The <md-breadcrumbs> custom element reads the top level router and displays a breadcrumb for each route fragment. Credits due to heruan's solution. This Materialize implementation is basically a copy of his work, adjusted to Materialize.
For simple manually-controlled breadcrumbs, use the classes provided by Materialize:
<nav>
<div class="nav-wrapper">
<div class="col s12">
<a href="#!" class="breadcrumb">First</a>
<a href="#!" class="breadcrumb">Second</a>
<a href="#!" class="breadcrumb">Third</a>
</div>
</div>
</nav>
You can add the primary
class to <nav>
to match your chosen primary color.