I bought a tempered glass screen protector installed and after about 2 week, I removed the screen protector. It left with "watermark" in the inner layer of the LCD screen and later the screen became not responding to touch. I have to send the unit to Sony repair center.
The name of the Tempered Glass Screen Protector I bought was:
RetinaGuard 視網盾 Sony Xperia Z2 眼睛防護 防藍光玻璃保護膜