Position-dependent mass Dirac equation and local Fermi velocity
- 13 December 2021
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 55 (1), 015307
- https://doi.org/10.1088/1751-8121/ac3ce0
Abstract
We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity v (f) to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of v (f). We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.Keywords
This publication has 55 references indexed in Scilit:
- Generalized spin and pseudo-spin symmetry: Relativistic extension of supersymmetric quantum mechanicsPhysics Letters B, 2011
- Scattering in one-dimensional heterostructures described by the Dirac equationJournal of Physics: Condensed Matter, 2009
- The electronic properties of grapheneReviews of Modern Physics, 2009
- Study of a class of non-polynomial oscillator potentialsJournal of Physics A: General Physics, 2006
- Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective massJournal of Physics A: General Physics, 2005
- Supersymmetry in quantum mechanicsAmerican Journal of Physics, 1986
- Self-consistent effective-mass theory for intralayer screening in graphite intercalation compoundsPhysical Review B, 1984
- Superlattice band structure in the envelope-function approximationPhysical Review B, 1981
- Space-Charge Effects on Electron TunnelingPhysical Review B, 1966
- Das freie Elektron im homogenen Magnetfeld nach der Diracschen TheorieThe European Physical Journal A, 1928