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It is common for students to use modern electronic structure codes (ESC) as black-boxes with little conceptual understanding of the underlying theoretical and computational details of the main components involved. What are needed are simplified problems that illustrate these concepts and are easily coded by senior undergraduate students.
An important concept in solid state physics is the first Brillouin zone (BZ) which uniquely determines the electronic energies and wavefunctions for electrons in a periodic potential. ESC calculate material properties using integrations over this zone. Higher order zones are also important; the BZ boundaries define Bragg planes and the constant energy Fermi surface for metals sometimes cross these planes. The shape of this surface is important in determining many metal properties and low energy interactions. Students can write a small code, in a language of their choice, that implements a simple algorithm to sort k-points into their respective Brillouin zones for any crystal lattice.
Using this algorithm, we visualize BZ of any order as well as deconstruct the Fermi surface for metals if it extends into higher order zones using the reduced-zone scheme. Visualizations are produced using the freely available plotting programs grace and gnuplot. We present results for 2D and 3D.
