New solutions for graphene with scalar potentials by means of generalized intertwining

Abstract

The intertwining relations between superpartner Hamiltonians are the main ingredients of well known Supersymmetrical Quantum Mechanics (SUSY QM). In the present paper, the generalized form of intertwining is used for investigation of a massless (zero energy) two-dimensional Dirac equation with scalar external potential. This equation is related to the description of graphene and some other materials in the field of external electrostatic potential. The use of modified intertwining relations allows to find analytically solutions for the wave functions in the field of some external scalar potentials which depend on both space coordinates. A few examples of this construction are given explicitly.

16 p.p.; published version

References in corpus (14)

• The electronic properties of graphene
• Quasi-bound states of quantum dots in single and bilayer graphene
• Electrostatic confinement of electrons in an integrable graphene quantum dot
• Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach
• Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields
• Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
• Trends in supersymmetric quantum mechanics
• SUSY approach to Pauli Hamiltonians with an axial symmetry
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• Construction of zero energy states in graphene through the supersymmetry formalism
• On zero energy states in graphene
• Universality and stability of the edge states of chiral-symmetric topological semimetals and surface states of the Luttinger semimetal
• Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system
• Zero Energy States for a Class of Two-Dimensional Potentials in Graphene

Cited by in corpus (8)

• Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
• Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation
• Complex Supersymmetry in Graphene
• A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
• Solvable Two-dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field
• SUSY design of smooth quantum rings in graphene
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping