Material currently does not have the exact equivalent of Bootstrap’s popover, but this can be easily reproduced simple by using a dropdown element with some customised CSS maybe. A quick example below:

The code will roughly look like:
<div class="dropdown-menu dropdown-menu-right" style="min-width: 320px; padding-top: 0 !important; padding-bottom: 0 !important;">
<div class="tile">
<div class="tile-inner text-black">
<strong>Notifications</strong>
</div>
</div>
<div class="tile">
<div class="tile-side pull-left">
<div class="avatar avatar-sm">
<img ...>
</div>
</div>
<div class="tile-inner text-black">
<span>...</span>
</div>
</div>
<div class="tile">
<div class="tile-side pull-left">
<div class="avatar avatar-sm">
<img ...>
</div>
</div>
<div class="tile-inner text-black">
<span>...</span>
</div>
</div>
<div class="tile">
<div class="tile-side pull-left">
<div class="avatar avatar-sm">
<img ...>
</div>
</div>
<div class="tile-inner text-black">
<span>...</span>
</div>
</div>
<a class="tile">
<div class="tile-inner text-black text-center">
<span>Show All</span>
</div>
</a>
</div>
Hope this helps.