"More or less punk-rock". I don't know where Atreyu and Disturbed comes into the picture, but well...
For some more sophisticated punkish rock, try some songs from Ameoeurs (Start with their selftitled song, or Faux Semblants), or a little more around Disturbed (I don't like Disturbed, as their lyrics are based on sterotypes, but the band i recommend has more potential, lyrical, and more technical musicwise), i will recommend the band Thrice.
Bear in mind, that songs from these bands, differ a lot. Amesoeurs goes under Post-punk, Black Metal, Pop-rock, Ambient, Symphonic, and Shoegaze, but all with different songs, while Thrice has changed their style gradually, throughout their career.