Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
arXiv:2006.01988 · doi:10.1088/1751-8121/abb6ad
Abstract
The quantum behavior of electrons in bilayer graphene with applied magnetic fields is addressed. By using second-order supersymmetric quantum mechanics the problem is transformed into two intertwined one dimensional stationary Schrödinger equations whose potentials are required to be shape invariant. Analytical solutions for the energy bound states are obtained for several magnetic fields. The associated spectrum is analyzed, and the probability and current densities are determined.
References in corpus (21)
- The electronic properties of bilayer graphene
- Electronic and optical properties of strained graphene and other strained 2D materials: a review
- Higher-Derivative Supersymmetry and the Witten Index
- Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers
- Observation of excited states in a graphene quantum dot
- Second Order Derivative Supersymmetry and Scattering Problem
- Higher-order supersymmetric quantum mechanics
- Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain
- Coulomb interaction in graphene: Relaxation rates and transport
- Supersymmetric Quantum Mechanics
- New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
- The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
- Riccati equation, Factorization Method and Shape Invariance
- Dirac electron in graphene under supersymmetry generated magnetic fields
- Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes
- Dirac electron in graphene with magnetic fields arising from first-order intertwining operators
- Trends in supersymmetric quantum mechanics
- Graphene coherent states
- Magnetic field barriers in graphene: an analytically solvable model
- Conditional electron confinement in graphene via smooth magnetic fields
- Coherent states for graphene under the interaction of crossed electric and magnetic fields
Cited by in corpus (11)
- Bilayer graphene in magnetic fields generated by supersymmetry
- Complex Supersymmetry in Graphene
- Bilayer graphene in periodic and quasiperiodic magnetic superlattices
- Reduction scheme for coupled Dirac systems
- Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials
- Strongly interacting matter in extreme magnetic fields
- Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
- Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
- Infinite families of shape invariant potentials with n parameters subject to translation
- Confinement in bilayer graphene via intra- and inter-layer interactions
- Spectral analysis of Dirac materials in position-dependent magnetic and electric fields via Heun functions