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Exact solution of the Dirac–Weyl equation in graphene ...

2017-1-1 · In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential.In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used.

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Two-dimensional gas of massless Dirac fermions in …

Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s ...

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The Dirac Equation - University of California, San Diego

2013-4-22 · The Dirac Equation Our goal is to find the analog of the Schrödinger equation for relativistic spin one-half particles, however, we should note that even in the Schrödinger equation, the interaction of the field with spin was rather ad hoc. There was no explanation of the gyromagnetic ratio of 2. One can incorporate spin into the non-relativistic equation by using the Schrödinger-Pauli ...

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The Dirac Equation - University of California, San Diego

2013-4-22 · The Dirac Equation Our goal is to find the analog of the Schrödinger equation for relativistic spin one-half particles, however, we should note that even in the Schrödinger equation, the interaction of the field with spin was rather ad hoc. There was no explanation of the gyromagnetic ratio of 2. One can incorporate spin into the non-relativistic equation by using the Schrödinger-Pauli ...

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DIRAC EQUATION FOR QUASI-PARTICLES IN …

2020-11-29 · There is evidence for existence of massless Dirac quasiparticles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points.

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Graphene properties from curved space Dirac …

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background.

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The $k \cdot p$ method and its application to …

Following Ando's approach, we show how the application of this method to graphene results in a description of its properties in terms of the Dirac equation. Then we find general expressions for the probability density and the probability current density in graphene and we compare this formulation with alternative existing representations.

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Graphene properties from curved space Dirac …

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background.

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Phys. Rev. B 86, 165433 (2012) - Dirac-equation ...

The presence of an extended line defect in graphene brings about some interesting electronic properties to such a truly two-dimensional (2D) carbon material, such as the energy-band engineering and valley filtering. By establishing an appropriate connection condition for the spinor wave function across the line defect, we find that the massless Dirac equation is still a valid theoretical model ...