What Can Impurities Tell Us About Quantum Matter?

Impurities can be a huge boon in the study of electronic properties of quantum matter. A known impurity placed in a host material can say a lot about the ground state of the host; conversely, the nature of impurities can be accurately deduced by studying how they behave in a well understood electronic phase. In this talk, I will review how different types of impurities are known to behave in metals, phases of conventional and unconventional superconductors, spin-orbit coupled materials etc. Later, I will argue that some of this conventional wisdom breaks down when the electronic bandwidth becomes the smallest scale in the problem.