Topological Insulators

Recently, there is a widespread interest in the study of certain group of materials called "Topological Insulators" which may be considered as a subgroup of Quantum Materials.

First, what are topological materials?

Before coming to this question, we should know what is topology. I have been writing a separate post on Topology. Topology is a rich topic and consider spending a reasonable amount of time to get a clear picture of what really it is.

The 2016 Nobel prize has been awarded to David J. Thouless (University of Washington), F. Duncan M. Haldane (Princeton University) and J. Michael Kosterlitz (Brown University). The citation says that the prize is awarded "for theoretical discoveries of topological phase transitions and topological phases of matter".

To understand, let me give a rough idea. There are certain properties (eg. conductor on the surface only) which are protected in topological insulators. Here the word 'protected' means that the property won't vanish in any condition. You can do whatever modification you want i.e., you can change the sphere shaped material to any shape you want as for as you don't create edges/holes. If band structure is obtained for those different shapes, all other bands may change. But, surface states are protected and they will be always remain. When a hole is created in the material, these surface states will be destroyed. That is why, experts say that the property is "topologically protected".

These materials are interesting because of the technological applications and also many exotic phenomena they exhibit. 

1. Majorana Fermion
2. Weyl semi-metal
3. Dirac Fermion 
4. etc.

Following is a presentation by Prof. Charles Kane

Topological Band Theory I: Part 1 of 6.

Here is the part 2 of 6 videos:

Part 3 of 6:

Part 4 of 6:

Part 5 of 6:

Here is the final part of the presentation.

Spend as much time on understanding the materials presented in this video.

An introductory talk on the "Topological Insulators" from The Zurich Physics Colloquium given by Prof. Osterwalder Jürg would be useful.


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