Unfortunately, with regard to the latest releases of angular material, there is no such directive for creating such a tree-like menu; you have to combine different directives, such as a sidebar and a vertical menu.
I used the sidebar in my project:
<section class="wrapper" layout="row" flex>
<md-sidenav class="md-sidenav-left md-whiteframe-z3 background-red" md-component-id="left" md-is-locked-open="$mdMedia('gt-md')">
<md-toolbar>
<img class="logo" src="images/logo.png" />
</md-toolbar>
<md-content ng-controller="LeftCtrl">
<menu></menu>
<md-button ng-click="close()" class="md-primary" hide-gt-md>
Close Sidenav Left
</md-button>
</md-content>
<div flex></div>
<div class="copy">Copyright © 2015</div>
</md-sidenav>
<md-content class="wrapper" flex>
<div class="wrapper ngview-wrapper" layout="column" layout-fill layout-align="top center" ng-view></div>
<div flex></div>
</md-content>
</section>
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