nigge, P. et al. Room temperature strain-induced Landau levels in graphene on a wafer-scale platform. Sci. Adv. 5, eaaw5593 (2019).
Mao, J. et al. Evidence of flat bands and correlated states in buckled graphene superlattices. Nature 584, 215–220 (2020).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
Xu, S.-Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018).
Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019).
Zhang, Y. & Fu, L. Terahertz detection based on nonlinear Hall effect without magnetic field. Proc. Natl Acad. Sci. USA 118, e2100736118 (2021).
Battilomo, R., Scopigno, N. & Ortix, C. Berry curvature dipole in strained graphene: a Fermi surface warping effect. Phys. Rev. Lett. 123, 196403 (2019).
Ho, S.-C. et al. Hall effects in artificially corrugated bilayer graphene without breaking time-reversal symmetry. Nat. Electron. 4, 116–125 (2021).
Kläui, M., Vaz, C., Heyderman, L., Rüdiger, U. & Bland, J. Spin switching phase diagram of mesoscopic ring magnets. J. Magn. Magn. Mater. 290–291, 61–67 (2005).
Volkov, O. M. et al. Experimental observation of exchange-driven chiral effects in curvilinear magnetism. Phys. Rev. Lett. 123, 077201 (2019).
Phatak, C., Petford-Long, A. K. & Heinonen, O. Direct observation of unconventional topological spin structure in coupled magnetic discs. Phys. Rev. Lett. 108, 067205 (2012).
Streubel, R. et al. Magnetism in curved geometries (Topical Review). J. Phys. D 49, 363001 (2016).
Rogers, J. A., Lagally, M. G. & Nuzzo, R. G. Synthesis, assembly and applications of semiconductor nanomembranes. Nature 477, 45–53 (2011).
Schmidt, O. G. & Eberl, K. Nanotechnology: thin solid films roll up into nanotubes. Nature 410, 168 (2001).
Smith, E. J., Makarov, D., Sanchez, S., Fomin, V. M. & Schmidt, O. G. Magnetic microhelix coil structures. Phys. Rev. Lett. 107, 097204 (2011).
Cui, X. et al. Rolling up transition metal dichalcogenide nanoscrolls via one drop of ethanol. Nat. Commun. 9, 1301 (2018).
Grimm, D. et al. Rolled-up nanomembranes as compact 3D architectures for field effect transistors and fluidic sensing applications. Nano Lett. 13, 213–218 (2012).
Müller, C. et al. Tuning giant magnetoresistance in rolled-up Co-Cu nanomembranes by strain engineering. Nanoscale 4, 7155–7160 (2012).
Thurmer, D. J., Bof Bufon, C. C. B., Deneke, C. & Schmidt, O. G. Nanomembrane-based mesoscopic superconducting hybrid junctions. Nano Lett. 10, 3704–3709 (2010).
Streubel, R. et al. Magnetic vortices on closely packed spherically curved surfaces. Phys. Rev. B 85, 174429 (2012).
Xu, S. et al. Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science 347, 154–159 (2015).
Zhao, Y.-P., Ye, D.-X., Wang, G.-C. & Lu, T.-M. Novel nano-column and nano-flower arrays by glancing angle deposition. Nano Lett. 2, 351–354 (2002).
Gibbs, J. G. et al. Nanohelices by shadow growth. Nanoscale 6, 9457–9466 (2014).
Eslami, S. et al. Chiral nanomagnets. ACS Photon. 1, 1231–1236 (2014).
Williams, G. et al. Two-photon lithography for 3D magnetic nanostructure fabrication. Nano Res. 11, 845–854 (2018).
Hunt, M. et al. Harnessing multi-photon absorption to produce three-dimensional magnetic structures at the nanoscale. Materials 13, 761 (2020).
Jung, W. et al. Three-dimensional nanoprinting via charged aerosol jets. Nature 592, 54–59 (2021).
Teresa, J. M. D. et al. Review of magnetic nanostructures grown by focused electron beam induced deposition (FEBID). J. Phys. D 49, 243003 (2016).
Huth, M., Porrati, F. & Dobrovolskiy, O. Focused electron beam induced deposition meets materials science. Microelectron. Eng. 185–186, 9–28 (2018).
Skoric, L. et al. Layer-by-layer growth of complex-shaped three-dimensional nanostructures with focused electron beams. Nano Lett. 20, 184–191 (2020).
Meng, F. et al. Non-planar geometrical effects on the magnetoelectrical signal in a three-dimensional nanomagnetic circuit. ACS Nano 15, 6765–6773 (2021).
Streubel, R. et al. Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies. Nat. Commun. 6, 7612 (2015).
Wolf, D. et al. Holographic vector field electron tomography of three-dimensional nanomagnets. Commun. Phys. 2, 87 (2019).
Volkov, O. M., Rössler, U. K., Fassbender, J. & Makarov, D. Concept of artificial magnetoelectric materials via geometrically controlling curvilinear helimagnets. J. Phys. D 52, 345001 (2019).
Makarov, D. et al. New dimension in magnetism and superconductivity: 3D and curvilinear nanoarchitectures. Adv. Mater. 34, 2101758 (2022).
Donnelly, C. et al. Complex free-space magnetic field textures induced by three-dimensional magnetic nanostructures. Nat. Nanotechnol. 17, 136–142 (2022).
Grollier, J. et al. Neuromorphic spintronics. Nat. Electron. 3, 360–370 (2020).
Pylypovskyi, O. V. et al. Curvilinear one-dimensional antiferromagnets. Nano Lett. 20, 8157–8162 (2020).
Pesin, D. & MacDonald, A. H. Spintronics and pseudospintronics in graphene and topological insulators. Nat. Mater. 11, 409–416 (2012).
Mannix, A. J. et al. Robotic four-dimensional pixel assembly of van der Waals solids. Nat. Nanotechnol. 17, 361–366 (2022).
Zamborlini, G. et al. Nanobubbles at GPa pressure under graphene. Nano Lett. 15, 6162–6169 (2015).
Khestanova, E., Guinea, F., Fumagalli, L., Geim, A. K. & Grigorieva, I. V. Universal shape and pressure inside bubbles appearing in van der Waals heterostructures. Nat. Commun. 7, 12587 (2016).
Villarreal, R. et al. Breakdown of universal scaling for nanometer-sized bubbles in graphene. Nano Lett. 21, 8103–8110 (2021).
Chang, C.-H., van den Brink, J. & Ortix, C. Strongly anisotropic ballistic magnetoresistance in compact three-dimensional semiconducting nanoarchitectures. Phys. Rev. Lett. 113, 227205 (2014).
Szameit, A. et al. Geometric potential and transport in photonic topological crystals. Phys. Rev. Lett. 104, 150403 (2010).
Papaj, M. & Fu, L. Magnus Hall effect. Phys. Rev. Lett. 123, 216802 (2019).
Schine, N., Ryou, A., Gromov, A., Sommer, A. & Simon, J. Synthetic Landau levels for photons. Nature 534, 671–675 (2016).
Can, T., Chiu, Y. H., Laskin, M. & Wiegmann, P. Emergent conformal symmetry and geometric transport properties of quantum Hall states on singular surfaces. Phys. Rev. Lett. 117, 266803 (2016).
van Thiel, T. C. et al. Coupling charge and topological reconstructions at polar oxide interfaces. Phys. Rev. Lett. 127, 127202 (2021).
Paskiewicz, D. M., Sichel-Tissot, R., Karapetrova, E., Stan, L. & Fong, D. D. Single-crystalline SrRuO3 nanomembranes: a platform for flexible oxide electronics. Nano Lett. 16, 534–542 (2016).
Hadjimichael, M. et al. Metal–ferroelectric supercrystals with periodically curved metallic layers. Nat. Mater. 20, 495–502 (2021).
Mercaldo, M. T., Ortix, C., Giazotto, F. & Cuoco, M. Orbital vortices in s-wave spin-singlet superconductors in zero magnetic field. Phys. Rev. B 105, L140507 (2022).
Laeven, T., Nijholt, B., Wimmer, M. & Akhmerov, A. R. Enhanced proximity effect in zigzag-shaped majorana Josephson junctions. Phys. Rev. Lett. 125, 086802 (2020).
Jensen, H. & Koppe, H. Quantum mechanics with constraints. Ann. Phys. 63, 586–591 (1971).
da Costa, R. C. T. Quantum mechanics of a constrained particle. Phys. Rev. A 23, 1982–1987 (1981).
Ortix, C. Quantum mechanics of a spin-orbit coupled electron constrained to a space curve. Phys. Rev. B 91, 245412 (2015).
Kravchuk, V. P. et al. Topologically stable magnetization states on a spherical shell: curvature-stabilized skyrmions. Phys. Rev. B 94, 144402 (2016).
Asano, Y. Josephson spin current in triplet superconductor junctions. Phys. Rev. B 74, 220501 (2006).
Acknowledgements
We acknowledge the numerous colleagues with whom we have collaborated on the topics described in this Review. We also acknowledge the Future and Emerging Technologies (FET) Programme within the Seventh Framework Programme for Research of the European Commission under FET-Open grant no. 618083 (CNTQC) for the financial support to the work performed by the authors on this topic. C.O. acknowledges support from a VIDI grant (Project 680-47-543) financed by the Netherlands Organization for Scientific Research (NWO). The work of D.M. and O.M.V. was financed in part via numerous national and European projects including German Research Foundation (DFG) grants MA 5144/9-1, MA 5144/13-1, MA 5144/28-1 and VO 2598/1-1, as well as the Helmholtz Association of German Research Centres in the frame of the Helmholtz Innovation Lab ‘FlexiSens’. Z.-J.Y. acknowledges support from the National Natural Science Foundation of China (grant no. 11974151).
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Gentile, P., Cuoco, M., Volkov, O.M. et al. Electronic materials with nanoscale curved geometries. Nat Electron 5, 551–563 (2022). https://doi.org/10.1038/s41928-022-00820-z
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