Material ui appbar doesn't scale down when on mobile
I had the same issue and I just found the answer here: https://github.com/mui-org/material-ui/issues/7130
You need to handle viewport in your index.html file, for example like that:
<meta name="viewport" content="width=device-width, initial-scale=1, user-scalable=0, maximum-scale=1, minimum-scale=1"/>