Abstract
Consequences of an exceedingly strong electric field (E field) on the ground state energetics and transport properties of a 2D spinless electron gas in a perpendicular magnetic field (a Quantum Hall Effect (QHE) configuration) are investigated to all orders in the fields. For a conventional semiconductor, we find fractional values of the Hall conductivity and some magnetoelectric coefficients for certain values of E and B fields that do not result from interactions or impurities, but are a pure consequence of a strong enough in-plane E field. We also determine analytically the ground state energy, and response properties such as magnetization and polarization as functions of the electromagnetic field in the strong E field limit. In the case of Graphene, we obtain more complex behaviors leading to the possibility of irrational Hall values. The results are also qualitatively discussed in connection to various mechanisms for the QHE-breakdown.
Highlights
The Quantum Hall Effect (QHE), discovered by von Klitzing et al in 1980, is the quantized response of a nearly 2D electronic system subjected to a perpendicular magnetic field B when a small electric field E runs through the system in a longitudinal direction transverse to B
This paper follows a thermodynamic methodology that tries to shed some light on both thermodynamic and transport properties of 2D conventional and quasi-relativistic electronic systems when placed inside a strong electric field that is transverse to the magnetic field; the electric field, when sufficiently strong, seems to cause energetic mixtures and seems to have the potential to lead to fractional quantization of the Hall conductivity
The paper is summarized as follows: In Section 2, the thermodynamic and transport properties of a conventional 2D non-interacting electron gas in the low electric field (E field) regime are described in more quantitative detail than usual, these properties being derived in the strong E field limit, while in Section 3, a 2D Graphene sheet is investigated with respect both to low and strong E field limit
Summary
The Quantum Hall Effect (QHE), discovered by von Klitzing et al in 1980, is the quantized response of a nearly 2D electronic system subjected to a perpendicular (to the 2D surface) magnetic field B when a small electric field E runs through the system in a longitudinal direction transverse to B. A corresponding calculation of the Hall conductivity in the strong E field regime shows a possibility of fractional, stable values, in a certain range of B values
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