Observation of intercalation-driven zone folding in quasi-free-standing graphene energy bands

Two-photon photoemission measurements reveal a near-zero-dispersion empty electronic state, approximately 2.6 eV above the Fermi energy and near the Brillouin zone center, induced by oxygen intercalation at the graphene-Ir(111) interface. While oxygen intercalation leads to quasi-free-standing graphene, electron diffraction shows $2\times 2$ periodicity due to the patterned intercalant. Near the zone center, large-wave-vector zone folding, driven by this $2\times 2$ periodicity, replicates states from near the Dirac cone that have little dispersion due to trigonal warping, explaining the nearly flat band. The zone-folding mechanism is supported by results from angle-resolved photoemission measurements and from density-functional-theory-based calculations of the unfolded energy bands. These results demonstrate zone-folding effects in graphene on a wave vector and energy scale that has largely been unexplored, and may open new opportunities to engineer the graphene electronic states.

Figure 1

LEED patterns of (a) Gr/Ir and (b) Gr/O/Ir. Iridium, graphene, and oxygen sublattices are highlighted by a dashed rhombus in yellow, red, and blue, respectively. AR-2PPE spectra (panel right) and their second derivatives with respect to energy (panel left) using the final-state energy scale ($\hslash \omega =4.66\mathrm{eV}$) for (c) preintercalated Gr/Ir, (d) intercalated Gr/O/Ir along $\mathrm{\Gamma }\text{−}M$. (e) Energy distribution curve at the $\mathrm{\Gamma }$ point for $p$- and $s$-polarized incident photons for Gr/O/Ir. Inset: final-state energy of the nearly flat band identified in (d) versus incident photon energy with a linear fit. (f) Energy diagram illustrating intermediate states probed by the second photon excitation, particularly the nearly flat band, in Gr/O/Ir with energy referred to the Fermi energy. The shaded areas present the momentum space accessible in our 2PPE experiments.

Figure 2

Supercells used for calculations: (a) $\mathrm{Gr}(9\times 9)/\mathrm{Ir}(8\times 8)$ and (b) $\mathrm{Gr}(9\times 9)/\mathrm{O}(2\times 2)/\mathrm{Ir}(8\times 8)$. Yellow arrows denote the dominant periodicity. Illustration of representative replicas from zone folding for the $\mathrm{\Gamma }\text{−}M$ line for (c) Gr/Ir and (d) $\mathrm{Gr}/\mathrm{O}(2\times 2)/\mathrm{Ir}$ in the $1\times 1$ graphene Brillouin zone. (e), (f) Color coded maps in the graphene Brillouin zone illustrating selected replicas induced by band folding by the stars of vectors illustrated in (c) and (d) and corresponding to the Gr/Ir and $\mathrm{Gr}/\mathrm{O}(2\times 2)/\mathrm{Ir}$ cases, respectively. $\mathrm{\Gamma }\text{−}K$ and $\mathrm{\Gamma }\text{−}{K}^{\prime }$ lines are not formally equivalent and highlighted points are distinguished by light and dark shades. $K^{\prime }$ folds to close to the midpoint of the $\mathrm{\Gamma }\text{−}K$ line.

Figure 3

Calculated spectral weights showing the unfolded, graphene $\pi$-state band structure for (a) Gr/Ir and (b) $\mathrm{Gr}/\mathrm{O}(2\times 2)/\mathrm{Ir}$ in false color on a logarithmic scale. (c) Magnification of the calculated spectral weight within the dashed white rectangle area in (a). In (a), (b), and (c), superposed lines show the pure graphene $\pi$-state bands $E_n\left(\mathbf{k}\right)$ (solid lines) and the replicas induced by zone folding from the star of superlattice reciprocal lattice vectors $E_n(\mathbf{k}+{\mathbf{g}}_{\mathit{i}})$, as illustrated in Figs. 2 and 2, respectively (dashed lines). (d) Brillouin zones of graphene primitive cell with red lines indicating the path along which electronic states were calculated. (e) Calculated pure graphene ${\pi }^{*}$ band, shifted in energy to align the Dirac point to the $p$-doped scenario in (b), also represented by constant energy contours (green curves) with Brillouin zone designations (black lines). A cut through the energy band is highlighted in red, corresponding to representative regions that are replicated by zone folding in Fig. 2, resulting in the band with near-zero dispersion.

Figure 4

(a)–(d) Calculated spectral weight versus energy with Gaussian broadening (0.3 eV HWHM) for the graphene $\pi$ band in Gr/Ir(111) (black) and $\mathrm{Gr}/\mathrm{O}(2\times 2)/\mathrm{Ir}\left(111\right)$ (blue) at selected points in the graphene Brillouin zone: (a) $M$ point, (b) $\mathrm{\Gamma }$ point, (c) halfway along $\mathrm{\Gamma }\text{−}K$, and (d) $K$ point. Arrows, color coded to indicate the origin of the zone-folding following Fig. 2, highlight extra spectral intensities due to zone-folding effects in the $2\times 2$ oxygen intercalated case.

Figure 5

(a)–(f) ARPES spectra of Gr/O/Ir, Gr/Ir, and O/Ir samples along the $\mathrm{\Gamma }\text{−}M$ and $\mathrm{\Gamma }\text{−}K$ directions. Each panel shows a false color map of raw data (right) and the second derivative with respect to energy (left). Red dashed lines show the calculated $\pi$ bands of free-standing graphene.

Figure 6

(a)–(d) ARPES energy distribution curves (EDCs) for Gr/O/Ir, O/Ir, and Gr/Ir samples at selected points in the graphene Brillouin zone: (a) $M$ point, (b) $\mathrm{\Gamma }$ point, (c) halfway along $\mathrm{\Gamma }\text{−}K$, and (d) $K$ point. Arrows indicate the extra spectral intensities predicted due to zone-folding effects induced by a $2\times 2$ potential perturbation.