- Open Access
Intercalant-induced Kekule ordering and gap opening in quasifreestanding graphene
Phys. Rev. B 113, 085426 – Published 19 February, 2026
DOI: https://doi.org/10.1103/ktj3-t5qk
Abstract
We present a comprehensive investigation of the structural and electronic properties of Sn-intercalated buffer layers on SiC(0001) using low-temperature scanning tunneling microscopy and spectroscopy (LT-STM and LT-STS), spot-profile analysis low-energy electron diffraction, and density functional theory (DFT) calculations. Sn intercalation effectively decouples the buffer layer, yielding quasifreestanding monolayer graphene while introducing local lattice distortions. Bias-dependent STM imaging revealed the coexistence of conventional and Kekulè-ordered graphene domains, governed by the underlying Sn(1×1) reconstruction at the SiC interface. The measured STS spectra exhibit good agreement with DFT results. However, achieving homogeneous Sn(1×1) domains remains challenging, apparently, due to strain within the Sn monolayer, which drives the emergence of Kekulè distortions and the associated electronic band-gap opening homogeneously in graphene. These findings highlight the crucial role of intercalant homogeneity and strain in tuning graphene's structural and electronic properties.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (67)
- A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater. 6, 183 (2007).
- T. O. Wehling, A. M. Black-Schaffer, and A. V. Balatsky, Dirac materials, Adv. Phys. 63, 1 (2014).
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306, 666 (2004).
- Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature (London) 438, 201 (2005).
- A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
- L. Brey and H. A. Fertig, Electronic states of graphene nanoribbons studied with the Dirac equation, Phys. Rev. B 73, 235411 (2006).
- Y.-W. Son, M. L. Cohen, and S. G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97, 216803 (2006).
- T. T. Nhung Nguyen, S. R. Power, H. Karakachian, U. Starke, and C. Tegenkamp, Quantum confinement in epitaxial armchair graphene nanoribbons on SiC sidewalls, ACS Nano 17, 20345 (2023).
- Y. Yan, J. Chen, N. Li, J. Tian, K. Li, J. Jiang, J. Liu, Q. Tian, and P. Chen, Systematic bandgap engineering of graphene quantum dots and applications for photocatalytic water splitting and reduction, ACS Nano 12, 3523 (2018).
- A. Varykhalov, M. R. Scholz, T. K. Kim, and O. Rader, Effect of noble-metal contacts on doping and band gap of graphene, Phys. Rev. B 82, 121101(R) (2010).
- S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, Substrate-induced bandgap opening in epitaxial graphene, Nat. Mater. 6, 770 (2007).
- C. Ghosal, M. Gruschwitz, J. Koch, S. Gemming, and C. Tegenkamp, Proximity-induced gap opening by twisted plumbene in epitaxial graphene, Phys. Rev. Lett. 129, 116802 (2022).
- R. Balog, B. Jørgensen, L. Nilsson, M. Andersen, E. Rienks, M. Bianchi, M. Fanetti, E. Lægsgaard, A. Baraldi, S. Lizzit, Z. Sljivancanin, F. Besenbacher, B. Hammer, T. G. Pedersen, P. Hofmann, and L. Hornekær, Bandgap opening in graphene induced by patterned hydrogen adsorption, Nat. Mater. 9, 315 (2010).
- J. Son, S. Lee, S. J. Kim, B. C. Park, H.-K. Lee, S. Kim, J. H. Kim, B. H. Hong, and J. Hong, Hydrogenated monolayer graphene with reversible and tunable wide band gap and its field-effect transistor, Nat. Commun. 7, 13261 (2016).
- C. Bao, H. Zhang, T. Zhang, X. Wu, L. Luo, S. Zhou, Q. Li, Y. Hou, W. Yao, L. Liu, P. Yu, J. Li, W. Duan, H. Yao, Y. Wang, and S. Zhou, Experimental evidence of chiral symmetry breaking in Kekulé-ordered graphene, Phys. Rev. Lett. 126, 206804 (2021).
- W. Yan, W.-Y. He, Z.-D. Chu, M. Liu, L. Meng, R.-F. Dou, Y. Zhang, Z. Liu, J.-C. Nie, and L. He, Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer, Nat. Commun. 4, 2159 (2013).
- M. Aoki and H. Amawashi, Dependence of band structures on stacking and field in layered graphene, Solid State Commun. 142, 123 (2007).
- Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, Direct observation of a widely tunable bandgap in bilayer graphene, Nature (London) 459, 820 (2009).
- C. Jeon, H.-C. Shin, I. Song, M. Kim, J.-H. Park, J. Nam, D.-H. Oh, S. Woo, C.-C. Hwang, C.-Y. Park, and J. R. Ahn, Opening and reversible control of a wide energy gap in uniform monolayer graphene, Sci. Rep. 3, 2725 (2013).
- J. Warmuth, A. Bruix, M. Michiardi, T. Hänke, M. Bianchi, J. Wiebe, R. Wiesendanger, B. Hammer, P. Hofmann, and A. A. Khajetoorians, Band-gap engineering by Bi intercalation of graphene on Ir(111), Phys. Rev. B 93, 165437 (2016).
- B. M. Cano, F. Calleja, D. Pacilè, M. G. Cuxart, M. Pisarra, A. Sindona, F. Martín, E. Salagre, P. Segovia, E. G. Michel, A. L. Vázquez de Parga, R. Miranda, J. Camarero, M. Garnica, and M. A. Valbuena, Engineering a spin-orbit bandgap in graphene-tellurium heterostructures, Adv. Funct. Mater. 35, 2425154 (2025).
- C. Ghosal, S. Ryee, Z. Mamiyev, M.-E. Federl, N. Witt, T. Wehling, and C. Tegenkamp, Mott states proximitized to a relativistic electron gas in epitaxial graphene, Phys. Rev. B 111, 235426 (2025).
- A. Blason and M. Fabrizio, Local Kekulé distortion turns twisted bilayer graphene into topological Mott insulators and superconductors, Phys. Rev. B 106, 235112 (2022).
- D. Eom and J.-Y. Koo, Direct measurement of strain-driven Kekulé distortion in graphene and its electronic properties, Nanoscale 12, 19604 (2020).
- Z. Mamiyev, N. O. Balayeva, C. Ghosal, D. R. T. Zahn, and C. Tegenkamp, Confinement induced strain effects in epitaxial graphene, Carbon 234, 120002 (2025).
- A. C. Qu, P. Nigge, S. Link, G. Levy, M. Michiardi, P. L. Spandar, T. Matthé, M. Schneider, S. Zhdanovich, U. Starke, C. Gutiérrez, and A. Damascelli, Ubiquitous defect-induced density wave instability in monolayer graphene, Sci. Adv. 8, eabm5180 (2022).
- D. L. Bergman, Realization of a vortex in the Kekulè texture of molecular graphene at a Y junction where three domains meet, Phys. Rev. B 87, 035422 (2013).
- Y. Guan, C. Dutreix, H. González-Herrero, M. M. Ugeda, I. Brihuega, M. I. Katsnelson, O. V. Yazyev, and V. T. Renard, Observation of Kekulé vortices around hydrogen adatoms in graphene, Nat. Commun. 15, 2927 (2024).
- O. V. Gamayun, V. P. Ostroukh, N. V. Gnezdilov, I. Adagideli, and C. W. J. Beenakker, Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture, New J. Phys. 20, 023016 (2018).
- C. Gutiérrez, C.-J. Kim, L. Brown, T. Schiros, D. Nordlund, E. Lochocki, K. M. Shen, J. Park, and A. N. Pasupathy, Imaging chiral symmetry breaking from Kekulé bond order in graphene, Nat. Phys. 12, 950 (2016).
- K. V. Emtsev, F. Speck, T. Seyller, L. Ley, and J. D. Riley, Interaction, growth, and ordering of epitaxial graphene on SiC{0001} surfaces: A comparative photoelectron spectroscopy study, Phys. Rev. B 77, 155303 (2008).
- M. N. Nair, I. Palacio, A. Celis, A. Zobelli, A. Gloter, S. Kubsky, J.-P. Turmaud, M. Conrad, C. Berger, W. de Heer, E. H. Conrad, A. Taleb-Ibrahimi, and A. Tejeda, Band gap opening induced by the structural periodicity in epitaxial graphene buffer layer, Nano Lett. 17, 2681 (2017).
- C. Bao, H. Zhang, X. Wu, S. Zhou, Q. Li, P. Yu, J. Li, W. Duan, and S. Zhou, Coexistence of extended flat band and Kekulé order in Li-intercalated graphene, Phys. Rev. B 105, L161106 (2022).
- M. Gruschwitz, S. Sologub, Z. Mamiyev, C. Ghosal, Y. Niu, A. Zakharov, and C. Tegenkamp, From stripes to hexagons: Strain-induced 2D Pb phases confined between graphene and SiC, Adv. Mater. Interfaces 12, e00617 (2025).
- K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide, Nat. Mater. 8, 203 (2009).
- Z. Mamiyev and C. Tegenkamp, Sn intercalation into the BL/SiC(0001) interface: A detailed SPA-LEED investigation, Surf. Interfaces 34, 102304 (2022).
- Z. Mamiyev and C. Tegenkamp, Exploring graphene-substrate interactions: Plasmonic excitation in Sn-intercalated epitaxial graphene, 2D Mater. 11, 025013 (2024) .
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- P. E. Blöchl, O. Jepsen, and O. K. Andersen, Improved tetrahedron method for Brillouin-zone integrations, Phys. Rev. B 49, 16223 (1994).
- A. Mattausch and O. Pankratov, Ab initio study of graphene on SiC, Phys. Rev. Lett. 99, 076802 (2007).
- M.-E. Federl, N. Witt, B. Yang, L. Weigl, N. Hofmann, J. Gradl, I. Piquero-Zulaica, J. V. Barth, N. Mishra, C. Coletti, T. O. Wehling, and I. Gierz, Nonequilibrium carrier dynamics and band structure of graphene on two-dimensional tin, Phys. Rev. B 111, 125158 (2025).
- The DFT data is deposited on the NOMAD [67] repository at doi: 10.17172/NOMAD/2026.01.28-4.
- V. V. Cheianov, V. I. Fal'ko, O. Syljuåsen, and B. L. Altshuler, Hidden Kekulé ordering of adatoms on graphene, Solid State Commun. 149, 1499 (2009).
- S.-H. Lee, H.-J. Chung, J. Heo, H. Yang, J. Shin, U.-I. Chung, and S. Seo, Band gap opening by two-dimensional manifestation of Peierls instability in graphene, ACS Nano 5, 2964 (2011).
- K. P. Nuckolls, et al., Quantum textures of the many-body wavefunctions in magic-angle graphene, Nature (London) 620, 525 (2023).
- H. Kim, et al., Imaging inter-valley coherent order in magic-angle twisted trilayer graphene, Nature (London) 623, 942 (2023).
- B. Harling, Z. Mamiyev, C. Tegenkamp, and M. Wenderoth, Mesoscopic scale study of lateral dynamics of Sn intercalation of the graphene buffer layer on SiC, Carbon 244, 120711 (2025).
- D. Momeni Pakdehi, P. Schädlich, T. T. N. Nguyen, A. A. Zakharov, S. Wundrack, E. Najafidehaghani, F. Speck, K. Pierz, T. Seyller, C. Tegenkamp, and H. W. Schumacher, Silicon carbide stacking-order-induced doping variation in epitaxial graphene, Adv. Funct. Mater. 30, 2004695 (2020).
- E. Tok, W. Ong, and A. Wee, 6H-SiC(0001) phase transition: evolution of the () magic clusters, Surf. Sci. 558, 145 (2004).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/ktj3-t5qk for additional STM images and spectroscopy analysis.
- N. A. Anderson, M. Hupalo, D. Keavney, M. C. Tringides, and D. Vaknin, Intercalated europium metal in epitaxial graphene on SiC, Phys. Rev. Mater. 1, 054005 (2017).
- S. Chen, M. Horn von Hoegen, P. A. Thiel, and M. C. Tringides, Diffraction paradox: An unusually broad diffraction background marks high quality graphene, Phys. Rev. B 100, 155307 (2019).
- X. Qiu, T. Zhu, Z. Fan, K. Wang, Y. Mu, B. Yang, D. Wu, H. Zhang, C. Wang, H. Wang, et al., Giant splitting of folded Dirac bands in Kekulé-ordered graphene with Eu intercalation, arXiv:2509.05633.
- E. Andrade, R. Carrillo-Bastos, and G. G. Naumis, Valley engineering by strain in Kekulé-distorted graphene, Phys. Rev. B 99, 035411 (2019).
- C. Schmitt, J. Erhardt, P. Eck, M. Schmitt, K. Lee, P. Keßler, T. Wagner, M. Spring, B. Liu, S. Enzner, M. Kamp, V. Jovic, C. Jozwiak, A. Bostwick, E. Rotenberg, T. Kim, C. Cacho, T.-L. Lee, G. Sangiovanni, S. Moser, et al., Achieving environmental stability in an atomically thin quantum spin Hall insulator via graphene intercalation, Nat. Commun. 15, 1486 (2024).
- L. Gehrig, C. Schmitt, J. Erhardt, B. Liu, T. Wagner, M. Kamp, S. Moser, and R. Claessen, Bismuthene under cover: Graphene intercalation of a large gap quantum spin Hall insulator, Adv. Mater. 37, 2502412 (2025).
- L. Ferbel, S. Veronesi, A. Rossi, S. Forti, Y. Vlamidis, C. Coletti, and S. Heun, Intercalated structures formed by platinum on epitaxial graphene on SiC(0001), Carbon 234, 119989 (2025).
- T. Cavallucci and V. Tozzini, Intrinsic structural and electronic properties of the buffer layer on silicon carbide unraveled by density functional theory, Sci. Rep. 8, 13097 (2018).
- Y. Zhang, V. W. Brar, F. Wang, C. Girit, Y. Yayon, M. Panlasigui, A. Zettl, and M. F. Crommie, Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene, Nat. Phys. 4, 627 (2008).
- S. Hacohen-Gourgy, I. Diamant, B. Almog, Y. Dubi, and G. Deutscher, Temperature dependance of the tunneling density of states in sub-micron planar metal/oxide/graphene junctions, Appl. Phys. Lett. 99, 172108 (2011).
- M. Scheidgen, L. Himanen, A. N. Ladines, D. Sikter, M. Nakhaee, Á. Fekete, T. Chang, A. Golparvar, J. A. Márquez, S. Brockhauser, S. Brückner, L. M. Ghiringhelli, F. Dietrich, D. Lehmberg, T. Denell, A. Albino, H. Näsström, S. Shabih, F. Dobener, M. Kühbach, et al., NOMAD: A distributed web-based platform for managing materials science research data, J. Open Source Softw. 8, 5388 (2023).