Metal to impress the music Phd

I guess if you have to use tech death, Lykathea Aflame is probably a good choice. If many people who like metal can't get into Gorguts or Crimson Massacre, then how is someone not familiar with metal going to get what's going on? It seems doubtful to me. Lykathea Aflame is at least much more melodic and accessible for a first time listener.

I Am The Black Wizards would probably be a good choice, as it is widely held as one of the best composed metal songs, and it has some relation to classical structure.
 
Cynic - Textures would be a good song to play him. It's insanely musical, well structured, and doesn't have any vocals to put him off.
 
show to him bands like spiral architect, atheist, cynic, spastic ink, even dream theater is a good stuff

Those are all good.

Necrophagist would be good maybe.

Symphony X's "The Odyssey" would be great, but I'm not sure it's as crazy as what you're lloking for. He's sure to appreciate that one though.

Cryptopsy are way too off the wall for him to appreciate.