Aharonov Bohm Effect - Impurity Scattering and Phase Coherence

In summary, the role of scattering in the Aharonov Bohm Effect is crucial in determining the level of phase coherence and the observation of conductance oscillations. Inelastic scattering destroys phase coherence and prevents the effect from being seen, while elastic scattering allows for some phase coherence but is dependent on the location of impurities. Averaging over different mesoscopic samples can still show weak localization effects and conductance oscillations, but these are not observed in macroscopic samples due to the presence of inelastic scattering. It is unlikely that the Aharonov Bohm Effect can be observed in a macroscopic sample, even with negligible inelastic scattering, due to the finite electrical resistance. However, further research on the behavior of the effect in single
  • #1
MSLion
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I'm having difficulties understanding the role of scattering on phase coherence in the Aharonov Bohm Effect.
In particular I am trying to reconcile the following points:

  • Inelastic scattering destroys phase coherence and prevents us to see the Aharonov Bohm Effect.
  • Elastic scattering does not, but the phase difference will depend on the exact impurity locations.
  • Averaging over different mesoscopic samples does not destroy all phase coherence effects. Time-reversed trajectories cause weak localization effect and oscillations in conductance with respect to magnetic field. This effect can bee seen if we align mesoscopic rings in parallel (cylinder).
  • Conductance oscillations are not observed in macroscopic samples.

Question:
What happens if I take a MACROscopic ring and cool it down until unelastic scattering becomes neglegible but I still have ring size much larger than mean free path between elastic scattering sites? Will I see the Aharonov Bohm Effect?

Since I think I'm seeing some contradiction here, I believe point 2 is somehow wrong and then the answer to my question would be NO.

However I'm quite confused and would appreciate any help.
 
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  • #2
My best guess is that in macroscopic object you can never completely eliminate inelastic scattering - there is always a finite electrical resistance.

In mesoscopic objects there are few inelastic scattering events, hence the amplitude of the AB effect is slightly reduced. As you increase the size you introduce more inelastic scatterers and the AB amplitude progressively reduces. I cannot see any reason for a sharp transition from one regime to the other.

If this is true, then it would be interesting to observe the AB amplitude in a single crystal sample with extremely high RRR as function of temperature and size.

Note that this is my best guess, after a nice cold beer, and not supported by any experiments or literature research.
 

1. What is the Aharonov-Bohm effect?

The Aharonov-Bohm effect is a phenomenon in quantum mechanics where the presence of an electromagnetic field affects the behavior of particles, even if they do not directly interact with the field. This effect was first proposed by Yakir Aharonov and David Bohm in 1959.

2. How does the Aharonov-Bohm effect relate to impurity scattering?

The Aharonov-Bohm effect can be observed in systems where impurities (such as defects or foreign atoms) are present. These impurities can create a potential barrier that affects the phase of the particles passing through it, leading to interference patterns and the Aharonov-Bohm effect.

3. What is phase coherence and why is it important in the Aharonov-Bohm effect?

Phase coherence refers to the ability of particles to maintain their phase relationship as they travel through a system. In the context of the Aharonov-Bohm effect, phase coherence is crucial because it allows the interference patterns to be observed, which are a direct consequence of the effect.

4. Is the Aharonov-Bohm effect a purely theoretical concept or has it been observed experimentally?

The Aharonov-Bohm effect has been observed experimentally in various systems, including electron beams, superconducting rings, and quantum dots. These experiments have provided evidence for the validity of the effect in real-world scenarios.

5. How does the Aharonov-Bohm effect challenge traditional notions of causality?

The Aharonov-Bohm effect challenges traditional notions of causality because it suggests that particles can be affected by fields even if they do not directly interact with them. This idea goes against the classical understanding of cause and effect, where an interaction is required for an effect to occur.

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