Abstract
We investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body thermodynamic properties and the Hall coefficient. The results suggest exotic possibilities that necessitate very careful experimental investigation. In this alternate form of Quantum Hall Effect, non-linear phenomena related to the global magnetization, energy and Hall conductivity (the latter depending on the strengths of magnetic B- and electric E-fields) emerge without using perturbation methods, to all orders of E-field and B-field strengths. Interestingly enough, when the value of the electric field is sufficiently strong, fractional quantization also emerges, whose topological stability has to be verified.
Highlights
We investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body thermodynamic properties and the Hall coefficient
In this alternate form of Quantum Hall Effect, non-linear phenomena related to the global magnetization, energy and Hall conductivity emerge without using perturbation methods, to all orders of E-field and B-field strengths
Dirac-type materials, such as Topological Insulators, monolayer graphene, and three-dimensional (3D) Dirac and Weyl semimetals, appear nowadays as stable topological phases of matter, displaying behavioral patterns that produce new physics at a very fundamental level and at the same time give the possibility of exotic future applications [1] [2] [3]
Summary
Dirac-type materials, such as Topological Insulators, monolayer graphene, and three-dimensional (3D) Dirac and Weyl semimetals, appear nowadays as stable ( very robust) topological phases of matter, displaying behavioral patterns that produce new physics at a very fundamental level and at the same time give the possibility of exotic future applications [1] [2] [3]. In words, when the work performed by the electric field is smaller than the energy gap at a certain X0 , no overlap is observed between the L.L.s n and n + 1. For strong enough electric field or for a small enough L.L. index, the above inequality will be true (see Figure 2); but as the L.L. index of occupied levels gets larger ( for a large number of electrons N) the energy gaps between adjacent L.L.s will become lower, until an inevitable gap closing occurs (Figure 2 providing a concrete example). There might be cases where overlaps start from n = 0 (for a low enough E-field), in which case iF = 0 , and all L.L.s with n > 0 overlap In this case, with no energy gap present at all, graphene will gain a metallic character. Equation (1.7) with input n= iF +1 becomes :
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