Topology change from a monopole to a dipole in Berry's phase

Abstract

The smooth topology change of Berry's phase from a Dirac monopole-like configuration to a dipole configuration, when one approaches the monopole position in the parameter space, is analyzed in an exactly solvable model. A novel aspect of Berry's connection ${\mathcal{A}}_k$ is that the geometrical center of the monopole-like configuration and the origin of the Dirac string are displaced in the parameter space. Gauss' theorem ${\int }_S(\nabla \times \mathcal{A})\cdot d\vec{S}={\int }_V\nabla \cdot (\nabla \times \mathcal{A})dV=0$ for a volume $V$ which is free of singularities shows that a combination of the monopole-like configuration and the Dirac string is effectively a dipole. The smooth topology change from a dipole to a monopole with a quantized magnetic charge $e_M=2\pi \hslash$ takes place when one regards the Dirac string as unobservable if it satisfies the Wu-Yang gauge invariance condition. In the transitional region from a dipole to a monopole, a half-monopole appears with an observable Dirac string, which is analogous to the Aharonov-Bohm phase of an electron for the magnetic flux generated by the Cooper pair condensation. The main topological features of an exactly solvable model are shown to be supported by a generic model of Berry's phase.

arXiv comment23 pages, 7 figures

References in corpus (12)

• Spin Hall effect
• Dissipationless Quantum Spin Current at Room Temperature
• Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space
• Anomalous Hall effect in ferromagnetic semiconductors
• Berry phase correction to electron density of states in solids
• Berry phase correction to electron density in solids and "exotic" dynamics
• Second quantized formulation of geometric phases
• Geometric phases and hidden local gauge symmetry
• Topological properties of Berry's phase
• Quantum anomaly and geometric phase; their basic differences
• Geometric phases for mixed states and decoherence
• Characteristics of Chiral Anomaly in View of Various Applications

Cited by in corpus (5)

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• No anomalous canonical commutators induced by Berry's phase
• Berry's phase and chiral anomalies
• A path integral derivation of the equations of anomalous Hall effect
• Lensing of Dirac monopole in Berry's phase