Solutions of the Bogoliubov-de Gennes equation with position dependent Fermi--velocity and gap profiles
arXiv:1612.01130 · doi:10.1016/j.physleta.2016.08.015
Abstract
It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions has also been confirmed both in the normal phase as well as in the super-conducting phase. We also show that a combination of Fermi velocity and gap parameter step-like profiles provides scattering solutions with normal reflection and transmission.
arXiv comment9 pages, 7 figures. Accepted for publication by Physics Letters A
References in corpus (18)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum gravity and minimum length
- Andreev reflection and Klein tunneling in graphene
- Specular Andreev reflection in graphene
- Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
- Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
- Josephson effect in ballistic graphene
- Dirac oscillator with nonzero minimal uncertainty in position
- Hydrogen-atom spectrum under a minimal-length hypothesis
- Velocity-modulation control of electron-wave propagation in graphene
- Minimal Length Uncertainty Relation and the Hydrogen Spectrum
- Scattering in one-dimensional heterostructures described by the Dirac equation
- Harmonic oscillator with minimal length uncertainty relations and ladder operators
- The effect of a velocity barrier on the ballistic transport of Dirac fermions
- One dimensional Coulomb-like problem in deformed space with minimal length
- Exact solution of the Klein Gordon equation in the presence of a minimal length
- Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
- Bound state in continuum like solutions in one-dimensional hetero-structures