Johan Félisaz

Brillouin zone visualization

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: ${\vec{a}}_{i} \cdot {\vec{b}}_{j} = 2 π δ_{i j}$

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.