# How to understand the spin of exciton?

In very recent years, exciton physics has been intensively explored as the emergence of 2D materials. Exciton is a bound electron-hole pair and is bosonic, namely hosting an integer spin.

• My first question is what the integer spin is? We all know the spin of an electron is $$\dfrac{1}{2}$$ and the hole will hold a positive charge compared to the kicked electron. Can we consider that the spin of the hole will be $$-\dfrac{1}{2}$$ and the exciton holds an integer spin $$0$$.

• My second question is how the formation of the exciton is affected by the spin of electrons? For example, the following figure from this paper indicates that the spin is closely related to the formation of the exciton.

• My third question is how can we demonstrate these spin-related exciton landscapes with first-principles calculations? • Interesting question. Ch 9 of Cohen and Louie's Fundamentals of Condensed Matter Physics has a brief explanation on the spin: basically it can be either a singlet ($S=0$) or triplet ($S=1$) state. Perhaps that helps address the first two questions.
– tmph
Feb 9 at 2:59
• +1 but you got lucky with Xivi76 answering all three questions right away. Otherwise I woukd have asked you to follow the "1 question per post" rule. Feb 9 at 3:40
• @NikeDattani Questions (1) and (2) are definitely inter-related. I'm not completely conversant with GW-BSE, so I wouldn't be able to do justice to question (3) - If OP wants to know how GW-BSE works, it should be a separate question for sure. Feb 9 at 4:43
• @Xivi76 I would have liked question (3) to be asked as a separate question, and your paragraph about it in your answer, could have been a comment or slightly extended answer. On some SE sites like the quantum computing stack exchange, the question would have been closed right away as being "too broad" because they are much more strict about multi-question posts. Here I would still like all posts to ask one question (within reason) but don't believe we need to close-vote to get there: I trust the users to do this one their own. The reasons why we want one question per post are large in number! Feb 9 at 5:26
• @NikeDattani I will consider your suggestion.
– Jack
Feb 11 at 7:56

• Sometimes one also encounters $S=2$ dark excitons. This can occur in e.g. semiconductor band structures with "heavy holes" that have spin-$3/2$. Feb 9 at 3:39