# Quantum Hall Effect and Edge States

In quantum hall effect we measure the hall conductance (in transverse direction) which is quantized. My question how do they take care of the edge states that are in the longitudinal side?

• Who are they? The experimentalists measuring the Hall resistance? – DaniH Dec 28 '13 at 12:37

So, when the experimentalist measure the "longitudinal voltage" they hook up the voltmeter to a single edge (see the voltmeter next to the $R_L$ in the link). Since a single edge is in equilibrium the voltmeter reads zero voltage (a voltmeters really measures the chemical potential difference between two points). This measurement is a convention for defining the longitudinal resistance, and in a quantum Hall plateau it gives zero.
On the other hand the transverse resistance or Hall resistance is measured (or “defined” if you wish) by hooking up the voltmeter between the two edges that are not in equilibrium (see the voltmeter next to the $R_L$ in the link). Since each of them is in equilibrium with the source and drain separately, the voltmeter reading will coincide with the source to drain chemical potential difference, and its ratio with the measured source to drain current will give the amazingly accurately quantized values that people see in the Hall plateaus.