Calculation of the Diamagnetic Susceptibility in a 2D Fermi Liquid

We present an investigation of the Landau diamagnetic susceptibility (χ_L) beyond what is found in traditional thermodynamic arguments. We first consider χ_L in the case of noninteracting fermions with an isotropic but otherwise arbitrary dispersion at T=0. In this scenario, we find that χ_L is determined entirely by the fermion dispersion and its derivatives at the Fermi surface. Then, we present a direct diagrammatic analysis of the self energy, Maki-Thompson, and Aslamazov-Larkin diagrams for the current-current correlator, which allows us to obtain corrections to χ_L up to second order in the Hubbard U. Lastly, to parallel results already established for the spin susceptibility, we search for nonanalytic corrections to χ_L in both magnetic field H and momentum Q, which will manifest themselves in two dimensions as a |H| and |Q| term, respectively.