visualize what chirality physically means

iamquantized

My difficultly is in trying to visualize what chirality physically means. In solid state system, people usually ascribed electron of one chirality to be electron in the conduction band while the opposite chirality belongs to an unoccupied state (hole) in the valence band. Can I then say the electron is left handed, while the hole is right handed. Electron spins clockwise while hole spins anti-clockwise. Is this correct?

Is there an example that describe how electron with different chirality can interacts? Is the electron hole interaction forming an exciton an example of this?

Timo

I think it's necessary to note that my response in http://www.physicsforums.com/showthread.php?t=184042 was for high energy particle physics, not for solid state physics. My knowledge about solid state physics is very limited. I see no reason why and how the chirality I described in my other post (being eigenstates of the projection operators mentioned) would fit to what you seem to say here. It might be (and even seems to me that way) that the term chirality has a different meaning in solid state physics.

ZapperZ

Er.. can you please cite an example, a textbook, etc. that actually considers such "chirality" in the conduction band? This is rather strange since the degeneracy of the conduction band for both spin states is built in to the statistics. No such chirality is considered when we write down the Bloch wavefunction.

Zz.

iamquantized

see example this http://arxiv.org/abs/cond-mat/0604323

olgranpappy

I vaguely recall that the "spinor" components are actually with respect to the sublattices in graphene and that the chirality conservation has something to do with the fact that electrons want to stay on the same sublattice they started on...

olgranpappy

here's one that is a little more baroque:

http://prola.aps.org/abstract/PRL/v53/i26/p2449_1

ZapperZ

Er.. I know about this. Spin polarized tunneling is nothing new. But you were talking about conduction bands!

Zz.

ZapperZ

We need to back up a bit and figure out how all of these are actually relevant to the original post. I don't see it.

If we are doing to discuss some exotic property of material science, then I can do that as well. But there's no such thing in the OP. "Chirality in the conduction band" is meaningless until something is defined here. Where exactly is chirality involved in the derivation of the conduction band. That's what I want to know. One may start with the ideal metal if one wish.

Zz.

iamquantized

In the usual treatment of graphene, people usually use a Dirac equation for describing the bandstructure which introduces chirality into the eigenstates. So, this results in the conduction and valence band electron states having opposite chirality. But frankly, I do not grasp the physical picture well enough to explain further than what I had said.

ZapperZ

This is a prime example where, when you ask a question the first time around, you should have been as complete as possible. Nowhere in your original post was there any mention of graphene or what you were getting at. Thus, the inclusion of "chirality" in your original puzzled me. Ordinary material has no "chirality" that affects their typical behavior.

Graphene isn't a "band" material. Very much like Mott-Hubbard insulator, you can't describe graphene using a typical band model, especially when you can have 2D structure that can behave both like a conductor and semiconductor at the same time. This is not the behavior of ordinary material, and certainly not the the typical conduction band what we know.

Zz.

iamquantized

I disagree. Graphene has a energy dispersion relationship just like any material. Its just that it has a UNIQUE dispersion relationship. The chirality aspect of graphene should exist in usual semiconductors like Si. Nothing can stop you if you insist to use a Dirac equation to describe the E-K dispersion of a semicon like Si in the vicinity of the band minima.

ZapperZ

But you do not get the band structure by simply describing the band minima!

Ultrathin graphite, for example, has a rather unusual electronic transport property, such as the anomolous quantum hall effect, something you do not get with a typical semiconductor or metal. This has been used often as the typical sign for non-standard electronic structure. This is despite the fact that you do get Dirac fermions in the vicinity of of the Fermi energy.

Zz.

iamquantized

Well.. you cannot get the full bandstructure with methods like k.p. or Dirac equation. But it allows you to describe the states in the vicinity of the band minima depending on where you do your k.p expansion. As a matter of fact, Dirac equation for graphene can be obtained from a k.p expansion at the Dirac point. In other words, if you do a k.p expansion i.e. taking the states at Dirac point as basis you can arrive at the Dirac equation. But one unique point about the k.p expansion is the basis are chosen at opposite Dirac point K and K' taken together.. This is not usually done for common semiconductor. Maybe this is where chirality enters the picture.. I am not sure.. I am figuring it out as I type this post.

But let me drop you another question which might help the discussion. In semiconductor like Si, how does one treat electron and hole in a single Hamiltonian picture? For example in the case of exciton, where electron and hole couples, I will need a Hamiltonian description that includes an electron and hole state. Lets consider a simple effective mass picture. Wouldn't this results in a Hamiltonian matrix like Dirac eqaution with postivie and negative sea of electrons?

ZapperZ

No. An exciton is normally treated as a Rydberg atom. It isn't as complicated as that.

Zz.

marcus

quantized---
did you happen to glance at the Wikipedia chirality article?
http://en.wikipedia.org/wiki/Chirality_%28physics%29
it is clear and simple AFAICS, though perhaps it wouldn't be responsive to your question (someone else may wish to comment---Wik not always reliable.)

iamquantized

Yes I know. But in treatment of exciton states in quantum dot, a Hamiltonian describing hole-electron coupling is neccessary. See for example http://www.sciencemag.org/cgi/conten...t/291/5503/451

iamquantized

Yes. I read it. thanks. Just that I cannot find resources that specifically relates chirality to solid state system and describing their interactions and relations to Dirac's equation... stuff of these sort.