Conductor with high electron mobility (mean free path)

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FusionJim
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Hello,

I want to know whether there exists a solid material that would have a conductivity similar to say copper or aluminum but where the "free electrons" aka conduction electrons would be free to move in one dimension.

Imagine a rectangular sheet of such material, suppose we have an electron current through the material. This current travels down the sheet vertically from the upper edge to the lower , meanwhile in the other dimension (the horizontal plane) it can move freely from left to right or vice versa.
When I say freely I mean where each electron has a large mean free path so an applied electric or magnetic field could make the vertical current sweep horizontally fast.

In general I am asking whether there is any such practical material that is solid state and also a good conductor (excluding some rare materials in rare parameter ranges like at or close to absolute zero , quantum effects and such) that can have a large mean free path for conduction electrons so that the spatial location of current within such material could be controlled?

From what I have read graphene comes close with large mean free path for electrons and given how thin a monolayer of graphene is the electrons can be controlled by an applied E field , but graphene at least for now doesn't look practical , and its single layer conductivity is also much worse than that of known commercially used conductors.
Although maybe I am wrong.
Appreciate your input.
 
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Electrical conductivity anisotropic might be what you are looking for.