A Rigorous Proof of the Landau-Peierls Formula and much more

We present a rigorous mathematical treatment of the zero-field orbital magnetic susceptibility of a non-interacting Bloch electron gas, at fixed temperature and density, for both metals and semiconductors/insulators. In particular, we obtain the Landau-Peierls formula in the low temperature and density limit as conjectured by Kjeldaas and Kohn (Phys Rev 105:806-813, 1957).