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Created page with "==Summary of bismuth‑Aharonov‑Bohm (A‑B) coupling research== * Individual single‑crystal bismuth nanowires show an oscillatory dependence of their low‑temperature resistance on the Aharonov‑Bohm flux, clear evidence of quantum interference of surface‑state electrons that encircle the wire cross‑section. [link.aps](https://link.aps.org/doi/10.1103/PhysRevB.77.075332) * These A‑B oscillations survive magnetic fields as high as the critical field of atta..."

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==Summary of bismuth‑Aharonov‑Bohm (A‑B) coupling research==

* Individual single‑crystal bismuth nanowires show an oscillatory dependence of their low‑temperature resistance on the Aharonov‑Bohm flux, clear evidence of quantum interference of surface‑state electrons that encircle the wire cross‑section. [link.aps](https://link.aps.org/doi/10.1103/PhysRevB.77.075332)

* These A‑B oscillations survive magnetic fields as high as the critical field of attached superconducting electrodes (≳10 T) and are attributed to the topological surface states of Bi, which possess strong Rashba spin‑orbit coupling and large effective g‑factors that enhance phase coherence. [arxiv](https://arxiv.org/abs/1406.4280)

* In crystalline Bi nanowires, proximity‑induced superconductivity yields a supercurrent that persists in fields above the electrode critical field; the critical current exhibits regular, SQUID‑like periodic modulations with magnetic flux, demonstrating flux‑sensitive, phase‑coherent transport in the Bi core. [pubs.acs](https://pubs.acs.org/doi/10.1021/nl901431t)

* Magnetotransport measurements on Bi‑based topological‑insulator ring structures (e.g., Sb₂Te₃) reveal Aharonov‑Bohm conductance oscillations originating from ballistic, quasi‑ballistic surface‑state transport around the ring perimeter, with a phase‑coherence length of ~600 nm at 2  2 K. [pmc.ncbi.nlm.nih](https://pmc.ncbi.nlm.nih.gov/articles/PMC10375586/)

* Theoretical treatments of collective Bernstein‑wave modes in bismuth under a static magnetic field show that the electron cyclotron (Larmor) motion couples to flux‑dependent phase effects, indicating that A‑B‑type quantization can modulate or activate Larmor‑resonance conditions. [pubs.aip](https://pubs.aip.org/aip/jap/article-pdf/50/11/6616/18385242/6616_1_online.pdf)

Taken together, these works establish bismuth as a premier material for observing and exploiting Aharonov‑Bohm interference: its high diamagnetism, strong spin‑orbit coupling, and robust surface‑state conduction enable magnetic‑field‑resistant quantum oscillations, flux‑tunable superconductivity, and coupling to spin‑precession phenomena, opening pathways for quantum‑coherent devices and spin‑based sensors.

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