The Aharonov-Bohm effect manifests itself in the interference of electron waves traveling through multiply-connected regions and the flux linked with the paths for the electron. Here, we consider the transmission of electrons in the presence of a magnetic field through a finite-width Möbius ring structure which displays a nontrivial topology. The results are compared with the transport through a flat annular ring and a cylindrical ring, with finite-width input and output contacts attached at the periphery in order to highlight the differences in the transmission and conductance patterns. We develop a model to account for the main features associated with the interference effects for propagating states on the Möbius ring. We demonstrate that the periodicity in the magnetic flux, in units of h/e, is weakly broken on 2D rings of finite width, so that the simple treatment proposed here is sufficient for interpreting results. The unusual states with half-integer values of ⟨Lz⟩⟨Lz⟩ present on Möbius rings display a different characteristic in transmission. Such resonant states are in constructive interference for transmission at magnetic fields where the contribution from ordinary states with integer ⟨Lz⟩⟨Lz⟩ is in destructive interference, and vice versa. This leads to an alternating dominance of the set of half-integer ⟨Lz⟩⟨Lz⟩ states and the set of integer ⟨Lz⟩⟨Lz⟩ states in transport with increasing magnetic fields. We calculate the conductance of the rings, using the Landauer-Büttiker formula, as a function of the magnetic field and the applied bias at contact reservoirs. The differences in the structures considered lend hope for possible for magnetic sensor applications.
Li, Z., & Ram-Mohan, L. R. (2013). The Aharonov-Bohm effect with a twist: Electron transport through finite-width Möbius rings. Journal of Applied Physics, 114(16). https://doi.org/10.1063/1.4827858
*denotes a WPI undergraduate student author