On the Dirac and Pauli operators with several Aharonov-Bohm solenoids

Abstract

We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov-Bohm solenoids and a regular part, and prove an Aharonov-Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invariant, and this operator does not have any zero-modes.

References in corpus (3)

• Pauli operator and Aharonov Casher theorem for measure valued magnetic fields
• On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field
• On the Pauli operator for the Aharonov-Bohm effect with two solenoids

Cited by in corpus (7)

• Electronic States of Graphene Grain Boundaries
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Pauli Hamiltonians with an Aharonov-Bohm Flux
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• The heat kernel for two Aharonov-Bohm solenoids in a uniform magnetic field
• The zero modes and zero resonances of massless Dirac operators
• Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition