Sublattice Interference as the Origin of $\sigma$ Band Kinks in Graphene

Kinks near the Fermi level observed in angle-resolved photoemission spectroscopy (ARPES) have been widely accepted to represent electronic coupling to collective excitations, but kinks at higher energies have eluded a unified description. We identify the mechanism leading to such kink features by means of ARPES and tight-binding band calculations on $\sigma$ bands of graphene, where anomalous kinks at energies as high as $\sim 4\mathrm{eV}$ were reported recently [Phys. Rev. Lett. 111, 216806 (2013)]. We found that two $\sigma$ bands show a strong intensity modulation with abruptly vanishing intensity near the kink features, which is due to sublattice interference. The interference induced local singularity in the matrix element is a critical factor that gives rise to apparent kink features, as confirmed by our spectral simulations without involving any coupling to collective excitations.

Figure 1

(a) Valence band structure of graphene along $k_{\mathrm{\Gamma }M}$ and $k_{\mathrm{\Gamma }K}$ directions, obtained from the tight-binding band calculations [30]. The shaded area represents projected substrate bands [31]. (b) 3D representation of two $\sigma$ bands for the boxed area in (a). The inset shows the Brillouin zone. Experimental ARPES spectra of $\sigma$ bands, taken at 15 K along (c) $k_{\mathrm{\Gamma }K}$ and (d) $k_{\mathrm{\Gamma }M}$ directions. Black curves overlaid are a fit with calculated dispersions based on the tight-binding model. The high-energy kink features are indicated by arrows.

Figure 2

(a)–(c) Constant-energy contours of tight-binding (TB) band calculations at binding energies marked at the bottom right. (d)–(f) Experimental ARPES intensity maps taken at corresponding binding energies with the photon energy of 36 eV. (g)–(i) Simulated ARPES intensity maps based on sublattice interference shown in Fig. 3. Overlaid lines are part of constant-energy contours shown in (a)–(c). The maximum intensity points in (d) and (g) slightly deviate from overlaid black lines due to the kink features.

Figure 3

The calculated interference-induced intensity maps for the $s$ orbital of (a) ${\sigma }_{\text{inner}}$ and (b) ${\sigma }_{\text{outer}}$ bands and for the $p$ orbital of (c) ${\sigma }_{\text{inner}}$ and ${\sigma }_{\text{outer}}$ bands. These maps are calculated based on the phase interference of initial-state wave functions coming from the two sublattices of graphene, as described in the text

Figure 4

(a) Matrix element as a function of $k$ obtained by curve fitting to ARPES data in Fig. 1. The red line overlaid is used for model simulations in (c). (b) Matrix elements in the form of $1–|1–k/k_0{|}^{\alpha }$, where $k_0=0.23{\AA }^{-1}$. (c)–(f) A series of spectral simulations using matrix elements shown in (a) and (b) and marked at the bottom right.