# Johan Félisaz

## Brillouin zone visualization

Lattice

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### What's the Brillouin zone exactly ?

The Brillouin zone is an essential concept in condensed matter physics.

Recall that if a lattice is described by lattice vectors $$\vec a_1, \vec a_2, \vec a_3$$, the reciprocal lattice vectors are defined by the following 9 constraints: \begin{equation*} \vec a_i \cdot \vec b_j = 2\pi \delta_{ij} \end{equation*}

On this reciprocal lattice, the Brillouin zone is defined to be the set of all points closer to the origin that any other lattice points.