Nonanalytic Corrections to the Landau Diamagnetic Susceptibility

We analyze potential non-analytic terms in the Landau diamagnetic susceptibility, $\chi_{dia}$, at a finite temperature $T$ and/or in-plane magnetic field $H$ in a two-dimensional (2D) Fermi liquid. To do this, we express the diamagnetic susceptibility as $\chi_{dia} = (e/c)^2 \lim_{Q\rightarrow0} \Pi^{JJ}_\perp (Q)/Q^2$, where $\Pi^{JJ}_\perp$ is the transverse component of the static current-current correlator, and evaluate $\Pi^{JJ}_\perp (Q)$ for a system of fermions with Hubbard interaction to second order in Hubbard $U$ by combining self energy, Maki-Thompson, and Aslamazov-Larkin diagrams. We find that at $T=H=0$, the expansion of $\Pi^{JJ}_\perp (Q)/Q^2$ in $U$ is regular, but at a finite $T$ and/or $H$, it contains $U^2 T$ and/or $U^2 |H|$ terms. Similar terms have been previously found for the paramagnetic Pauli susceptibility. We obtain the full expression for the non-analytic $\delta \chi_{dia} (H,T)$ when both $T$ and $H$ are finite, and show that the $H/T$ dependence is similar to that for the Pauli susceptibility.