Which of these is most relevant to photonics research?

[zahbaz]

I have been assigned to research one of three topics as a term paper. This is for an upper level undergraduate course in electromagnetism.

Could you advise me on which topic best aligns with research in photonics?

• Hall Effect: Research the classical, quantum, and anomalous Hall effect.
• Aharonov-Bohm effect: The B field outside an infinite solenoid is zero, but the magnetic vector potential is nonzero. Describe the AB effect and current developments in research.
• Magnetic monopole: Describe the search for the monopole and it's potential impact on theory if discovered.

I already know about the classical Hall Effect. It's the most familiar topic, yet I'm looking to put time into researching the most interesting of the three. I'm joining a photonics lab. Other interests would include nuclear physics and QFT.

 

[radium]

These topics actually have a lot of similarities. They are all consequences of gauge invariance and have some associated nontrivial topology. Since the vector potential appears in the action, and the integral around a closed loop is the B flux through a bounded surface, you cannot set it to zero everywhere or have a gauge that is well defined everywhere. Instead, you must make the difference a multiple of 2 \pi times some integer (or some filling fraction for the FQHE). This gives you some winding number
In QH effect this is the hall conductance which is the integral of the Berry curvature of the filled bands. For the aharonov bohm effect this is the interference pattern which is shifted depending on the flux though the particle never sees a field. For certain values of the flux it returns to the original pattern.