Collective excitations in graphene in magnetic field

TL;DR

This paper develops a quantum hydrodynamics framework to analyze collective electron excitations in graphene under magnetic fields, revealing how the excitation dispersion depends on magnetic field orientation and strength.

Contribution

It introduces a graphene quantum hydrodynamics model based on the Dirac equation, providing new insights into collective excitations in magnetic fields.

Findings

Perpendicular magnetic field does not affect dispersion.

Dispersion depends on magnetic field strength and orientation.

Wave propagation characteristics vary with system parameters.

Abstract

Collective excitations in graphene monolayer are studied. Equations describing collective properties of electrons in graphene are obtained. The basic ideas of the method of many-particle quantum hydrodynamics are used for the derivation. As starting point of the derivation we use the Dirac equation for massless electrons which is usually used for description of electrons in graphene [D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)], where the Coulomb interaction is taken into account. We study dispersion properties of collective excitations by means derived here graphene quantum hydrodynamics equations (GQHD). We consider graphene in the external magnetic field which directed at an angle to the graphene sample. We do it in a linear approximation of the GQHD equations. We observe that the magnetic field directed perpendicular to the graphene plane had no influence on dispersion of the collective excitations. For the magnetic field directed at an angle to the graphene we obtain dependence of wave dispersion on system parameters: strength of magnetic field, wave vector, direction of wave propagation relatively to the magnetic field.