Did Google already released a defined style or a component for this new circular FAB button or should I implement the design on my own?
The button is described here:
Google now provides an official library, called design library, containing the Fab Button. Just add the following Gradle dependency:
compile 'com.android.support:design:22.2.0'
Afterwards you can use the fab button like this:
More information can be found in their announcement
http://android-developers.blogspot.ch/2015/05/android-design-support-library.html
or on the javadoc page
http://developer.android.com/reference/android/support/design/widget/FloatingActionButton.html