# Plotting a bandstructure along High-symmetry points when kx,ky,kz is known

Suppose you know kx,ky,kz points along with the corresponding energies. Basically, you know about the 4-D E(k) dispersion.

How you do then convert that data into the bandstructure plots you commonly see which show E(k) along a closed path through high-symmetry points through the Brillouin zone?

As you move though the paths between the high-symmetry points you calculate the E($\vec{k}$) where is a vector of $k_{x}$,$k_{y}$,$k_{z}$. To map the movement along the paths between the HSP you start with $\Gamma$ at (0,0,0) and the first point along the path, say from $\Gamma$-$X$ you add the length between your first point,in this case (0,0,0), to the next point you calculated E($\vec{k}$). For the first point after $\Gamma$ you would do $|\vec{k}_{1}-\vec{k}_{0}|$ which is just the length of $\vec{k}_{1}$ since $\Gamma$ is always (0,0,0). The next point is $|\vec{k}_{1}-\vec{k}_{0}|$ + $|\vec{k}_{2}-\vec{k}_{1}|$. So the abscissa is the length between the points and the ordinate is the Energy at each point along the lines connecting HSP. So $\Gamma-X-M-\Gamma-R-X$|$M-R$ for simple cubic. Be careful when you reach the end of the first path and begin the second because they are not continuous as you move though the Bravais Lattice.