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## Main Question or Discussion Point

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

[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?

[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?