Confined Dirac Fermions in a Constant Magnetic Field
arXiv:0904.0587 · doi:10.1103/PhysRevA.80.012109
Abstract
We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a positive and negative energy solution, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number, k = 0, \pm 1, \pm 2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wavefunction is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.
15 pages, 3 tables
References in corpus (6)
- Unconventional Integer Quantum Hall effect in graphene
- Electron interactions in graphene in a strong magnetic field
- Fractional Quantum Hall Effect in Graphene
- SU(4) composite fermions in graphene: New fractional quantum Hall states
- Composite Dirac fermions in graphene
- Anomalous Quantum Hall Effect on Sphere
Cited by in corpus (8)
- Two-Dimensional Quantum ring in a Graphene Layer in the presence of a Aharonov-Bohm flux
- Noncommutative Dirac oscillator in an external magnetic field
- Gate-Tunable Graphene Quantum Dot and Dirac Oscillator
- Factorization of Dirac Equation in Two Space Dimensions
- Factorization of Dirac Equation and Graphene Quantum Dot
- Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
- Path Integral Confined Dirac Fermions in a Constant Magnetic Field
- Diamagnetism of Confined Dirac Fermions in Disordered Graphene