TY  - JOUR
AU  - Apinyan, Vardan
AU  - Sahakyan, Mane
PY  - 2020
DA  - 2020/07/01
TI  - Dirac's Spectrum from Newton’s Laws in Graphene
JO  - Recent Progress in Materials
SP  - 016
VL  - 02
IS  - 03
AB  - The present report provides a phenomenological theory for monolayer graphene, in which two worlds, the quantum and the classical, meet and complete each other in the most natural manner. In the present report, electron mass-vortex representation is introduced, and the surface tension excitation states in the monolayer graphene are defined. The band-mass of the electrons at the Dirac’s point was calculated through the mathematical introduction of a mass-dispersion relation. As a consequence, the Dirac’s energy dispersion in monolayer graphene from classical Newton’s law was obtained. Within the scope of the semiclassical theory, it was demonstrated that there was the presence of surface spin tension vectorial field, which, possibly, closely links the surface tension and the spin tension states of the helical surface. The surface tension associated with the confinement of the electron band mass-vortex at the Dirac's point was calculated, and the relaxation time of the surface tension state was predicted with accuracy. Moreover, it was demonstrated, phenomenologically, that the manifolds on S(6) are not integrable (which had been a long-standing problem in the group theory). The principal reason for this was attributed to the irreducibility of the spinorial group Spin(6)R at the Dirac's point, because of band-mass formation and confinement via the gravitational field.
SN  - 2689-5846
UR  - https://doi.org/10.21926/rpm.2003016
DO  - 10.21926/rpm.2003016
ID  - Apinyan2020
ER  -