Universal explicit expression for quantum Hall conductance at any temperatures and chemical potentials

Abstract

This paper generalises the theorem already obtained [Solid State Commun. 127 (2003) 505] for the high mobility, dissipationless, integer quantum Hall systems at T=0 K to the T>0 K situations. The results obtained are again suitable at both microscopic and macroscopic scales. In comparison [Solid State Commun. 127 (2003) 505], this generalised form gives a universal explicit expression for the Hall conductance σ xy ( μ, T) between any two points selected in such a system as a function of chemical potential and temperature. Further, thermal deviation Δ σ xy ( μ, T) from the exact quantised values of σ xy ( μ, T) and the minimum slopes of Hall plateaux in the T>0 cases, observed already in experiments, are also derived in theory. Similar to those in the T=0 K case [Solid State Commun. 127 (2003) 505], the overall quantum Hall behaviour of the system can again be obtained from this theory by simply selecting two points on the two Hall contacts.