From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)

TL;DR

This paper discusses experimental observations and theoretical modeling of the pseudogap phase in high-temperature superconductors, exploring the nature of the order parameter and its relation to phase transitions from a metallic to a superconducting state.

Contribution

It provides detailed experimental analysis and mean-field simulations of various density wave and nematic orders related to the pseudogap in high-Tc superconductors.

Findings

Evidence supporting finite-Q order in pseudogap phase

Mean-field models partially reproduce experimental band dispersions

Discussion on the limitations of current density wave interpretations

Abstract

In this supporting material for the main paper (the preceding submission), we show, in addition to the related information for the experiments, additional discussion that cannot fit in the main paper (due to the space constraint). It includes further discussion about our experimental observations, wider implications of our main findings with various reported candidates for the pseudogap order, and a simple mean-field argument that favors interpretations based on a finite-Q order (density wave) for the pseudogap seen by ARPES (whether "the pseudogap order" is a single order or contains multiple ingredients, is an independent, open issue). We also include a detailed simulation section, in which we model different candidates (various density wave/nematic order) for the pseudogap order in simple forms using a mean-field approach, and discuss their partial success as well as limitations in describing the experimental observations. These simulations are based on a tight-binding model with parameters fitted globally (and reasonably well) to the experimental band dispersions (by tracking the maximum of the energy distribution curve), which could be useful for further theoretical explorations on this issue.