Low Temperature Physics: 47, 662 (2021); https://doi.org/10.1063/10.0005555
Dynamics of quasi-particles in graphene with impurities and sharp edges from the kp-method standpoint
Theoretische Physik III, Ruhr-Universitaet Bochum, Bochum D-44801, Germany
Received March 3, 2021, published online June 25, 2021
Dynamics of quasi-particles in graphene with an impurity and a sharp edge is considered with the kp-method that allows an unified approach without usage of any models. Dirac and Weyl equations are derived by the above-mentioned method. The wave function and its envelope function together with the scattering amplitude are found in the Born approximation. The wave functions are shown to be a superposition of virtual Bloch functions which exponential decay outward from the impurity and the edge. At distances much greater that the atomic spacing the wave functions are explicitly presented. Green’s functions for Shrödinger and Dirac equations are derived as well. Boundary conditions for the Dirac equation for graphene with a sharp edge are also derived.
Key words: scattering of quasiparticles in graphene, Weyl and Dirac equations, kp-approximation, Green’s functions.