I found the left side menu on the material ui demo page: http://www.material-ui.com/#/components/app-bar quite appealing. However, it doesn't seem to be one of the components that material ui provided.
Is there any component library with a side menu like that?
The Drawer, is the side-menu component material-ui provides, so that you can use both Drawer and AppBar components together in your case I think. They have a Responsive Drawer example which will probably prove very helpful.