PS4 Controller model CUH-ZCT1. Released in November 2013 by Sony Computer Entertainment, this six-axis, 3.7 V lithium ion battery controller is uncomplicated to repair. (NOTE: Teardown guide is NOT for this model)
Try resetting your controller "On the back of your controller, you will find a tiny hole – the reset button is inside this hole. Use a small, unfolded paper clip (or something similar) to press and hold the reset button for at least five seconds. Your controller should now have been reset." - Playstation
Try using a cotton swap and some isopropyl alcohol to clean around the button as it is probably sticking causing the issue of the button being pressed when it is not.
If that doesn't seem to fix it you can always replace the button using this guide on Ifixit R2/L2 button replacement guide and you should be able to find replacement buttons here from Ifixit as well R2 button assembly