I would like to achieve a mobile menu which is always visible on the bottom of my page. I don't know if there is a specific name for such menus but I've found a page which does exactly this menu:
What is the best way to achieve exactly this for tablet and smaller devices using materialize?
There is something called a Toolbar in Materialize.
<div class="fixed-action-btn toolbar">
<a class="btn-floating btn-large red">
<i class="large material-icons">mode_edit</i>
</a>
<ul>
<li class="waves-effect waves-light"><a href="#!"><i class="material-icons">insert_chart</i></a></li>
<li class="waves-effect waves-light"><a href="#!"><i class="material-icons">format_quote</i></a></li>
<li class="waves-effect waves-light"><a href="#!"><i class="material-icons">publish</i></a></li>
<li class="waves-effect waves-light"><a href="#!"><i class="material-icons">attach_file</i></a></li>
</ul>
</div>
But it's not the same what you are looking for. You have to modify this or you need to create your own.
Fab for toolbar: http://materializecss.com/buttons.html