Showing anatta from modern psychology or neuroscience? I have heard Ajahn Brahm say in a talk, if I recall, that modern science or psychology has demonstrated anatta in some way. 

It seems unnecessary to invoke science to validate any of Buddhism, but until one can see no self from direct experience, looking at science may be beneficial for the purpose of gaining an intellectual understanding. 

Is there any useful research or writing is there that shows anatta from the perspective of modern psychology or neuroscience? 

I'd think something like this would be produced by the Mind &amp; Life Institute. All I could find is this blurb crediting Evan Thompson. It doesn't say much.
Yes. Please see Quartz article dated February 9, 2018 by Ephrat Livni, entitled "Scientists studying psychoactive drugs accidentally proved the self is an illusion". Research papers are linked in it.

Also, please see the TED Talk by neuroscientist Anil Seth entitled "Your brain hallucinates your conscious reality" which was published on YouTube on July 18, 2017.