Density of states of a graphene crystal in the tight-binding approximation

The density of states was calculated by taking 6.7 × 106 evenly distrubuted points in the first Brillouin zone, calculating the energy of the points, and plotting the distribution of the resulting energies. Since there are 2 states per atom, the integral of the density of states in units of eV-1 atom-1 over all states should be 2.

D(E) [1/(eV atom)] 

E [eV]


ε =


t =


 area of the unit cell =


 valence electrons per unit cell =


The tight-binding calculation for atoms arranged in a 2-d crystal like graphene can be found here. In this calculation, ε and t are arbitrary parameters. For graphene, ε = 0, t = 2.8 eV, and the area of a unit cell 5.245×10-20 m-2. The Matlab file used to generate the density of states is graphenedos.m.

The density of states is tabulated in eV-1 atom-1 and eV-1 m-2 below. The data in the right column can be copied and pasted into one to the pages that calculate the temperature dependence of thermodynamic quantities.