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We demonstrate a remarkable property of metallic Fermi liquids: thetransverse conductivity assumes a universal value in the quasi-static ($\omega\rightarrow 0$) limit for wavevectors $q$ in the regime $l_{\rm mfp}^{-1} \ll q\ll p_{\rm F}$, where $l_{\rm mfp}$ is the mean free path and $p_{\rm F}$ isthe Fermi momentum. This value is $(e^2/h) \mathcal{R}_{\rm FS}/q$ in twodimensions (2D), where $\mathcal{R}_{\rm FS}$ measures the local radius ofcurvature of the Fermi surface in momentum space. Even more surprisingly, wefind that U(1) spin liquids with a spinon Fermi surface have the same universaltransverse conductivity. This means such spin liquids behave effectively asmetals in this regime, even though they appear insulating in standard transportexperiments. Moreover, we show that transverse current fluctuations result in auniversal low-frequency magnetic noise that can be directly probed by a spinqubit, such as a nitrogen-vacancy center in diamond, placed at a distance $z$above of the 2D metal or spin liquid. Specifically the magnetic noise is givenby $C\omega \mathcal{P}_{\rm FS}/z$, where $\mathcal{P}_{\rm FS}$ is theperimeter of the Fermi surface in momentum space and $C$ is a combination offundamental constants of nature. Therefore these observables are controlledpurely by the geometry of the Fermi surface and are independent of kinematicdetails of the quasi-particles, such as their effective mass and interactions.This behavior can be used as a new technique to measure the size of the Fermisurface of metals and as a smoking gun probe to pinpoint the presence of theelusive spinon Fermi surface in two-dimensional systems. We estimate that thisuniversal regime is within reach of current nitrogen-vacancy centerspectroscopic techniques for several spinon Fermi surface candidate materials.

The universal shear conductivity of Fermi liquids and spinon Fermi surface states and its detection via spin qubit noise magnetometry