Dear all,
I want to calculate the oscillator strength of CsPbBr3 perovskite quantum wells, following the reasoning of Andreani et al.Article Excitons in confined systems: from quantum well to bulk behaviour
To do this I need to determine the so-called 'spin-orbit factor', in the case of perovskites. The author describes the spin-orbit factor more elaborately in page 69 of the following book (Confined electrons and photons by Burstein and Weisbuch): https://link.springer.com/content/pdf/10.1007%2F978-1-4615-1963-8.pdf
The definition given there is that the spin-orbit factor is 'two times the singlet component in each irreducible representation', which I assume includes the representations for the valence and conduction bands, and for the exciton envelope function.
However, this formulation is confusing to me - what is meant by 'the singlet component'?
Also, since for perovskites the triplet state is emissive, I assume that the spin-orbit factor will be 'double the triplet component' in each irreducible representation, instead.
I have very little experience with group theory, so I would highly appreciate a simple explanation of how I can determine the spin-orbit factor for CsPbBr3 in the orthorhombic (Pnma) crystal phase. Thank you in advance.
Kind regards,
Claudiu
Dear Claudiu Iaru
For strontium ruthenate (the first reported perovskite superconductor) the spin-orbit factor was an intense matter of discussion 22 years ago in order to determine the pairing symmetry of the bounded Cooper pair.
It was nicely explained in the following article:
Article The Intriguing Superconductivity of Strontium Ruthenate
The idea is that in strontium ruthenate, the superconducting state is a triplet pairing state of the type ~ ( px + i py ) which involves the use of the spin Pauli matrices to describe the different orientations of the spin s with respect to the angular momentum L in a pair of bounded electrons, please check fig 2 of the above-mentioned reference.
Best Regards.
Dear Pedro L. Contreras E. ,
Thank you for your answer. It gives me some context as to where else the spin-orbit constant is involved.
However I should have probably specified that I am interested strictly in lead halide perovskites, in the context of photoluminescence, and the oscillator strength of interband transitions. Specifically, my material is CsPbBr3, which has an orthorhombic (Pnma) crystal structure.
As such, I do not immediately see a link to strontium ruthenate which, as I understand from your included reference, has a somewhat different crystal structure, meaning that the exciton fine structure and optical selection rules, will likely also be different from Pnma CsPbBr3.
Kind regards,
Claudiu Iaru
Dear Claudiu Iaru,
Thank you for the answer. Yes, it is totally a different question. I checked the reference you mention, but it is not clear how the spin-orbit Rashba coupling (SOC) is related to these excitonic systems in the paper. It is although related to SOC Rashba type coupling, and not to the spin-orbit factor, I mentioned in bounded pairs in my previous post.
Please check the following reference:
Article Importance of Spin–Orbit Coupling in Hybrid Organic/Inorgani...
Also, check figure 6 in the following reference. I guess the effect you are looking for is similar to the lifting by the crystal field of the bottom conduction band degeneracy with the decrease in the bandgap and the appearance of a SOC mentioned in figure 6, of course, the crystal symmetry field plays a role as well in the splitting and the appearance of SOC term:
Article Electronic model for self-assembled hybrid organic/perovskit...
For a general understanding of the spin-orbit term in the solid-state, the following external link is very illustrative:
https://staff.aist.go.jp/v.zayets/spin3_32_SpinOrbit.html
And check here the role of the SOC in excitonic systems:
https://link.springer.com/article/10.1134/S0021364013030028
Best Regards.
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