Brillouin Zone of a 2D Square Lattice: Tight Binding Approximation

extend BZ

1

2

3

4

show mesh
show box

show axes
cut segment in BZ

quality

low

medium

high

colors

Rainbow

plot

contour

density

pseudo3D

3D view

default

above

front

for comparison:

lattice

square

linear

lattice  lattice electron dispersion

square free electron dispersion

linear  Dirac-electron dispersion

This Demonstration considers the Brillouin zone (BZ)

s

-band dispersion relations for a two-dimensional square crystal lattice under the tight binding approximation. Plots are shown for the first energy

s

-band dispersion in the first and extended Brillouin zones. You can compare the parabolic dispersion curves of free electrons in free space and the linear dispersion curves of Dirac-electrons (as in graphene at

K

-points).