Fig. 1: Heterogeneous gap filling in Bi2201.

a, The average spectra of eight different doping levels, labelled by their Tc; UD, underdoped; OPT, optimally doped; OD overdoped; EF, Fermi energy. The shaded areas indicate the energy range used in the fitting procedure. The blue arrows show the average extracted gap magnitude. For the UD25K and OPT35K samples, the red arrows in the righthand images indicate the pseudogap as determined by He et al.32. The inset in the top spectrum indicates the position of the samples on the superconducting dome. b–d, Spectra along 3 nm line-cut for the OD23K, OD12K and OD3K samples, respectively. These raw, unprocessed spectra indicate the high degree of electronic inhomogeneity in these samples. e, A line-cut of spectra from a self-consistent BdG simulation from the centre of a superconducting puddle (r = 0) to the metallic environment, which shows the van Hove singularity modelled to be close to the Fermi level (main text and Supplementary Section IV for details). The boundary of the puddle is indicated by the red spectrum. The pairing interaction is non-zero inside the puddle (that is, inside the red line) and is zero outside it. The energy unit is relative to the hopping parameter t1, and the length unit is relative to the coherence length ξ (Supplementary Section IV). DOS, density of states. f, Typical topography measured on the OD12K sample on the same length scale as b–d.