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

The quasistatic transverse conductivity of clean Fermi liquids at long wavelengths displays a remarkably universal behavior: it is determined solely by the radius of curvature of the Fermi surface and does not depend on details such as the quasiparticle 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 distinct transverse conductivity relative to parabolic Fermions, with a rich wave vector dependence that includes divergences, oscillations, and zeros. We discuss how this can be probed by measuring the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>T</a:mi><a:mn>1</a:mn></a:msub></a:math> relaxation time of spin qubits, such as NV centers or nuclear spins, placed near such 2D systems.