Coexistence of sharp quasiparticle dispersions and disorder features in graphite

Angle resolved photoelectron spectroscopy (ARPES) on azimuthally disordered graphite demonstrates that sharp quasiparticle dispersions along the radial direction can coexist with a complete lack of dispersion along the azimuthal direction. This paradoxical coexistence can be explained in terms of van Hove singularities in the angular density of states. In addition, nondispersive features at the energies of band maxima and saddle points are observed and possible explanations are discussed. This work opens a possibility of studying the electronic structure of layered materials using ARPES even when large single crystals are difficult to obtain.

Figure 1

(a) Fermi energy intensity map. The hexagonal Brillouin zone (dashed lines) and Fermi surface (shaded circles) expected for single crystalline graphite are drawn schematically. (b) Intensity map vs binding energy and in-plane momentum along the solid line in (a) taken at $60\mathrm{eV}$ photon energy. Arrow marks the Fermi energy crossing point $\left(k_F\right)$. The inset shows energy distribution curve (EDC) at $k_F$ taken at $25\mathrm{eV}$ photon energy in the high angular resolution (0.1°) mode. (c) Second derivative of raw data in (b) with respect to energy. Local density approximation (LDA) dispersions along both $\Gamma \text{−}{\rm K}\text{−}{{\rm M}}^{\prime }$ direction (solid lines) and $\Gamma \text{−}{\rm M}\text{−}{\Gamma }^{\prime }$ direction (dashed lines) are plotted for comparison. The Brillouin zones are labeled on top of this panel for the two high symmetry directions.

Figure 2

Dispersions for azimuthal angles $\varphi =0°$ (panel a); 10° (panel b); and 20° (panel c). The $\varphi$ angle is defined in the inset of panel a. LDA band dispersions along $\Gamma \text{−}{\rm K}\text{−}{{\rm M}}^{\prime }$ (solid lines) and $\Gamma \text{−}{\rm M}\text{−}{\Gamma }^{\prime }$ (dotted lines) are plotted for comparison. (d) Calculated dispersions for single crystalline graphite along an arc (shown in the inset) with radius equal to $\Gamma {\rm K}$ distance. (e) Calculated density of states $D_{\varphi }\left(E\right)$ for single crystalline graphite by integrating over an arc from $A$ to $B$ (see inset of panel d). Singular peaks in $D_{\varphi }\left(E\right)$ occur at energies corresponding to band energy extrema, some of which are shown in panel (c,d) as shaded circles and open circles for $A$ ($\Gamma {\rm K}$ direction) and $B$ ($\Gamma {\rm M}$ direction), respectively.

Figure 3

(a) First derivative of raw data taken at $55\mathrm{eV}$ photon energy. (b) EDCs at $\Gamma$ point (thin line) and $k_{\Vert }=0.4{\mathrm{\AA }}^{-1}$ (thick line). The positions of these two cuts are shown as dotted lines in a. (c) EDCs for the momentum range indicated by a horizontal white line (from $k_1$ to $k_{12}$), marked in panel a.