Extended Data Fig. 2: Quadrature scaling in overdoped Tl2201.

a, ρ_ab(H, T) as measured in Tl2201 with T_c = 26.5 K. H² behaviour cedes to a H-linear resistivity at high fields. b, c, Scaling plots of [ρ_ab(H, T) − ρ_ab(0, 0)]/T versus H/T for overdoped Tl2201 (T_c = 26.5 K). As shown in c, there is a clear breakdown of the scaling at low H/T. d, e, Scaling plots of [ρ_ab(H, T) − ρ_ab(0, T)]/T versus H/T for the same sample where ρ(0, T) = ℱ(T) = ρ₀ + A_gT + BT². Note that A_g does not correspond to A, the full T-linear coefficient of the zero-field resistivity, since part of that is contained within the quadrature form. The inclusion of these additional T-dependent terms makes the data collapse over the full range of T. Taking the derivative with respect to H (as done in the main text) provides another means of isolating the quadrature MR from ℱ(T). The dashed lines in all panels represent the quadrature expression \(\Delta {\rho }_{ab}(H)=\alpha {k}_{{\rm{B}}}T\sqrt{1+{(\beta {\mu }_{0}H/T)}^{2}}\) (ρ₀ = 15.5 μΩ cm, A_g = 0.14 μΩ cm K⁻¹, B = 0.003 μΩ cm K⁻², αk_B = 0.04 μΩ cm K⁻¹, γμ_B = 0.20 μΩ cm T⁻¹). f, The derivatives with respect to magnetic field of the measured curves shown in a. g, When plotted against H/T, the derivatives presented in f collapse onto a universal curve (with the exception of those sections of each field sweep that are in the mixed state).