From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material) (1103.2363v1)

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.

• The paper demonstrates that Pb-Bi2201 transitions from a single-band metal to a high-Tc superconductor via two distinct thermal phase transitions.
• It employs ARPES, PKE, and TRR techniques to reveal changes in band dispersion and symmetry-breaking signals that mark the pseudogap and superconducting states.
• The findings highlight the role of density-wave orders and electronic symmetry breaking, offering new insights for modeling high-temperature superconductivity.

Summary of the Study on Transition from a Single-Band Metal to a High-Temperature Superconductor

This paper presents a comprehensive investigation into the transformation of Pb$_{0.55}$Bi$_{1.5}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+\delta}$ (Pb-Bi2201), focusing on the transition from a single-band metal phase to a high-temperature superconducting state, facilitated through two distinct thermal phase transitions. The authors employ an array of experimental techniques to elucidate the underlying electronic structure and order parameters that characterize these transformations.

Experimentation

The research utilizes high-quality single crystals of Pb-Bi2201, synthesized using the travel solvent floating zone method. These samples, near optimal doping levels, underwent post-annealing to finely tune their electronic properties. The authors determined carrier concentrations from Fermi surface volumes, corroborating the values with existing literature. The materials demonstrated an onset superconducting transition temperature ($T_c$) of 38 K and a pseudogap temperature ($T^*$) of 132 K, assessed using various methods, including Angle-Resolved Photoemission Spectroscopy (ARPES), Polar Kerr Effect (PKE), and Time-Resolved Reflectivity (TRR).

Key Findings

1. ARPES Analysis: ARPES data indicate that the transformation involves significant changes in band dispersion, notably the opening of a pseudogap near the antinodal region at $T^*$. The paper presents evidence of a $d$-wave gap formation along the Fermi surface within the superconducting state.
2. Polar Kerr Effect: PKE results show symmetry-breaking transitions suggestive of time-reversal symmetry breaking commencing below $T^*$. The PKE signal is postulated to correspond to a secondary order parameter driven by a primary symmetry-breaking transition, potentially electronic in nature.
3. Time-Resolved Reflectivity: TRR measurements confirm the presence of distinct phase responses above and below $T^*$, with the superconducting signal attributed to cooper pair breaking.
4. Simulations and Implications: Theoretical simulations suggest that a combination of density-wave orders can describe the observed phenomena in the superconducting and pseudogap states. It provides evidence indicating a non-zero momentum order parameter, although specific identification remains open to further theoretical exploration, including density-wave and nematic orders.

Implications and Future Directions

The paper's results contribute significantly to understanding the pseudogap phenomenon in cuprate superconductors, suggesting that the pseudogap state may involve broken symmetry states, such as electronic order parameters breaking rotational or time-reversal symmetry. This finding corroborates with previous research in the field and confirms the consistency of this behavior across various cuprate families.

Future research directions may focus on furthering our understanding of the nature of the pseudogap phase by exploring more sophisticated models involving fluctuations and strong electron correlations. In addition, experimental advancements could refine the resolution, offering deeper insights into the relationship between charge, spin, and pairing orders in the pseudogap and superconducting phases.

The paper adds to the body of knowledge regarding high-temperature superconductivity and the interplay of multiple phases, offering pathways to explore novel materials and theoretical models in condensed matter physics. Given the complex interplay of orders suggested within the paper, the exploration of novel pseudogap candidates and an in-depth computational approach to electron correlations and disorder impacts could be fruitful areas for advancing the field.