# Properties of the Dirac point and Topological Insulators

1. Jan 14, 2014

### etwc

I understand that the centring of the Fermi energy at the Dirac point is a highly sought after property in Topological Insulators but I'm unsure as to exactly why? I see that the state at the conical intercept will be unique but I'm not sure of what is theorised to happen to the electrons occupying this state and what unique properties will be transferred upon the electrons that do occupy it.

2. Jan 15, 2014

### DrDu

I am not quite sure what you mean. Topological insulators like BiSb don't have a Dirac point, at least not in the bulk.

3. Jan 15, 2014

### Hypersphere

The surface states tend to have them though, see e.g. Joel Moore's article.

I am also not quite sure what the question is actually about. If the Fermi energy is at (or close to) the Dirac point, then the low-energy states will have a linear dispersion relation. This is a clear signal, and quite new in several ways (thus worth studying). In general, people tend to be more interested in the excitations close to the Fermi energy than in the actual state occupying the Fermi energy.

EDIT: Or rather, it is in that regime that TI:s are special, so why wouldn't one want to work there?

Last edited: Jan 15, 2014
4. Jan 16, 2014

### etwc

I apologies for being to vague in my initial question, I think my confusion with the subject came through.

I'm aware of the dissipationless conduction of electrons in the surface state but I was hoping for an explanation of some of the other properties predicted for the electrons that lie in this surface state and also an explanation of the properties of electrons that lie exactly at the Dirac point. For example would the electrons at the Dirac point lie within the conduction band, the valence band or neither? Or is it more like a node? Where there can't be occupancy.

In this paper by Robert Cava, http://pubs.rsc.org/en/content/articlepdf/2013/tc/c3tc30186a he states of the electrons in the surface state 'their energy quantization is more Dirac-like (i.e. photon-like) than bulk-electron-like. These states have inspired predictions of new kinds of electronic devices and exotic physics, including proposals for detecting a long sought neutral particle obeying Fermi statistics called the “Majorana Fermion” '

Why are they 'photon-like'? Is this to do with the spin-locked states? I.e. like cooper pairs.

5. Jan 16, 2014

### DrDu

Electrons near a Dirac cone behave more photon like as they have a linear dispersion relation as Hypersphere already pointed out. Specifically $E\propto k$ and therefore the group velocity is $v=\partial E/\partial k=const$, i.e. the group velocity is independent of crystal momentum just like the velocity of photons is independent of momentum.