The fundamental properties of all materials---such as their colour, hardness, or electrical conductivity---are determined, in the end, by the laws of quantum mechanics. Quantum materials are different because quantum mechanics adds an extra twist to the usual story. This can happen for many reasons, for example because of confined geometry, topological effects, or collective behaviour, but ultimately it always comes back to the fact that electrons (and sometimes atoms!) behave like waves, and not particles.
In recent years, I have been working with students and collaborators on developing models for two families of quantum materials: high temperature superconductors and strontium titanate interfaces.