I was looking at a derivation of the Landau levels in a crystal, and I had a question about the Landau gauge. The situation under consideration is a two dimensional system of non-interacting particles, exposed to a uniform magnetic field B directed along the z-axis (perpendicular to the plane of the two-dimensional system). In the ''Landau gauge,'' it is claimed that the vector potential can be written as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec{A} = - By \hat{x}[/tex].

I can see, however, that the vector potential

[tex] \vec{A} = - \frac{1}{2}B(x \hat{y} - y \hat{x}) [/tex]

would produce the same magnetic field. My questions are as follows. First, what is the Landau gauge? Secondly, does the selection of this gauge in this case correspond to the assumption that current flows in the x-direction?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question about the Landau gauge

**Physics Forums | Science Articles, Homework Help, Discussion**