[Paper Review] Diverse fluctuations and anisotropic Gr{\" u}neisen parameter behavior in iron-based superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and their correlation with superconductivity

Chiaki Fujii, Shalamujiang Simayi+11 more|arXiv (Cornell University)|Jan 9, 2018

Iron-based superconductors research3 citations

TL;DR

This study investigates elastic softening and anisotropic Grüneisen parameters in Co-doped Ba(Fe₁₋ₓCoₓ)₂As₂, revealing that c-axis lattice fluctuations and C₄ symmetry structural fluctuations near the quantum critical point (QCP) strongly correlate with high-temperature superconductivity. The anisotropic Grüneisen parameters show enhanced inter-plane strain contributions near QCP, indicating that c-axis elongation and in-plane compression synergistically enhance superconducting transition temperature (T_sc).

ABSTRACT

In this study, the temperature dependence of elastic constants $C_{11}$, $C_{33}$, $C_{ m E} = (C_{11}-C_{12})/2$, $C_{66}$ and $C_{44}$ of the iron-based superconductor Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ (0 $\leqq x \leqq$ 0.245) have been measured. This system shows a large elastic softening in $C_{66}$ towards low temperatures. In addition to $C_{66}$, which originates from orthorhombic structural fluctuation, the samples near the optimal concentration show remarkable structural fluctuation in $C_{11}$ and $C_{33}$ elastic modes, which correspond to $Γ_{1}$ (C4) symmetry. It suggests the existence of diverse fluctuations in this system. Gr{\" u}neisen parameters were analyzed under some assumptions for structural and magnetic transition temperatures. Results showed that the Gr{\" u}neisen parameters for the inter-plane strain are remarkably enhanced toward the QCP, while those for the in-plane stress tend to turn down near the QCP. Gr{\" u}neisen parameters for the superconducting transition are anisotropic and shows remarkable Co-concentration dependence, suggesting that the in-plane isotropic compression and inter-layer elongation enhance the superconductivity. The correlation of Gr{\" u}neisen parameters between $T_{ m S}$, $T_{ m N}$ and $T_{ m sc}$ shows $c$-axis elongation and its relevant role in the emergence of superconductivity in this system.

Motivation & Objective

• To understand the role of structural fluctuations in iron-based superconductors, particularly in Ba(Fe₁₋ₓCoₓ)₂As₂.
• To analyze the anisotropic Grüneisen parameters and their correlation with superconducting transition temperature (T_sc).
• To determine how elastic softening in different crystallographic modes relates to electronic instabilities near the quantum critical point (QCP).
• To explore the impact of uniaxial pressure and chemical doping on T_sc enhancement via lattice engineering.

Proposed method

• Measurement of temperature-dependent elastic constants C₁₁, C₃₃, C_E, C₄₄, and C₆₆ in single-crystalline Ba(Fe₁₋ₓCoₓ)₂As₂ (x = 0 to 0.245).
• Analysis of elastic anomalies using Grüneisen parameter formalism under assumptions for structural and magnetic transition temperatures.
• Correlation of elastic softening in C₆₆ (C₂ symmetry) and C₁₁/C₃₃ (C₄ symmetry) with proximity to the quantum critical point.
• Evaluation of the relationship between elastic anomaly in the normal state (ΔCₙ) and superconducting state (ΔCₛ), assuming full-gap s₊₊ pairing symmetry.
• Use of charge susceptibility model to interpret band contributions to elastic anomalies and their suppression below T_sc.
• Comparison of Grüneisen parameters for in-plane stress (Ωₐ) and inter-plane strain (Ω_c), revealing their opposite sign and cancellation in bulk Ω.

Experimental results

Research questions

• RQ1 How do elastic softening in C₆₆, C₁₁, and C₃₃ modes correlate with superconducting transition temperature in Co-doped Ba(Fe₁₋ₓCoₓ)₂As₂?
• RQ2 What is the role of anisotropic Grüneisen parameters in stabilizing or enhancing T_sc near the quantum critical point?
• RQ3 Why does the superconducting elastic anomaly (ΔCₛ) not fully compensate the normal-state anomaly (ΔCₙ), and what does this imply about the pairing symmetry?
• RQ4 How do C₂ and C₄ structural fluctuations cooperate to promote high-T_sc in iron-based superconductors?
• RQ5 Can uniaxial pressure or chemical doping enhance T_sc by promoting c-axis elongation and in-plane compression?

Key findings

• C₆₆ exhibits strong elastic softening due to orthorhombic structural fluctuations, with the largest softening near optimal doping (x ≈ 0.116).
• C₁₁ and C₃₃ show significant softening near optimal doping, indicating the presence of C₄ symmetry (Γ₁) structural fluctuations, suggesting diverse fluctuation modes near the QCP.
• The Grüneisen parameter for inter-plane strain (Ω_c) is strongly enhanced toward the quantum critical point, while that for in-plane stress (Ωₐ) decreases, indicating anisotropic lattice response.
• The ratio of superconducting elastic anomaly (ΔCₛ) to normal-state anomaly (−ΔCₙ) is 0.28, implying that only 28% of the band electrons contribute to elastic softening, with 72% being gapless or non-superconducting.
• ΔCₛ vanishes rapidly with increasing Co concentration, becoming nearly zero at x = 0.116 despite a residual T_sc = 10.5 K, indicating a breakdown of simple BCS-like behavior.
• The correlation between C₃₃ and C₆₆ softening suggests cooperative effects between C₂ (C₆₆) and C₄ (C₁₁/C₃₃) fluctuations near the QCP, which may drive high-T_sc in this system.