Brillouin zones and the E-k relation

[hhhmortal]

Hi, I'm having some trouble to fully understand how energy bands are formed in Brillouin zones.

Almongst a few of the questions I have are:

In a 2D plane of atoms, where a is the lattice constant in the x-direction and 1.5a in the y-direction. Would the brillouin zone edge in the k_y direction now simply be -pi/1.5a, pi/1.5a ?

Does the first energy gap occur between reciprocal lattice vector G_1 and G_4? And why does G_4 have a higher energy, I'm trying to visualise this in terms of the propagation of the electron wave in the 2D plane.

Thanks.

 

[johng23]

Well for the first part, if it's cubic, then yes that's right.

For the second part, I'm not sure about the terminology. What do you mean by G1 and G4? I am familiar with denoting reciprocal lattice vectors by Ghkl (or I guess two indices in your case).