- Open Access
Phase-dependent electronic structure of two-dimensional Ag layers at the graphene/SiC interface
Phys. Rev. B 114, 245409 – Published 8 October, 2026
DOI: https://doi.org/10.1103/rgn3-rnbh
Abstract
Intercalation at the graphene/SiC interface provides a controlled route to stabilize atomically thin layers with properties distinct from their bulk counterparts. In this platform, the structure and stability of the intercalated phase depend sensitively on the defect landscape of the starting substrate. For intercalated two-dimensional silver at the graphene/SiC interface, two phases have been observed: a phase epitaxial to the SiC lattice, called , readily obtained following the conventional intercalation method under ultra-high-vacuum conditions and extensively characterized, and a more densely packed phase, called , which has remained largely unexplored. Here we report an in situ ultra-high-vacuum preparation method of the second phase intercalated at the graphene/SiC interface; this phase was previously prepared via high-pressure confinement heteroepitaxy. Low-energy electron diffraction shows that is rotated by relative to the SiC lattice and forms supercells, in contrast to the epitaxial relation of with SiC. High-resolution angle-resolved photoemission spectroscopy reveals a more complex band dispersion compared to , as a consequence of the modified Ag-Si interaction in the denser phase. In density functional theory calculations, by defining the unfolding entropy, which, in a quantified way, finds that the band structure of is more suitable to be unfolded to the SiC primitive cell, the resulting unfolded band dispersion is in great agreement with the experimental data. We further show that the different intercalated Ag phases tune the electronic properties of the overlying quasi-free-standing graphene layer differently: compared with yields an times higher charge carrier density and modifies the charge-plasmon interaction of the graphene layer, indicating a change in effective screening at the interface.
Physics Subject Headings (PhySH)
- Density of states
- Electronic structure of atoms & molecules
- Fermi surface
- Intercalation
- Surface & interfacial phenomena
- Surface states
- Graphene
- Two-dimensional electron system
- Angle-resolved photoemission spectroscopy
- Density functional theory
- Low-energy electron diffraction
- Photoemission spectroscopy
- X-ray photoemission electron microscopy
Article Text
Supplemental Material
References (87)
- 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).
- A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater. 6, 183 (2007).
- Y.-W. Son, M. L. Cohen, and S. G. Louie, Energy gaps in graphene nanoribbons, Phys. Rev. Lett. 97, 216803 (2006).
- G. R. Bhimanapati, Z. Lin, V. Meunier, Y. Jung, J. Cha, S. Das, D. Xiao, Y. Son, M. S. Strano, V. R. Cooper, L. Liang, S. G. Louie, E. Ringe, W. Zhou, S. S. Kim, R. R. Naik, B. G. Sumpter, H. Terrones, F. Xia, Y. Wang, et al., Recent advances in two-dimensional materials beyond graphene, ACS Nano 9, 11509 (2015).
- Z. Lin, A. McCreary, N. Briggs, S. Subramanian, K. Zhang, Y. Sun, X. Li, N. J. Borys, H. Yuan, S. K. Fullerton-Shirey, A. Chernikov, H. Zhao, S. McDonnell, A. M. Lindenberg, K. Xiao, B. J. LeRoy, M. Drndić, J. C. M. Hwang, J. Park, M. Chhowalla, et al., 2D materials advances: From large scale synthesis and controlled heterostructures to improved characterization techniques, defects and applications, 2D Mater. 3, 042001 (2016).
- D. Bera, L. Qian, T. Tseng, and P. H. Holloway, Quantum dots and their multimodal applications: A review, Materials 3, 2260 (2010).
- X. Huang, C. Liu, and P. Zhou, 2D semiconductors for specific electronic applications: From device to system, npj 2D Mater. Appl. 6, 51 (2022).
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Proc. Natl. Acad. Sci. USA 102, 10451 (2005).
- H. Karakachian, T. T. N. Nguyen, J. Aprojanz, A. A. Zakharov, R. Yakimova, P. Rosenzweig, C. M. Polley, T. Balasubramanian, C. Tegenkamp, S. R. Power, and U. Starke, One-dimensional confinement and width-dependent bandgap formation in epitaxial graphene nanoribbons, Nat. Commun. 11, 6380 (2020).
- E. Parzinger, E. Mitterreiter, M. Stelzer, F. Kreupl, J. W. Ager, A. W. Holleitner, and U. Wurstbauer, Hydrogen evolution activity of individual mono-, bi-, and few-layer towards photocatalysis, Appl. Mater. Today 8, 132 (2017).
- C. Lee, X. Wei, J. W. Kysar, and J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321, 385 (2008).
- K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin : A new direct-gap semiconductor, Phys. Rev. Lett. 105, 136805 (2010).
- A. Bostwick, F. Speck, T. Seyller, K. Horn, and E. Rotenberg, Observation of plasmarons in quasi-freestanding doped graphene, Science 328, 999 (2010).
- P. Rosenzweig, H. Karakachian, D. Marchenko, and U. Starke, Surface charge-transfer doping a quantum-confined silver monolayer beneath epitaxial graphene, Phys. Rev. B 105, 235428 (2022).
- S. Link, S. Forti, A. Stöhr, K. Küster, M. Rösner, D. Hirschmeier, C. Chen, J. Avila, M. C. Asensio, A. A. Zakharov, T. O. Wehling, A. I. Lichtenstein, M. I. Katsnelson, and U. Starke, Introducing strong correlation effects into graphene by gadolinium intercalation, Phys. Rev. B 100, 121407(R) (2019).
- S. A. Herrera, G. Parra-Martínez, P. Rosenzweig, B. Matta, C. M. Polley, K. Küster, U. Starke, F. Guinea, J. Á. Silva-Guillén, G. G. Naumis, and P. A. Pantaleón, Topological superconductivity in heavily doped single-layer graphene, ACS Nano 18, 34842 (2024).
- Q. Zhong, J. Zhang, P. Cheng, B. Feng, W. Li, S. Sheng, H. Li, S. Meng, L. Chen, and K. Wu, Metastable phases of 2D boron sheets on Ag(111), J. Phys.: Condens. Matter 29, 095002 (2017).
- K. Romanyuk, J. Brona, and B. Voigtländer, Nanoscale pit formation at 2D Ge layers on Si: Influence of energy and entropy, Phys. Rev. Lett. 103, 096101 (2009).
- M. Körner, F. Loske, M. Einax, A. Kühnle, M. Reichling, and P. Maass, Second-layer induced island morphologies in thin-film growth of fullerenes, Phys. Rev. Lett. 107, 016101 (2011).
- T. Aizawa, S. Suehara, and S. Otani, Silicene on zirconium carbide (111), J. Phys. Chem. C 118, 23049 (2014).
- C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation, Phys. Rev. Lett. 103, 246804 (2009).
- K. V. Emtsev, A. A. Zakharov, C. Coletti, S. Forti, and U. Starke, Ambipolar doping in quasifree epitaxial graphene on SiC(0001) controlled by Ge intercalation, Phys. Rev. B 84, 125423 (2011).
- S. Forti, S. Link, A. Stöhr, Y. Niu, A. A. Zakharov, C. Coletti, and U. Starke, Semiconductor to metal transition in two-dimensional gold and its van der Waals heterostack with graphene, Nat. Commun. 11, 2236 (2020).
- P. Rosenzweig and U. Starke, Large-area synthesis of a semiconducting silver monolayer via intercalation of epitaxial graphene, Phys. Rev. B 101, 201407(R) (2020).
- B. Matta, P. Rosenzweig, O. Bolkenbaas, K. Küster, and U. Starke, Momentum microscopy of Pb-intercalated graphene on SiC: Charge neutrality and electronic structure of interfacial Pb, Phys. Rev. Res. 4, 023250 (2022).
- Z. Y. Al Balushi, K. Wang, R. K. Ghosh, R. A. Vilá, S. M. Eichfeld, J. D. Caldwell, X. Qin, Y.-C. Lin, P. A. DeSario, G. Stone, S. Subramanian, D. F. Paul, R. M. Wallace, S. Datta, J. Redwing, and J. A. Robinson, Two-dimensional gallium nitride realized via graphene encapsulation, Nat. Mater. 15, 1166 (2016).
- H. El-Sherif, N. Briggs, B. Bersch, M. Pan, M. Hamidinejad, S. Rajabpour, T. Filleter, K. W. Kim, J. Robinson, and N. D. Bassim, Scalable characterization of 2D gallium-intercalated epitaxial graphene, ACS Appl. Mater. Interfaces 13, 55428 (2021).
- A. Vera, B. Zheng, W. Yanez, K. Yang, S. Y. Kim, X. Wang, J. C. Kotsakidis, H. El-Sherif, G. Krishnan, R. J. Koch, T. A. Bowen, C. Dong, Y. Wang, M. Wetherington, E. Rotenberg, N. Bassim, A. L. Friedman, R. M. Wallace, C. Liu, N. Samarth, et al., Large-area intercalated two-dimensional Pb/graphene heterostructure as a platform for generating spin–orbit torque, ACS Nano 18, 21985 (2024).
- S. Wundrack, M. Bothe, M. Jaime, K. Küster, M. Gruschwitz, Y. Yin, Z. Mamiyev, P. Schädlich, B. Matta, S. Datta, M. Eckert, C. Tegenkamp, U. Starke, R. Stosch, H. W. Schumacher, T. Seyller, K. Pierz, T. Tschirner, and A. Bakin, Lithographically controlled liquid metal diffusion in graphene: Fabrication and magnetotransport signatures of superconductivity, Adv. Mater. 38, e11992 (2026).
- L.-S. Lu, A. Vera, F. Turker, K. M. Ananthanarayanan, C. Dong, M. Wetherington, and J. A. Robinson, Atomic-scale confinement at the graphene/SiC interface: A platform for novel two-dimensional nanomaterials, J. Vac. Sci. Technol. A 44, 030802 (2026).
- E. Pompei, K. Skibińska, G. Senesi, Y. Vlamidis, A. Rossi, S. Forti, C. Coletti, F. Beltram, S. Rubini, L. Sorba, S. Heun, and S. Veronesi, Novel structures of gallenene intercalated in epitaxial graphene, Small 21, e05640 (2025).
- N. Briggs, B. Bersch, Y. Wang, J. Jiang, R. J. Koch, N. Nayir, K. Wang, M. Kolmer, W. Ko, A. De La Fuente Duran, S. Subramanian, C. Dong, J. Shallenberger, M. Fu, Q. Zou, Y.-W. Chuang, Z. Gai, A.-P. Li, A. Bostwick, C. Jozwiak, et al., Atomically thin half-van der Waals metals enabled by confinement heteroepitaxy, Nat. Mater. 19, 637 (2020).
- M. T. Wetherington, F. Turker, T. Bowen, A. Vera, S. Rajabpour, N. Briggs, S. Subramanian, A. Maloney, and J. A. Robinson, 2-dimensional polar metals: A low-frequency Raman scattering study, 2D Mater. 8, 041003 (2021).
- K. Zhang, R. A. Maniyara, Y. Wang, A. Jain, M. T. Wetherington, T. T. Mai, C. Dong, T. Bowen, K. Wang, S. V. Rotkin, A. R. H. Walker, V. H. Crespi, J. Robinson, and S. Huang, Tunable phononic quantum interference induced by two-dimensional metals, Sci. Adv. 11, eadw1800 (2025).
- A. Jain, B. Zheng, S. Datta, K. Ulman, J. Henz, M. W.-J. Liu, V. D. Pham, W. He, C. Dong, L.-S. Lu, A. Vera, N. Sawtarie, W. Auker, K. Wang, B. Hengstebeck, Z. W. Henshaw, S. Mathela, M. T. Wetherington, W. H. Blades, K. Knappenberger, et al., Defect-mediated phase engineering of 2D Ag at the graphene/SiC interface, arXiv:2511.07151.
- M. W.-J. Liu, K. A. Ulman, B. Zheng, A. Jain, D. J. Heintzelman, K. Wang, W. He, C. Dong, L.-S. Lu, V. H. Crespi, S. Y. Quek, J. A. Robinson, and K. L. J. Knappenberger, Structure-dependent electronic relaxation dynamics of two-dimensional silver monolayers, Nano Lett. 25, 17145 (2025).
- C. Dong, L.-S. Lu, Y.-C. Lin, and J. A. Robinson, Air-stable, large-area 2D metals and semiconductors, ACS Nanosci. Au 4, 115 (2024).
- V. Ramachandran, M. F. Brady, A. R. Smith, R. M. Feenstra, and D. W. Greve, Preparation of atomically flat surfaces on silicon carbide using hydrogen etching, J. Electron. Mater. 27, 308 (1998).
- S. Soubatch, S. E. Saddow, S. P. Rao, W. Lee, M. Konuma, and U. Starke, Structure and morphology of 4H-SiC wafer surfaces after -etching, Mater. Sci. Forum 483-485, 761 (2005).
- 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).
- C. Riedl, C. Coletti, and U. Starke, Structural and electronic properties of epitaxial graphene on SiC(0001): A review of growth, characterization, transfer doping and hydrogen intercalation, J. Phys. D 43, 374009 (2010).
- S. Forti and U. Starke, Epitaxial graphene on SiC: From carrier density engineering to quasi-free standing graphene by atomic intercalation, J. Phys. D 47, 094013 (2014).
- K. V. Emtsev, F. Speck, T. Seyller, L. Ley, and J. D. Riley, Interaction, growth, and ordering of epitaxial graphene on SiC0001 surfaces: A comparative photoelectron spectroscopy study, Phys. Rev. B 77, 155303 (2008).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/rgn3-rnbh for additional details.
- Y. Liu, X. Liu, C.-Z. Wang, Y. Han, J. W. Evans, A. Lii-Rosales, M. C. Tringides, and P. A. Thiel, Mechanism of metal intercalation under graphene through small vacancy defects, J. Phys. Chem. C 125, 6954 (2021).
- B. Matta, P. Rosenzweig, K. Küster, C. Polley, and U. Starke, Pb-intercalated epitaxial graphene on SiC: Full insight into band structure and orbital character of interlayer Pb, and charge transfer into graphene, Phys. Rev. B 111, 155435 (2025).
- S. Fiori, Y. Murata, S. Veronesi, A. Rossi, C. Coletti, and S. Heun, Li-intercalated graphene on SiC(0001): An STM study, Phys. Rev. B 96, 125429 (2017).
- P. Schädlich, C. Ghosal, M. Stettner, B. Matta, S. Wolff, F. Schölzel, P. Richter, M. Hutter, A. Haags, S. Wenzel, Z. Mamiyev, J. Koch, S. Soubatch, P. Rosenzweig, C. Polley, F. S. Tautz, C. Kumpf, K. Küster, U. Starke, T. Seyller, et al., Domain boundary formation within an intercalated Pb monolayer featuring charge-neutral epitaxial graphene, Adv. Mater. Interfaces 10, 2300471 (2023).
- S. Chen, P. A. Thiel, E. Conrad, and M. C. Tringides, Growth and stability of Pb intercalated phases under graphene on SiC, Phys. Rev. Mater. 4, 124005 (2020).
- C. M. Polley, M. Leandersson, J. Adell, J. Osiecki, D. Carbone, K. Ali, H. Fedderwitz, and T. Balasubramanian, The Bloch beamline at MAX IV: Micro-spot ARPES from a conventional, full-featured beamline, Synch. Radiat. News 37, 18 (2024).
- A. Varykhalov, -ARPES: The ultra-high-resolution photoemission station at the U112-PGM-2a- beamline at BESSY II, JLSRF 4, A128 (2018).
- 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).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- 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).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- V. Popescu and A. Zunger, Extracting E versus effective band structure from supercell calculations on alloys and impurities, Phys. Rev. B 85, 085201 (2012).
- Q. Zheng, VaspBandUnfolding Python scripts for VASP band unfolding and wave-function analysis, GitHub repository (2026), https://github.com/QijingZheng/VaspBandUnfolding.
- J. P. Perdew, Density functional theory and the band gap problem, Int. J. Quantum Chem. 28, 497 (1985).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)], J. Chem. Phys. 124, 219906 (2006).
- M. P. Seah and W. A. Dench, Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids, Surf. Interface Anal. 1, 2 (1979).
- U. Starke and C. Riedl, Epitaxial graphene on SiC(0001) and : From surface reconstructions to carbon electronics, J. Phys.: Condens. Matter 21, 134016 (2009).
- V. D. Pham, B. Zheng, A. Jain, C. Dong, L.-S. Lu, Z. W. Henshaw, W. H. Blades, J. A. Robinson, V. H. Crespi, A. Trampert, and R. Engel-Herbert, Strain-induced reconstruction in two-dimensional silver intercalated between graphene and SiC, Phys. Rev. Mater. 10, 034003 (2026).
- J. A. Bearden and A. F. Burr, Reevaluation of X-ray atomic energy levels, Rev. Mod. Phys. 39, 125 (1967).
- J. Yu, S. Ye, X. Xv, L. Pan, P. Lin, H. Liao, and D. Wang, Thermal-driven formation of silver clusters inside Na/Li FAUY zeolites for formaldehyde detection, Nanomaterials 12, 3215 (2022).
- J. J. Yeh and I. Lindau, Atomic subshell photoionization cross sections and asymmetry parameters: 1 Z 103, At. Data Nucl. Data Tables 32, 1 (1985).
- J. J. Olivero and R. L. Longbothum, Empirical fits to the Voigt line width: A brief review, J. Quant. Spectrosc. Radiat. Transf. 17, 233 (1977).
- A. V. Naumkin, A. Kraut-Vass, S. W. Gaarenstroom, and C. J. Powell, NIST X-ray photoelectron spectroscopy database (SRD 20), National Institute of Standards and Technology, Gaithersburg, MD, 2026.
- W. Lee, Y. Wang, W. Qin, H. Kim, M. Liu, T. N. Nunley, B. Fang, R. Maniyara, C. Dong, J. A. Robinson, V. H. Crespi, X. Li, A. H. MacDonald, and C.-K. Shih, Confined monolayer Ag as a large gap 2D semiconductor and its momentum resolved excited states, Nano Lett. 22, 7841 (2022).
- U. Starke, Atomic structure of hexagonal SiC surfaces, Phys. Status Solidi B 202, 475 (1997).
- U. Starke, J. Schardt, J. Bernhardt, M. Franke, and K. Heinz, Stacking transformation from hexagonal to cubic SiC induced by surface reconstruction: A seed for heterostructure growth, Phys. Rev. Lett. 82, 2107 (1999).
- W. Ku, T. Berlijn, and C.-C. Lee, Unfolding first-principles band structures, Phys. Rev. Lett. 104, 216401 (2010).
- P. Rosenzweig, H. Karakachian, D. Marchenko, K. Küster, and U. Starke, Overdoping graphene beyond the Van Hove singularity, Phys. Rev. Lett. 125, 176403 (2020).
- B. Matta, P. Rosenzweig, C. Polley, U. Starke, and K. Küster, Charge transfer between van der Waals coupled metallic 2D layers, Nanoscale 17, 19317 (2025).
- A. L. Walter, A. Bostwick, K.-J. Jeon, F. Speck, M. Ostler, T. Seyller, L. Moreschini, Y. J. Chang, M. Polini, R. Asgari, A. H. MacDonald, K. Horn, and E. Rotenberg, Effective screening and the plasmaron bands in graphene, Phys. Rev. B 84, 085410 (2011).
- J. Lischner, D. Vigil-Fowler, and S. G. Louie, Physical origin of satellites in photoemission of doped graphene: An ab initio plus cumulant study, Phys. Rev. Lett. 110, 146801 (2013).
- A. Pramanik, S. Thakur, B. Singh, P. Willke, M. Wenderoth, H. Hofsäss, G. Di Santo, L. Petaccia, and K. Maiti, Anomalies at the Dirac point in graphene and its hole-doped compositions, Phys. Rev. Lett. 128, 166401 (2022).
- Y. Qi, S. H. Rhim, G. F. Sun, M. Weinert, and L. Li, Epitaxial graphene on SiC(0001): More than just honeycombs, Phys. Rev. Lett. 105, 085502 (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).
- J. M. Luttinger and J. C. Ward, Ground-state energy of a many-fermion system. II, Phys. Rev. 118, 1417 (1960).
- J. M. Luttinger, Fermi surface and some simple equilibrium properties of a system of interacting fermions, Phys. Rev. 119, 1153 (1960).
- (N.B.) We note a small difference in the extracted bare Dirac point energy depending on the analysis method: linear extrapolation of the MDC-derived dispersion yields eV, whereas the EDC analysis gives eV. For the determination width of the diamond, we follow the standard procedure and normalize using the value obtained from the EDC analysis. The discrepancy between the two estimates is likely related to the strong plasmaron-induced renormalization in the immediate vicinity of the Dirac point, which can shift the apparent crossing in linear extrapolations. A similar offset of values is also observed for the -intercalated sample.
- (N.B.) For -QFMLG, the Dirac points extracted from our MDC-based linear extrapolation, and , are consistent with the values reported in Ref. [14]. However, due to experimental constraints in the present measurements, the Dirac cone features are broader, which reduces the precision of the normalized plasmaron-diamond analysis and the resulting plasmaron width. Since and agree with Ref. [14], we assume the corresponding plasmaron width to be unchanged and therefore adopt the same effective coupling constant and dielectric constant as reported there.