Remarks on Fermions in a Dipole Magnetic Field
- URL: http://arxiv.org/abs/2107.10076v1
- Date: Wed, 21 Jul 2021 13:42:03 GMT
- Title: Remarks on Fermions in a Dipole Magnetic Field
- Authors: Jeff Murugan, Jonathan P. Shock, Ruach Pillay Slayen
- Abstract summary: This work is a continuation of our recent study of non-relativistic charged particles, confined to a sphere enclosing a magnetic dipole at its center.
We extend our computations in two significant ways. The first is to a relativistic spin-$frac12$ fermion and the second concerns the interpretation of the physics.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This work is a continuation of our recent study of non-relativistic charged
particles, confined to a sphere enclosing a magnetic dipole at its center. In
this sequel, we extend our computations in two significant ways. The first is
to a relativistic spin-$\frac{1}{2}$ fermion and the second concerns the
interpretation of the physics. Whereas in a previous paper, we speculated on
the possibility of observing such condensed matter systems in the astrophysics
of extreme magnetic sources such as neutron stars, the physical systems in this
study are more down-to-earth objects such as a $\mathsf{C}_{60}$ fullerine
enclosing a current loop. We unpack some of the details of our previous
analysis for the spinless fermion on the dipole sphere and adapt it to solve
the eigenvalue problem for the single-particle Dirac Hamiltonian. In the
strong-field/small-radius limit, the spectrum of the spin-$\tfrac{1}{2}$
Hamiltonian, like the spinless case, exhibits a Landau level structure in the
$|m|\ll Q$ regime. It features a new, additional (approximately) zero-energy
lowest Landau level which persists into the $|m|<Q$ regime. As in the spinless
system, the spectrum exhibits level-crossing as the strength of the magnetic
field increases, with the wavefunctions localising at the poles in the
strong-field/small-radius limit.
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