No, this isn't going to be an in-depth study of the topic. Alas, I don't think I have the tools or knowledge to pull that off if it were my intention. We're just going to look at a pair of music videos that are influenced by the movement.
The Red Hot Chili Peppers are a band that I like, but can't say I love. I respect what they've done, but it's rarely among my favorite stuff. A notable exception is the song "Otherside". I find it absolutely transcendent. There's also the little matter of its official video.
"Otherside" by Red Hot Chili Peppers
In terms of pure execution, I usually cite this as my favorite music video ever. The use of German expressionism is really clever and gives it a unique flavor compared to most promo films. Plus, I like the balance between the band's performance (ingeniously realized) and the nominal storyline. The color, the effects, even the motion of this video is just a thing of beauty.
Of course, German expressionism extended beyond the art world into the film world.
"Nosferatu" by Blue Öyster Cult
"Nosferatu" is a Blue Öyster Cult song from the 1977 album Spectres. The best remembered tune from Spectres is undoubtedly "Godzilla", but "Nosferatu" has a dreamlike, ethereal quality that makes it a stand-out track. It was inspired by F.W. Murnau's 1922 silent horror film NOSFERATU, an unauthorized retelling of Dracula starring Max Schreck.
As you have probably gathered, some enterprising souls in this day and age have put together a video of clips from NOSFERATU set to BOC's tribute. The music and the film meld together almost effortlessly. NOSFERATU is still creepy and unnerving despite (because of?) its advanced age. The imagery really holds up, too. And this fan project ably demonstrates that songwriters Helen Wheels and Joe Bouchard did their homework.
Can you illustrate further examples of German expressionism turning up in popular music?