STALEMATE

In the C square grid, one has a 2D

Brillouin zone with high symmetry

points labelled G, X, M, G in the

band structure of the material.

If one explores the crystal orbitals

at these purely real points in the BZ,

and particularly at high symmetry

point labelled M, one sees in fact

for the pi band, one has an in-phase

orbital in a given unit cell, surrounded

on the sides by out-of-phase orbitals

in adjacent unit cells, and in-phase

orbitals on unit cells lying diagonally

disposed to the parent unit cell.Thus

the square grid, in a p-orbital basis

exhibits a checkerboard square type

of pattern, and there is nothing you can

do anymore. The in-phase p-orbitals

symbolize angels in crystalline direct space,

and the out-of-phase p-orbitals symbolize

devils in the crystalline direct space of the

square grid of C. It is, indeed, as if the angels

and the devils are held into a kind of virtual

stalemate at symmetry point M of the BZ