1-D crystal, one band

1-D crystal, two bands (trans-polyacetylene)

2-D square lattice

2-D hexagonal lattice

Graphene

2-D boron nitride

Carbon nanotubes

simple cubic 3-D

fcc

bcc

hexagonal

Dispersion relation

Density of states

Density of states

Fermi surface

Chemical potential

The density of states for graphene is symmetric around the Fermi energy so the chemical potential is nearly temperature independent.

The density of states for simple cubic is symmetric around the Fermi energy so the chemical potential is nearly temperature independent.

Internal energy distribution

Internal energy

The electronic contribution to the internal energy density is small for graphene since the density of states is zero at the Fermi energy.

Helmholtz free energy

Entropy

Specific heat

The specific heat for graphene is small because the density of states is zero at the Fermi energy.

Pressure

Bulk modulus