Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields

Abstract

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.

11 pages, 5 figures, accepted for publication in Journal of Physics Condensed Matter

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Two Dimensional Atomic Crystals
• Electronic Properties of Disordered Two-Dimensional Carbon
• Unconventional Integer Quantum Hall effect in graphene
• Novel electric field effects on Landau levels in Graphene

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• Quantum Oscillations in Nodal Line Systems
• Quantum-oscillation-modulated angular dependences of the positive longitudinal magnetoconductivity and planar Hall effect in Weyl semimetals
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• Analytical Solution of (2+1) Dimensional Dirac Equation in Time-Dependent Noncommutative Phase-Space
• Quantum capacitance oscillations in graphene under crossed magnetic and electric fields
• New solutions for graphene with scalar potentials by means of generalized intertwining
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• Current modulation in graphene p-n junctions with external fields
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• Quantum oscillations of the nonlinear planar effects signifying chiral anomaly in Weyl Semimetals
• Density of states and differential entropy in Dirac materials in crossed magnetic and in-plane electric fields
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• Strain-induced collapse of Landau Levels in real Weyl semimetals
• In-plane electric field effect on a spin-orbit coupled two-dimensional electron system in presence of magnetic field
• Peculiarities of the Landau level collapse in graphene ribbons in crossed magnetic and in-plane electric fields
• WKB energy levels in gapped graphene under crossed electromagnetic fields
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• Bound states for massive Dirac fermions in graphene in a magnetic step field
• Zigzag edge states in graphene in the presence of in-plane electric field
• Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor
• Role of electrical field in quantum Hall effect of graphene
• Electronic orbital angular momentum and magnetism of graphene