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Bilayer Graphene Nanoribbon Transport Model
Published in Razali Ismail, Mohammad Taghi Ahmadi, Sohail Anwar, Advanced Nanoelectronics, 2018
Hatef Sadeghi, Seyed Mahdi Mousavi, Meisam Rahmani, Mohammad Taghi Ahmadi, Razali Ismail
A remarkable anomalous quantum Hall effect (QHE) appears in GNR, which is σxy = ±4(N + 1/2)e2/h, where N is the integer “Landau level” index [5,32,47]. BGN also shows the anomalous QHE, but with the standard sequence of σxy = ±4(N + 1/2)e2/h. Since the first plateau at N = 0 is absent in the unbiased case, BGN stays metallic at the neutrality point. Biased BGN exhibits a plateau at zero Hall conductivity σxy = 0, which may only be due to the opening of a sizable gap between the valence and conduction bands [5,32,48]. Additionally, it is notable that both GNR and BGN have a zeroth Landau level located at the charge-neutrality point, which are eightfold degenerate in BGN and fourfold degenerate in GNR [49], and the Berry phase for carriers in BGN is 2π while it is π in GNR [27].
Sensing with Graphene
Published in Sunipa Roy, Chandan Kumar Sarkar, MEMS and Nanotechnology for Gas Sensors, 2017
Sunipa Roy, Chandan Kumar Sarkar
The conventional Hall effect demonstrates that an electric current, flowing through a rectangular metallic conductor, under the presence of a transverse magnetic field, produces a potential difference (Hall potential) between the two opposite faces. The ratio of the potential difference with respect to the current which is called Hall resistivity is directly proportional to the applied magnetic field. Hall effect is generally employed for the measurement of this magnetic field. It was observed that in a 2D structure, Hall resistivity becomes quantized at a temperature close to the absolute zero, holding an approximate value of h/ne2 (where h is the Planck’s constant, n a positive integer number and e is the electric charge). Hall resistivity was found only for the odd value of n which is a consequence of quantum mechanical effect named Berry’s phase. This phenomenon is called quantum Hall effect. Compared to other 2D electron system, graphene shows some peculiar nature in characterizing the quantum Hall effect. For SLG, however, the Hall conductivity is quantized if the filling factor is a half-integer whereas for conventional 2D systems, the Hall resistance emerges when the filling factor is an integer. The formation of discrete Landau levels is crucial to the quantization of the Hall resistance and conductivity.
The Boltzmann equation and the relaxation time approximation
Published in DAVID K. FERRY, Semiconductor Transport, 2016
The quantized energy levels described by (3.176) are termed Landau levels, after the original work on the quantization carried out by Landau. Transport across the magnetic field (e.g., in the plane of the orbital motion) shows interesting oscillations due to this quantization. Let us consider this motion in the two-dimensional plane to which the magnetic field is normal. In looking at (3.175), one must consider the fact that the electrons will fill up the energy levels to the Fermi energy level. Thus there are in fact several Landau levels occupied, and therefore the electrons exhibit several distinct values of the orbital velocity v0. In computing the effective radius, it is then necessary to sum over these levels. If there are n, electrons per square centimeter, this sum can be written as
Pancharatnam metals with integer and fractional quantum Hall effects
Published in Philosophical Magazine, 2021
We can readily deduce that for a given temperature and sample type, in Equation (10) is a constant and therefore, the physics of quantum Hall effect is actually contained within the electron–electron scattering rate variable, , and not due to constant or varying Landau-level filling factor, ν. In particular, whenever achieved a constant value or a plateau for a given and , the filled (or fully occupied) Landau levels is not the cause for such observation, but due to constant . For example, any non-zero value (be it a constant or a variable) for , strictly implies is also non-zero such that cannot be non-zero in the absence of scattering rate as falsely advocated to be so in Ref. [1], and later, the same ‘absence-of-scattering-rate’ is adopted in the subsequent work and extension [2–8,10,11], including the author of this work [12].
Chiral fermion asymmetry in high-energy plasma simulations
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
J. Schober, A. Brandenburg, I. Rogachevskii
The CME occurs in magnetised relativistic plasmas, in which the number density of left-handed fermions differs from the one of right-handed fermions (see e.g. Kharzeev et al.2013, Kharzeev 2014, Kharzeev et al.2016, for reviews). This asymmetry is described by the chiral chemical potential2 which is defined as the difference between the chemical potential of left- and right-handed fermions, and , respectively.3 In the presence of a magnetic field, the momentum vectors of the fermions at the lowest Landau level align with the field lines while their direction depends on the handedness of the fermion; see the illustration in Figure 1. A non-vanishing leads to the occurrence of the electric current where is the fine structure constant and ℏ is the reduced Planck constant (Vilenkin 1980, Alekseev et al.1998, Fröhlich and Pedrini 2000, Fukushima et al.2008, Son and Surowka 2009). The presence of indicates that the CME is a quantum effect.