Quantum gravity

Physics

Geometric phase

Quantization (signal processing)

Magnetic moment

Algorithm

Magnetic field

Geometric quantization

Electron magnetic dipole moment

Canonical quantization

Magnetic dipole

Condensed matter physics

Computer science

Quantum mechanics

Quantum

Physical Review Letters

The modern semiclassical theory of a Bloch electron in a magnetic field encompasses the orbital magnetization and geometric phase. Beyond this semiclassical theory lies the quantum description of field-induced tunneling between semiclassical orbits, known as magnetic breakdown. Here, we synthesize the modern semiclassical notions with quantum tunneling-into a single Bohr-Sommerfeld quantization rule that is predictive of magnetic energy levels. This rule is applicable to a host of topological solids with unremovable geometric phase, that also unavoidably undergo breakdown. A notion of topological invariants is formulated that nonperturbatively encode tunneling, and is measurable in the de Haas-van Alphen effect. Case studies are discussed for topological metals near a metal-insulator transition and overtilted Weyl fermions.

Geometric Phase and Orbital Moment in Quantization Rules for Magnetic Breakdown