Integer quantum hall effect between any two points in the system

The Hall current flowing across an arbitrary curve connecting any two points selected in a high mobility, dissipation free, integer quantum Hall system shows quantised nature with respect to the potential difference between the two points. The Hall conductance can therefore be defined between any two points in the sample. For a given system, the behaviour of this Hall conductance depends on the potential difference between the two selected points only. The overall quantum Hall behaviour can be derived in a special case when the two points are selected at the Hall contacts.