Electrons in a 2D lattice: Energy contours and density of states

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This JAVA applet calculates the energy contours for the electrons in a 2 dimensional, hexagonal lattice. The energy band is represented by a tight binding approximation:

E=-2 t (2 cos 0.5k_xa * cos 0.866k_ya + cos k_xa) + 2 t' (2 cos 0.866k_ya * cos 1.5k_xa + cos 1.73k_ya),

where a is the lattice spacing. On the plots the energy is measured in units of the nearest neighbor overlap integral t. t' is the the overlap integrals to second neighbor atoms. For any physical situation t'/t is always less than 1 and for larger values the plots may not get drawn at all.

The density of states is plotted on the right hand side. In order to save computing time, the DOS is calculated on a rather crude grid, resulting in the loss of fine details.

Finally, the Fermi energy (represented by red contour lines on the plot) can be specified. The corresponding band occupancy is calculated.

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