Berry phase effects on the transverse conductivity of Fermi surfaces and their detection via spin qubit noise magnetometry

The quasi-static transverse conductivity of clean Fermi liquids at long wavelengths displays a remarkably universal behaviour: it is determined solely by the radius of curvature of the Fermi surface and does not depend on details such as the quasi-particle mass or their interactions. Here we demonstrate that Berry phases do not alter such universality by directly computing the transverse conductivity of two-dimensional electronic systems with Dirac dispersions, such as those appearing in graphene and its chiral multilayer variants. Interestingly, however, such universality ceases to hold at wave-vectors comparable to the Fermi radius, where Dirac fermions display a vividly distict transverse conductivity relative to parabolic Fermions, with a rich wave-vector dependence that includes divergences, oscillations and zeroes. We discuss how this can be probed by measuring the $T_1$ relaxation time of spin qubits, such as NV centers or nuclear spins, placed near such 2D systems.