Here is how to root any 2011 Xperia running any of the 4.1.B.0.587 4.1.B.0.431 / 4.1.A.0.562 and 4.0.2.A.0.62 firmware . No need to downgrade kernels or anything, just root it straight away
Go to settings > Security > Mark "Unknown sources"
Settings > Developer options > Mark USB debugging
Settings > Xperia > connectivity > USB connection mode > select MSC mode
PC Companion installed on your PC.
1) Connect your phone to PC ( IMPORTANT > Skip PC Companion installation pop up on your phone.) and wait for the adb drivers to be installed. If these drivers don't get installed, phone would not be detected by Eroot.
Make sure nothing else ( specially flashtool ) is running on your PC in the background.
2) Download this rooting toolkit. Google Drive /// MediaFire /// 4-Shared and run it. If any downloading starts, cancel it by clicking the green button. Don't let the eroot download anything.
It should now detect your phone and show an option to "-root". Just click on it, wait till it finishes
3)Rooting done ( For confirmation see if any Super User app has been installed )
4) If by chance it fails for the first time, give it another go. it won't harm your phone in any way. If you still face problem, click on show content below
Go to your C:/ Drive / User/Username/AppData/Roaming/ folder and delete the eRoot folder.
If it says cannot be deleted then open up task manager on your PC and kill bec.exe . Then delete eroot folder.
Still not working ? used the archived method to root 2011 Xperia here below the animated Xperia picture.
5) While posting in the thread for help, remember to give details. Don't just write > "it's not working, help please ".
"Confirmed working on" List