3D and 2D reciprocal lattice vectors (Python example)

When I started using Density Functional Theory and, even more, when trying to re-create its results in a meaningful piece of material, like a nanoribbon or a nanowire, a lot of the problems came during geometry creation. This is natural, as DFT is a theory to derive quantities like eigenenergies, in a crystal lattice with periodicity. But when trying to switch to a model that is finite in one or more directions, you have to start a sort of mix and match procedure.

During this time (and assuming you are not the one who writes the software), visualizing vectors is maybe the less useful thing to do. Still, there are cases where you need it in order to get a better understanding of things, like visualizing Weyl points.

On the universality of Landau theories

There is a lot of buzz going on about topological materials and the quantum Hall effect these days that mark the 40 years since its discovery. If you know a few things about topological materials, you will definitely know that the theory behind them is about a macroscopic mechanism that originates from microscopic (quantum) effects.

There is a similar class of problems, maybe less famous at the present time, namely that of polarization in materials, which has its own counterpart “The modern theory of polarization” that was developed in the ’90s. What these two have in common is exactly the emergence of macroscopic phenomena from microscopic ones.