A New Class of Solvable Two-dimensional Scalar Potentials for Graphene
arXiv:2209.12539 · doi:10.1140/epjp/s13360-022-03326-x
Abstract
In the present paper, a systematic approach is presented for solution of two-dimensional massless Dirac equation with external electrostatic potential applied. This approach is based on the new - asymmetric - form of SUSY-like intertwining relations. It allows to build a wide variety of pairs of SUSY-partner external scalar potentials. If one of them is simple enough to be solvable, its partner is also solvable although it may have a non-trivial dependency on both coordinates. Physically, this kind of problems is related to the description of graphene and some other materials with external potential. Solvability obtained by means of asymmetric form of SUSY intertwining relations allows to extend the class of analytically solvable two-dimensional models.
30 p.p
References in corpus (10)
- The electronic properties of 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
- Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
- Guiding Dirac fermions in graphene with a carbon nanotube
- Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
- 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
- Generalization of SUSY Intertwining Relations: New Exact Solutions of Fokker-Planck Equation