Question 1.1 of Drude model

Physics Q&A
1

In question 1.1 of the Drude model it is stated that the Hall voltage and Hall resistance do not depend on the geometry of the xy-sample. Now I do understand the independence of the width W, but the sample still does have a thickness H (eventhough incredibly small). So the current density would formally be j_x=\frac{I_x}{WH}. In the screenshot below, however, it is stated that j_x=\frac{I_x}{W}, which seems to be the current surface density K_x and not current density j_x. Eitherway, I thought the Hall resistance still does depend on the geometry, namely thickness H, is this reasoning correct? Hopefully someone could help me with resolving this confusion.

Thank you in advance.

Greetings,

Jelle

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{536AD0E5-0657-418E-A876-6B82DADA43C2}1087×476 22.8 KB

2

You are correct with both considerations. We are indeed considering surface current density, and indeed it doesn’t matter whether we would consider current density as long as thickness is kept fixed.

To add more context, usually, when talking about 2D materials (like quantum wells) people consider properties per unit length, not per unit cross-section.