A Coherent and Unified Single Particle Description of the Integer and Fractional Quantum Hall Effects

Abstract

There are compelling reasons to seek a new coherent description of the Quantum Hall Effects (QHE). The theoretical descriptions of the 'Integer' (IQHE) and the 'Fractional' (FQHE) quantum Hall effects are very different at present, despite their remarkable phenomenological similarity. In particular, the fractional effect invokes multi-particle dynamics and collective phenomena in the presence of a dominant Coulomb interaction, in a complex hierarchical scheme, whereas the integer effect is mostly a simple weakly interacting single particle scenario. The experimental situation, in contrast, shows that both the effects appear seamlessly, intermingling progressively, as either the magnetic field or the carrier density is monotonically varied. I argue and prove that a crucial physics input that is missing in the current theories is the relativistic gravitational contribution of all the matter-energy in the Universe. The dynamically induced relativistic gravitational potentials play a startling role to modify the quantum degeneracy, by coupling to the mass of electrons in the noninertial cyclotron orbitals. The key point is that the quantum degeneracy of Landau levels, due to the applied magnetic field, is modified by the relativistically induced cosmic gravitomagnetic field, thereby making the degeneracy dependent on the number density of the electrons. I successfully derive the main characteristics and the full sequence of both IQHE and FHQE in a seamless unified single particle scenario, without any quasiparticles, particle-flux composites, or extraneous postulates. Apart from correctly reproducing all the observed filling factors in the IQHE and the FQHE for the filling factors ν ≥ 1/3, this new theory of the QHE based on the cosmic gravitational effects has the natural explanation for the absence of the QHE at even fractions for ν < 1. Further, there is a consistent description of the edge state physics, for both charge transport and thermal transport, in the FQHE states. The gravitational paradigm shows clearly the physical reason for the phenomenological success of the effective theories with the quasiparticles like the Composite Fermions.