Bilayer graphene in magnetic fields generated by supersymmetry
arXiv:2101.05391 · doi:10.1088/1751-8121/abf870
Abstract
The effective Hamiltonian for electrons in bilayer graphene with applied magnetic fields is solved through second-order supersymmetric quantum mechanics. This method transforms the corresponding eigenvalue problem into two intertwined one dimensional stationary Schrödinger equations whose potentials are determined by choosing at most two seed solutions. In this paper new kinds of magnetic fields associated to non-shape-invariant SUSY partner potentials are generated. Analytic solutions for these magnetic fields are found, the associated spectrum is analyzed, and the probability and current densities are explored.
arXiv commentIn this new version of the work, we correct the current density expression as well as some plots and include a new appendix to explain how to obtain the right form of the current density for bilayer graphene interacting with magnetic fields
References in corpus (28)
- The electronic properties of bilayer graphene
- 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
- Second Order Derivative Supersymmetry and Scattering Problem
- Higher-order supersymmetric quantum mechanics
- The finite difference algorithm for higher order supersymmetry
- New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
- Supersymmetric Quantum Mechanics
- The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
- The confluent algorithm in second order supersymmetric quantum mechanics
- Dirac electron in graphene under supersymmetry generated magnetic fields
- -symmetric invisible defects and confluent Darboux-Crum transformations
- Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes
- Wronskian formula for confluent second-order supersymmetric quantum mechanics
- Dirac electron in graphene with magnetic fields arising from first-order intertwining operators
- Trends in supersymmetric quantum mechanics
- Graphene coherent states
- Wronskian differential formula for confluent supersymmetric quantum mechanics
- Magnetic field barriers in graphene: an analytically solvable model
- On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
- Wronskian differential formula for k-confluent SUSY QM
- Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
- Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
- Hyperconfluent third-order supersymmetric quantum mechanics
- The generalized zero-mode supersymmetry scheme and the confluent algorithm
- Recursive Representation of Wronskians in Confluent Supersymmetric Quantum Mechanics
- Conditional electron confinement in graphene via smooth magnetic fields
- Confluent Second-Order Supersymmetric Quantum Mechanics and Spectral Design
Cited by in corpus (9)
- Complex Supersymmetry in Graphene
- Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
- Bilayer graphene in periodic and quasiperiodic magnetic superlattices
- Reduction scheme for coupled Dirac systems
- Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
- Phase-space representation of coherent states generated through SUSY QM for tilted anisotropic Dirac materials
- Strongly interacting matter in extreme magnetic fields
- Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
- Confinement in bilayer graphene via intra- and inter-layer interactions