Yes, especially in research-level topics. There are several research groups that work with finding ways to apply differential geometry concepts to solid state systems (although condensed matter seems to be the preferred term nowadays). See for example the book by Altland and Simons, Condensed Matter Field Theory, Chapter 9 "Topology". This book is suitable for a masters degree level class with a solid state class and a quantum field theory as prerequisites. The specified chapter has a (very!) brief primer on differential geometry, but I would probably have found it unintelligible if I had not had a proper differential geometry class first. The chapter will give you the very basics of what kind of research people are doing.
Some keywords to start with are topological (insulators|superconductors|order|field theories), quantum hall effect, composite fermions. Maybe these two talks (not by me) can be a good introduction: What is topological matter & why do we care? I, II.