J. Dustan Stokes, Hari P. Dahal, Alexander V. Balatsky, Kevin S. Bedell
The virial theorem is applied to graphene and other Dirac Materials for
systems close to the Dirac points where the dispersion relation is linear. From
this, we find the exact form for the total energy given by $E =
\mathcal{B}/r_s$ where $r_s a_0$ is the mean radius of the $d$-dimensional
sphere containing one particle, with $a_0$ the Bohr radius, and $\mathcal{B}$
is a constant independent of $r_s$. This result implies that, given a linear
dispersion and a Coulombic interaction, there is no Wigner crystalization and
that calculating $\mathcal{B}$ or measuring at any value of $r_s$ determines
the energy and compressibility for all $r_s$. In addition to the total energy
we calculate the exact forms of the chemical potential, pressure and inverse
compressibility in arbitrary dimension.
View original:
http://arxiv.org/abs/1201.6424
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