Extended Data Fig. 2: Extracting ΔS from κ(T) in R2G.
From: Fluctuating magnetism and Pomeranchuk effect in multilayer graphene
a, High-resolution measurement of κ = ∂μ/∂ne for different temperatures at D = 0.5 V nm−1. b, The difference in κ between pairs of temperatures, \(\Delta \kappa \times {({T}_{{\rm{H}}}-{T}_{{\rm{L}}})}^{-1}=\)\((\kappa ({T}_{{\rm{H}}})-\kappa ({T}_{{\rm{L}}}))/\Delta T\approx {{\rm{d}}}^{2}S/{\rm{d}}{n}_{{\rm{e}}}^{2}\) measured at high |ne|, at which no broken symmetries are observed at low temperature. c, \({{\rm{d}}}^{2}S/{\rm{d}}{n}_{{\rm{e}}}^{2}\) in the low-|ne| regime of broken symmetries. d, Data from panel b integrated with respect to ne to give dS/dne. The bounds of integration are −1.25 × 1012 cm−2 and −0.55 × 1012 cm−2. e, Data from panel c integrated with respect to ne to give dS/dne. The bounds of integration are −0.55 × 1012 cm−2 and 0, chosen to correspond to the band edge at low |ne|, the onset of appreciable Δκ at high |ne|. f, Data in panel d integrated with respect to ne to give ΔS. The entropy is found to be ΔS ≪ 0.1 kB throughout this range. g, Data in panel e integrated with respect to ne to give ΔS. These data are shown in the main text as Fig. 2a. The grey lines in panels f and g show the Fermi liquid entropy ΔSFL calculated from single-particle band structure at finite temperature T = 2 K. Evidently, the measured entropy at finite displacement field exceeds the theoretical expectations of a degenerate Fermi liquid by more than an order of magnitude. Details about this data analysis are given in Methods.
