Pancharatnam metals with integer and fractional quantum Hall effects

ABSTRACT

Weakly interacting Fermi liquid can exhibit integer or fractional quantum Hall effect at sufficiently low temperatures, and in the presence of variable applied magnetic and/or electric fields. The said effects have been captured only incompletely by means of the Klitzing conductance formula, $e^2/h$ multiplied by the dimensionless filling factor (integer or fractional), ν because scattering rate cannot be absent for any conductor that is neither a perfect conductor at zero Kelvin (in the absence of phonons, scattering rate, Cooper pairing and Meissner effect) nor a superconductor. Here, we shall derive the proper microscopic resistance formula based on the notion of Pancharatnam phase retardation that captures both integer and fractional quantum Hall effects. We then compute the Planck constant from the Pancharatnam resistance formula, as well as provide a formal proof for this new formula. We shall unambiguously elaborate why the Pancharatnam resistance formula gives the complete physics of electron transport phenomena responsible for the quantum Hall effects, which include the changes to longitudinal and Hall resistance, as well as the temperature effect.

KEYWORDS:

• Integer and fractional quantum Hall effects
• Pancharatnam phase
• non-zero scattering rate
• longitudinal and quantum Hall resistance

PACS:

• 73.43.Cd
• 73.43.Qt

Acknowledgments

Madam Sebastiammal Savarimuthu, Mr Albert Das Arulsamy and Madam Roosiyamary Lourdhusamy have supported this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).