Do you have to cite your external examiner in your PhD thesis? Maybe. There are reasons why you might need to, but the mere fact that they are your examiner isn't enough.
"I've just found out who my external examiner is, so I need to make sure I cite them"
The assumption seems to be that the examiner will give you a hard time for not citing them, but there are a few problems with this way of thinking.
First, do you want the kind of examiner who will punish you for not citing them? While there are plenty of insecure, narcissistic academics out there, the majority are not like this.
It can cause more problems to cite your examiner badly. If you haven't properly read their work, or if you misrepresent it, or if it's obvious you're just citing them to score points with them, you're inviting a difficult conversation in your defence.
Of course, it's likely that your examiner will have some relevant publications, but the same rules should apply to their work as any other citation.
- It should be placed in an appropriate context
- It should be a good example of the kind of work you are writing about
- You should have read it and have a clear reason for citing it (other than the fact that they are your examiner)
My own external examiner had invented one of the experimental techniques I used, so I would have cited him anyway. If your only reason for citing them is that they are your examiner, it's probably better not to.