Nature of the surface states at the single-layer graphene/Cu(111) and graphene/polycrystalline-Cu interfaces

S. Pagliara, S. Tognolini, L. Bignardi, G. Galimberti, S. Achilli, M. I. Trioni, W. F. van Dorp, V. Ocelík, P. Rudolf, and F. Parmigiani

Phys. Rev. B 91, 195440 – Published 27 May 2015

Abstract

Single-layer graphene supported on a metal surface has shown remarkable properties relevant for novel electronic and optoelectronic devices. However, the nature of the electronic states derived from unoccupied surface states and quantum well states, lying in the real-space gap between the graphene and the solid surface, has not been explored and exploited yet. Herein, we use ultraviolet nonlinear angle-resolved photoemission spectroscopy to unveil the coexistence at the graphene/Cu(111) interface of a highest occupied Shockley surface state (HOSS) and the two lowest unoccupied surface states (LUSS). The experimental results and electronic structure calculations, based on one-dimensional model potential, indicate that the two unoccupied states originate from the hybridization of an $n = 1$ image potential state with a quantum well state. The hybridized nature of these unoccupied states is benchmarked by a similar experiment done on single-layer graphene grown on copper polycrystalline foil where only the image state survives being the quantum well state at this interface inhibited.

Received 9 June 2014
Revised 16 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.195440

Authors & Affiliations

S. Pagliara¹, S. Tognolini¹, L. Bignardi^2,*, G. Galimberti¹, S. Achilli³, M. I. Trioni³, W. F. van Dorp², V. Ocelík², P. Rudolf², and F. Parmigiani^4,†

¹I-LAMP and Dipartimento di Matematica e Fisica, Università Cattolica, 25121 Brescia, Italy
²Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747AG Groningen, The Netherlands
³Dipartimento di Chimica, Università degli Studi di Milano and CNR-ISTM, via Golgi 19, 20133 Milano, Italy
⁴Università degli Studi di Trieste - Via A. Valerio 2, Trieste 34127, Italy Elettra - Sincrotrone Trieste S.C.p.A, Strada Statale 14, km 163.5, 34149 Basovizza, Trieste, Italy International Faculty - University of Köln, Germany

^*Current address: Physikalisches Institut, University of Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany (DE).
^†fulvio.parmigiani@elettra.trieste.it

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Issue

Vol. 91, Iss. 19 — 15 May 2015

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Images

Figure 1
(a) Representative Raman spectrum of graphene/Cu(111) and of HOPG. The relevant peaks of the graphene spectrum are marked. The excitation wavelength employed was $λ = 633$ nm. (b) Low-energy electron diffraction pattern of graphene/Cu(111) collected with a primary beam energy of 80 eV.
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Figure 2
(a) Electron back scattering diffraction map acquired on a graphene grown on Cu foil sample. (b) Orientation distribution of the image reported in (a). The dominant crystalline orientation is (001).
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Figure 3
(a) Photoemission processes (arrows) from the Cu $d$ band and from the surface states (HOSS, LUSS1, LUSS2, see text) at the single-layer graphene/Cu(111) interface. (b) Nonlinear photoemission spectrum obtained by using the experimental setup shown in (c), at normal emission $(k_{∥} = 0)$ and with a photon energy of 4.10 eV. The HOSS, LUSS1, and LUSS2 emissions, observed with $p$ -polarized light, are completely quenched in the $s$ -polarized light spectrum.
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Figure 4
(a) Linear photoemission spectrum collected at normal emission $(k_{∥} = 0)$ with a photon energy of 6.28 eV and $p$ -polarized light at the single-layer graphene/Cu(111) interface. (b) Energy position vs $k_{∥}$ momentum for the Shockley surface state measured at $h ν = 6.28$ eV. A parabolic fit (line) gives an effective mass of $0.45 \pm 0.05 m_{E}$ . (c) Single-layer graphene/Cu(111) nonlinear photoemission spectra measured at normal emission $(k_{∥} = 0)$ in $p$ and $s$ polarization and 4.1 eV photon energy. The $p$ -polarized spectrum results well interpolated by three structures. (d) Energy position vs $k_{∥}$ momentum for the Shockley surface state (HOSS), LUSS1, and LUSS2 interface states measured at $h ν = 4.10$ eV photon energy. The effective masses reported in the figure are obtained from the parabolic fit (line) of the measured band dispersion.
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Figure 5
Comparison between nonlinear photoemission spectra measured at $k_{∥} = 0$ using $p$ -polarized laser pulses at $h ν = 4.10$ eV on graphene grown on polycrystalline Cu foil and on clean Cu foil. The emission measured from the single-layer graphene on the Cu foil detected in the 7.0–8.5 eV ${E-E}_{F}$ energy region is well fitted by a single Lorentzian and a Fermi-Dirac function. The inset shows the single-layer graphene/Cu-poly foil LUSS band dispersion. The effective mass for this state is deduced from the parabolic fit (solid line) of the ARPES data.
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Figure 6
(a) One-dimensional potential used to simulate the graphene/Cu(111) interface. (b) The calculated density of states (DOS) points out the presence of three states whose binding energies are comparable with the HOSS, LUSS1, and LUSS2 binding energies measured in the two-photon photoemission spectrum of Fig. 3. In (c), the probability amplitude of HOSS, LUSS1, and LUSS2 states is plotted.
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