Seems like Google doesn't display some special characters if they are used in
<title></title>. What are the characters that will be visible in SERPs for site titles?
Here is an article about icon characters and how they can be used so that your listing in the SERPs catches the eye. It does appear to be somewhat out of date because I don't see many of characters in the SERPs anymore for the examples they have.
That isn't to say that it isn't possible. When doing a research query for this question, I came across this listing which abuses special characters, probably through rich snippets:
One of the sites that was in the article appears to have found some icon characters that still work when used in title tags: