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. Author manuscript; available in PMC: 2021 Sep 10.
Published in final edited form as: Phys Today. 2019 Jan;72(1):10.1063/pt.3.4111. doi: 10.1063/pt.3.4111

FIGURE 3. PHASE ENGINEERING.

FIGURE 3.

Quantum mechanical particles experience magnetic fields by acquiring Aharonov–Bohm (AB) phases. (a) In an AB interferometer, a magnetic field B is confined to the interior of a solenoid and is zero outside it. Nevertheless, a particle that travels on opposite sides of the solenoid will acquire a phase difference proportional to the enclosed magnetic flux Φ. That flux equals the line integral of the vector potential A around the solenoid. The charge is specified by q. (b) Particles that tunnel in a lattice experience an applied magnetic field in much the same way as in the AB effect. Their tunneling motion from one site to another acquires a so-called Peierls phase, such that the sum of the phases around a closed loop equals the enclosed flux.