Bound states of massive fermions in the Aharonov--Bohm-like fields

Abstract

Bound states of massive fermions in the Aharonov-Bohm like fields have analytically been studied. The Hamiltonians with the Aharonov--Bohm like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct self-adjoint Dirac Hamiltonians with the Aharonov-Bohm (AB) potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic flux and depends upon fermion spin and extension parameter; it is a periodical function of the magnetic flux. We also construct self-adjoint Hamiltonians for the so-called Aharonov-Casher (AC) problem, show that nonrelativistic neutral massive fermions can be bound by the Aharonov-Casher background, determine the range of extension parameter in which fermion bound states exist and find their energies as well as wave functions.

9 pages, to appear in the EPJC, 2014

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• Linear confinement of generalized KG-oscillator with a uniform magnetic field in Kaluza-Klein theory and Aharonov-Bohm effect
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• The 2D $\kappa$-Dirac oscillator
• Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field
• On planar quantum dynamics of a magnetic dipole moment in the presence of electric and magnetic fields
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• Spin-$0$ scalar particle interacts with scalar potential in the presence of magnetic field and quantum flux under the effects of KKT in $5D$ cosmic string space-time
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• Radiative dynamical mass of planar charged fermion in a constant homogeneous magnetic field
• Vacuum polarization of charged massless fermions in Coulomb and Aharonov--Bohm fields
• Effects of Kaluza-Klein theory and potential on a generalized Klein-Gordon oscillator in the cosmic string space-time
• Quantum influence of topological defects on a relativistic scalar particle with Cornell-type potential in cosmic string space-time with a spacelike dislocation
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• Self-adjoint extension approach for singular Hamiltonians in (2+1) dimensions
• Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem
• Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials
• Quantum states of a neutral massive fermion with an anomalous magnetic moment in an external electric field