How does the length of a 2D conductor affect the transverse Hall resistance?

[siyuphysic]

I am reading a research note"quantum hall effect" from arxiv website. I'm told that the resistance of a 2D conductor depends in general on the so-called aspect ratio L/W via some factor f(L/W) . However, in the case of the transverse Hall resistance it is the length of the conductor itself that plays the role of the cross section, such that the Hall resistivity and the Hall resistance truly coincide, i.e. f = 1.

I don't really understand about the transverse hall resistance "the lenth of the condutor itself plays the role of cross section ".

 

[azntoon]

Can you explain a bit more about that? The transverse Hall resistance is an effect that occurs in two-dimensional conductors, such as those made from semiconductors. When a current is passed through the conductor, the current will flow in a direction perpendicular to the direction of the applied magnetic field. This results in a voltage drop across the conductor that is proportional to the length of the conductor (L). This transverse voltage drop is known as the Hall voltage and its magnitude is given by the expression VH = EH L, where EH is the Hall coefficient. The transverse Hall resistance is then given by RH = VH/I, where I is the current passing through the conductor. The Hall resistance is independent of the width (W) of the conductor, since it is only related to the length of the conductor. Therefore, in the case of the transverse Hall resistance, the length of the conductor plays the role of the cross section, such that the Hall resistivity and the Hall resistance truly coincide, i.e. f = 1.