How can I use Public Key Authentication for SFTP in ES File Explorer?
Your question made me try to use the same configuration.

Solution

Generate your key pair in OpenSSH key file format, I used my linux workstation:

 ssh-keygen -t rsa -C "KEYNAME"


(I left passphrase empty but I think it will work with it too, add the public key to your host:

 cat ~/.ssh/id_rsa.pub &gt;&gt; ~/.ssh/authorized_keys


(Assuming that's the same machine you want to connect to)
Copy private key id_rsa to your phone and use that one. :)

I found the clue on logcat:

 W/System.err(27250): com.jcraft.jsch.JSchException: invalid privatekey: /sdcard/key.ppk


and this answer brought me in the right direction.

How to copy private key from connectBot export workaround

Only private keys without passphrase can be copied, so you can change password and set it empty, this key is NOT compatible with ES File Explorer.