Are there excitons with spin=0?

[phy127]

I am actually curious about the spin of excitons.
Since an exciton is a bount electron-hole pair, its spin is the sum of the spin of electron and hole, AM I RIGHT?
If I use the usual addition of angular momentum in quantum mechanics, I get spin 2,1, and 0.
I used the fact that electrons have z-spin=+-1/2, light holes z-spin=+-1/2, and heavy holes z-spin=+-3/2. Is my method correct?

However, when I look at publications about excitons, there are only two spins,
spin=1 bright excitons, and
spin=2 dark excitons

What happened to the spin=0?
Maybe there's no such thing but what will the spin of an exciton made of z-spin=1/2 electron and a z-spin=-1/2 light hole?

z-spin = means projection on z-axis.
Thanks!

 

[Bill_K]

Sure, normally an exciton can either be singlet (S = 0) or triplet (S = 1). When a heavy hole is involved, the spin can be S = 1 or 2, but it's only the S = 2 state that's a dark state.

 

[phy127]

Thanks for the quick reply.

This means there are 8 distinct exciton states? Which can be identified by their spin projection.
4 bright excitons (S=1)
2 dark excitons (S=2)

Are the S=0 states bright? I can't think of I way how it can couple to photon.

I'm studying exciton-photon coupling in microcavities to form polaritons.
It seems most publications about the exciton spin is not that detailed so I want to confirm if my understanding is correct.

 

[Cthugha]

Thanks for the quick reply.

This means there are 8 distinct exciton states? Which can be identified by their spin projection.
4 bright excitons (S=1)
2 dark excitons (S=2)

Are the S=0 states bright? I can't think of I way how it can couple to photon.

The S=0 states are usually dark. If you have a special geometry, for example lying nanowires, where the optical axis is aligned perpendicular to the symmetry axis, these states can become optically allowed and will then couple to linearly polarized light. However, that is not the common case.

I'm studying exciton-photon coupling in microcavities to form polaritons.
It seems most publications about the exciton spin is not that detailed so I want to confirm if my understanding is correct.

In microcavities you usually do not couple bulk material to the light field, but quantum well excitons or sometimes quantum dot excitons. While light and heavy holes are energetically degenerate in bulk, the confinement/strain present in quantum wells leads to different energy shifts of the light and heavy holes due to their different effective masses. Most materials used for growing quantum wells in microcavities, including the omnipresent GaAs, have a zincblende-like structure where the heavy hole is significantly lower in energy than the light hole and therefore only heavy-hole excitons are considered and light-hole excitons can be neglected.

If you want light holes to become important, you can introduce additional strain or maybe magnetic fields to shift the energy levels around.

 

[phy127]

Thanks Cthugha. You explain just so well.

Yes, my study is on microcavities with embedded with quantum wells, the very microcavity used in polariton studies today. Again, you're right, I am introducing different strains to manipulate the valence band energies. The strain may be introduced externally by mechanical stress or or during growth of the microcavity. I am only doing numerical calculations since our university don't have the capacity for an experiment. As I'm reviewing the theory, I found some subtleties which are not explained in journals.

I am a newbie in this field of quantum optics in semiconductors. Sorry for being such a "kid" carrying a lot of questions. Please be patient with me. :)

1. Do heavy holes couple differently to light compared to light holes? I mean, is it an inherent property, or just a function of energy, effective mass, etc.. (I know this is my job to look this up, but I just need some directions so my mind will not go haywire.)

2. Are the two polarization of photons degenerate in the microcavity? Is there a way to sort of lift that degeneracy?

3. In coupling/interaction between the excitons and cavity photon, only the in-plane momentum is conserved, right? Now, if I introduce strain in the quantum well, it can warp the band, producing a non-parabolic dispersion which is obvious for large momentum. Will this affect the dispersion of the exciton greatly? Or it is just unaffected since it's size is very much greater than the lattice constant?

I hope you can give me some insights. Such a newbie, but I'm really interested in this field, quantum optics and semiconductors in general. Thank you in advance. :)

 

[Cthugha]

Thanks Cthugha. You explain just so well.
1. Do heavy holes couple differently to light compared to light holes? I mean, is it an inherent property, or just a function of energy, effective mass, etc.. (I know this is my job to look this up, but I just need some directions so my mind will not go haywire.)

Well, this is a matter of the dipole matrix elements/oscillator strengths of the transitions in question. I remember that for GaAs based quantum dots, the transition rates for heavy hole excitons are three times higher than for light hole excitons as a rule of thumb. For quantum wells I am not sure, though.

2. Are the two polarization of photons degenerate in the microcavity? Is there a way to sort of lift that degeneracy?

This depends on the system you want to probe. There is a for example a difference whether you are interested in the simple lower polariton or a condensed polariton system. In any way, cavities usually have an angle-dependent splitting between TE and TM modes. See for example Phys. Rev. B 59, 5082–5089 (1999) by Panzarini et al. for details.

3. In coupling/interaction between the excitons and cavity photon, only the in-plane momentum is conserved, right? Now, if I introduce strain in the quantum well, it can warp the band, producing a non-parabolic dispersion which is obvious for large momentum. Will this affect the dispersion of the exciton greatly? Or it is just unaffected since it's size is very much greater than the lattice constant?

That also depends on the kind of strain you want to apply. Is it local strain created by placing a small tip on the sample? Then you basically create a spatial trap due to the spatially varying energy of the exciton. Or are you rather thinking about strain pulses? To be honest I am not sure how much this changes the dispersion of the exciton. However, in terms of polaritons, the dispersion of the exciton compared to the dispersion of the cavity photon is flat anyway due to the effective masses differing by at least 3 orders of magnitude.

The Snoke group did a lot of experiments on stressed polariton samples. Maybe a look at Phys. Rev. B 81, 125311 (2010) by Balili et al. and references therein is some help.

Generally speaking, the book on microcavities by Kavokin and Baumberg is also a very comprehensive review on the topic.

 

[phy127]

Thank you very much Cthugha.. I think I'm ready to read again..
Just cleared some doubts.

I hope you will still be there if I have some queries again.
Thanks very much again. :)