<button md-icon-button (click)="start.toggle()">
<button md-icon-button (click)="logout()">
<md-sidenav #start mode="side" opened="true">
<a [routerLink]="view.link" md-list-item *ngFor="let view of views" (click)="sidenav.close()">
You can follow the plunker example I have linked in this git issue here: click
It's similar to what you need, but the icons are on the other side of the sidenav, thus you would need more animation in order to keep with that structure.
But I'm pretty sure this will give you a good idea how to collapse the sidenav, leaving a portion of it still visible.