that the Nernst signal is directly sensitive to the Berry phase $\theta_B = \pi \gamma$. Note that the Hall conductance is precisely ${e^2}/{(2h)}$ in the PHS theory with $\gamma=1$ ($\theta_B=\pi$), and otherwise deviates from this quantized value. In principle, this deviation can be used to distinguish the Dirac and PH breaking CFL states [@Son15], however in practice this deviation is a very small correction, of order $\mathcal{O}{\left(}k_F\ell{\right)}^{-2}$, to the total Hall conductance, and will be challenging to measure. In contrast, we see that the Nernst signal is directly proportional to the composite Fermi surface Berry phase, and is thus a direct measurement (rather than small correction) of the topological properties of the composite Fermi surface.

To extract $\theta_B$ from a Nernst effect measurement, it is desirable to independently determine the relevant parameters in Eq. (\[eq:Nernst\]) through other transport measurements, rather than relying on theoretical calculation in some particular model. To this end, $\sigma_0$ can be obtained by the longitudinal electrical conductivity $\sigma^{xx}\approx \frac{1}{(4\pi)^2\sigma_0}$, and the logarithmic derivative of $\sigma_0$ can be obtained from the longitudinal thermopower measurement $S^{xx}\approx \frac{\scriptsize{\L}Tk_F}{v_F}\frac{{\partial}\ln \sigma_0}{{\partial}\ln k_F}$. Together, these measurements allow for an experimental determination of the composite Fermi-surface Berry phase via the expression (valid when 