Keep in mind I have no idea what I am doing... this returns the url that you want:
$current_user = wp_get_current_user();
$current_name = $current_user->user_login;
$url = site_url('/author/');
echo $url . $current_name;
So after adding all but the last line of that to define the two partsabove the 'href' I think you could then say:
'href' => $url . $current_name;
or one more step (probably unnecessary)
$current_user = wp_get_current_user();
$current_name = $current_user->user_login;
$url = site_url('/author/');
$new_url = $url . $current_name;
'href' =>$new_url;
I am sure someone else probably knows a better way but at least this should get you going in the right direction.