Phase diagram and skewness of distribution
This protocol is extracted from research article:
Unusual behavior of cuprates explained by heterogeneous charge localization
Sci Adv, Jan 25, 2019; DOI: 10.1126/sciadv.aau4538

The gap distribution is usually skewed to the high-energy side (see also Supplementary Text) (12, 60). To quantify and assess the impact of this tendency, we parametrized the distribution as a Gaussian multiplied by its integralEmbedded Image(6)where α is a dimensionless parameter that controls the skewness of the distribution, and ϕ is a normalized Gaussian distribution with mean Δp and full width at half maximum δ. The skewness can be continuously varied by changing α. For α = 0, the distribution reduces to a simple Gaussian.

In fig. S1, we tested different values of the skew parameter and different functional forms for the gap distribution to demonstrate that this yields essentially the same phase diagrams. The main features are rather insensitive to the choice of distribution shape, mainly due to the fact that the resistivity calculation involves an integral over energy. Along with skewed Gaussians, we tested a shifted gamma distribution that features a heavier tail at high energies and gives a broader linear-T resistivity region on the overdoped side of the phase diagram.

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