Visualize what chirality physically means

In summary: 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...
  • #1
iamquantized
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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?
 
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  • #2
I think it's necessary to note that my response in https://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.
 
  • #3
iamquantized said:
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?

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 into the statistics. No such chirality is considered when we write down the Bloch wavefunction.

Zz.
 
  • #4
ZapperZ said:
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 into the statistics. No such chirality is considered when we write down the Bloch wavefunction.

Zz.

see example this http://arxiv.org/abs/cond-mat/0604323
 
  • #5
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...
 
  • #6
ZapperZ said:
Er.. can you please cite an example, a textbook, etc. that actually considers such "chirality" in the conduction band?

here's one that is a little more baroque:

http://prola.aps.org/abstract/PRL/v53/i26/p2449_1
 
  • #8
olgranpappy said:
here's one that is a little more baroque:

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

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.
 
  • #9
ZapperZ said:
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.

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.
 
  • #10
iamquantized said:
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.

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.
 
  • #11
ZapperZ said:
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.

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.
 
  • #12
iamquantized said:
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.

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 anomalous 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.
 
  • #13
ZapperZ said:
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 anomalous 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.

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. Let's consider a simple effective mass picture. Wouldn't this results in a Hamiltonian matrix like Dirac eqaution with postivie and negative sea of electrons?
 
  • #14
iamquantized said:
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. Let's consider a simple effective mass picture. Wouldn't this results in a Hamiltonian matrix like Dirac eqaution with postivie and negative sea of electrons?

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

Zz.
 
  • #15
quantized---
did you happen to glance at the Wikipedia chirality article?
http://en.wikipedia.org/wiki/Chirality_(physics)
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.)
 
  • #16
ZapperZ said:
No. An exciton is normally treated as a Rydberg atom. It isn't as complicated as that.

Zz.

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/content/abstract/291/5503/451
 
  • #17
marcus said:
quantized---
did you happen to glance at the Wikipedia chirality article?
http://en.wikipedia.org/wiki/Chirality_(physics)
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.)

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.
 
  • #18
EDITED: Rereading the WP article, it seems I misunderstood a few statements.
 
Last edited:

1. What is chirality?

Chirality refers to the property of an object or molecule to have a non-superimposable mirror image. This means that the molecule cannot be rotated or flipped to match its mirror image, similar to how our hands are non-superimposable mirror images of each other.

2. How is chirality represented visually?

Chirality is represented visually using Fischer projections or Newman projections, which show the relative positions of atoms in a molecule. Another common way to represent chirality is using wedge and dash bonds in structural formulas.

3. What is the significance of chirality in chemistry?

Chirality is significant in chemistry because it affects the physical, chemical, and biological properties of a molecule. Chiral molecules can have different interactions with other molecules and can exhibit different biological activities, making them important in drug development and other fields.

4. How can we determine if a molecule is chiral or not?

A molecule is chiral if it has at least one chiral center, which is a carbon atom bonded to four different groups. This can be determined by examining the molecule's structure and identifying any chiral centers. Alternatively, experimental methods such as X-ray crystallography or NMR spectroscopy can also be used to determine chirality.

5. What is the difference between enantiomers and diastereomers?

Enantiomers are molecules that are non-superimposable mirror images of each other, while diastereomers are molecules that have more than one chiral center and are not mirror images of each other. Enantiomers have the same physical and chemical properties, while diastereomers have different properties.

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