Syed Ali Raza Supervisor: Dr. Pervez Hoodbhoy. Topological Insulators. What are Topological insulators?. Fairly recently discovered electronic phases of matter. Theoretically predicted in 2005 and 2007 by Zhang, Zahid Hassan and Moore. Experimentally proven in 2007.
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Syed Ali Raza
Supervisor: Dr. PervezHoodbhoy
Topological Insulators
If the particle was initially in the nth state of Hi then it will be carried to the nth state of Hf .
Berry potential is also not defined globally.
A global vector potential is not possible in the presence of a magnetic monopole.
There is a singularity which is equal to the full monopole flux
Dirac String
The vector potential does not describe a monopole at the origin, but one where a tiny tube (the dirac string) comes up the negative z axis, smuggling in the entire flux.
As it is spherically symmetric, we can move the dirac string any where on the sphere with a gauge transformation.
Patch up the two different vector potentials at the equator.
The two potentials differ by a single valued gauge transformation and you can recover the diracquantisationcondition from it.
You can also get this result by Holonomy (Wilczek)