Fig. 1: In-plane Hall coefficient R_H across the T–H phase diagram of striped cuprates.

a, b Regions of T and H with different signs of R_H for La_1.7Eu_0.2Sr_0.1CuO₄ and La_1.48Nd_0.4Sr_0.12CuO₄, respectively. c, d Comparison of the results for R_H to the other transport data^3,4 for La_1.7Eu_0.2Sr_0.1CuO₄ and La_1.48Nd_0.4Sr_0.12CuO₄, respectively. T_c(H) (black squares): boundary of the vortex solid in which \({\rho }_{xx}\)(T < T_c) = 0 and R_H = 0, as expected for a superconductor. The upper critical field H_c2(T) ~ H_peak(T); H_peak(T) (dark green dots) are the fields above which the magnetoresistance changes from positive to negative^3,4. The low-T, viscous vortex liquid (VL) regime (light violet) is bounded by T_c(H) and, approximately, by T_peak(H) (positions of the peak in \({\rho }_{xx}\)(T); open blue diamonds), H^*(T) (crossover between non-Ohmic and Ohmic behavior³; open royal squares), or H_peak(T); here the behavior is metallic (d\({\rho }_{xx}\)/dT>0) with \({\rho }_{xx}\)(T → 0) = 0 and R_H = 0. The field-revealed normal state (blue) exhibits anomalous behavior: \({\rho }_{xx}\)(T) has an insulating, \({\mathrm{ln}}\,(1/T)\) dependence^3,4, but R_H = 0 despite the absence of superconductivity. At high T (yellow), R_H>0 and drops to zero at T = T₀(H) (magenta triangles). In the high-T VL regime (H < H_peak; dark beige), R_H becomes negative before vanishing at lower \(T={T}_{0}^{\prime}(H)\) (magenta squares), as the vortices become less mobile. The h/4e² symbols (open brown diamonds) show the (T, H) values where the sheet resistance changes from R_□/layer < R_Q = h/4e² at higher T, to R_□/layer>R_Q at lower T. Zero-field values of T_SO and T_CO are also shown; T_PG ~ 175 K and ~ 150 K for La_1.7Eu_0.2Sr_0.1CuO₄ and La_1.48Nd_0.4Sr_0.12CuO₄, respectively⁵⁵. All dashed lines guide the eye. In all panels, gray horizontal marks indicate measurement temperatures in different runs, the resolution of which defines vertical error bars for T₀ and \({T}_{0}^{\prime}\); horizontal error bars reflect the uncertainty in defining \({T}_{0}^{\prime}\) within our experimental resolution (see Supplementary Fig. 3 for the raw R_H(H) data).