= Solution
An <angle-resolved photoemission spectroscopy> intensity map locates occupied <electronic band structure> through its bright dispersing ridges. For a nearly isotropic <graphene> cone,
$$
E_\pm(\mathbf q)=E_D\pm\hbar v_F|\mathbf q|,\qquad
\boxed{v_F=\frac1\hbar\left|\frac{dE}{dk}\right|.}
$$
Fit straight lines to the reasonably linear portions of the ridges, avoiding the broad central crossing, and extrapolate them to locate the <Dirac point> energy $E_D$. The PDF places the crossing near $k_y=0$ and plotted energy roughly $1.4$–$1.5\,\mathrm{eV}$. On a lower branch, a representative change from approximately $(|k_y|,E)=(0.10\,\mathrm{\mathring A}^{-1},0.9\,\mathrm{eV})$ towards $(0,1.5\,\mathrm{eV})$ gives a slope near $6\,\mathrm{eV\,\mathring A}$. Allowing for the ridge width gives about $5$–$7\,\mathrm{eV\,\mathring A}$, hence
$$
\boxed{v_F\simeq(0.8\text{--}1.1)\times10^6\,\mathrm{m\,s^{-1}},\quad\text{approximately }10^6\,\mathrm{m\,s^{-1}}.}
$$
Here $1\,\mathrm{eV\,\mathring A}/\hbar=1.52\times10^5\,\mathrm{m\,s^{-1}}$.
To determine the carrier <Fermi energy>, identify the <Fermi level> from a calibrated photoemission cutoff, then measure its separation from the Dirac point:
$$
\boxed{E_F^{\rm cone}=|E_{\rm F,plot}-E_D|=\hbar v_F k_F,\qquad p_F=\hbar k_F.}
$$
The separation of the two Fermi crossings gives $2k_F$ for a cut through the cone centre. This determines the doping energy relative to the Dirac point; the absolute plotted energy origin is not itself a Fermi energy.
\b[The reproduced panel has no marked Fermi level or stated energy-zero calibration.] Its upper ridges end near $1.9\,\mathrm{eV}$, but that alone does not prove that the endpoint is a Fermi cutoff. If it is the intended cutoff, the estimate is $E_F^{\rm cone}\simeq0.4$–$0.5\,\mathrm{eV}$ and $k_F\sim0.06$–$0.08\,\mathrm{\mathring A}^{-1}$. If instead the plotted numbers are binding energies measured from an unstated Fermi zero, the inferred separation would be roughly $1.4$–$1.5\,\mathrm{eV}$. The supplied figure securely supports the slope estimate, but it does not distinguish these energy-reference conventions; an unconditional numerical Fermi energy requires the missing calibration.
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