May 19, 2008

Fig. 1: Real (blue) and imaginary (red) parts
of the graphene spin susceptibility as a function of
frequency for various values of q. Top: Four values
of q from 0 to half a reciprocal lattice
vector, or 2π/3 in the direction of a bond. Bottom:
Four values of q from 2π/3 to 4π/3 in the same
direction. The computer code that generated this graph is
available here. I plotted using
gnuplot. The plot file is shown
here. |

This report shows how the calculation for graphene's density of states described in my previous report can be modified to generate the spin susceptibility

It is functionally the same calculation except for inclusion of the matrix element

where we have as before

As a practical matter we first compute the imaginary part

where sgn denotes the sign, and then hilbert transform

The LaTeX source for the above equations is available here.