[Paper Review] Specific heat of Ba$_{0.59}$K$_{0.41}$Fe$_{2}$As$_{2}$, and a new method for identifying the electron contribution: two electron bands with different energy gaps in the superconducting state

C. R. Rotundu, Thomas Forrest+2 more|arXiv (Cornell University)|Nov 1, 2014

Iron-based superconductors research40 references3 citations

TL;DR

This study presents a novel analysis method for specific heat data in the iron-based superconductor Ba$_{0.59}$K$_{0.41}$Fe$_2$As$_2$ (T$_c$ = 36.9 K), directly extracting the electron contribution without relying on approximate lattice contribution subtraction. The method reveals two distinct electron bands with energy gaps differing by a factor of 3.8, where 77% of the electron density of states originates from the larger-gap band, challenging conventional models and indicating strong electron correlation effects with no theoretical precedent for the observed effective mass enhancement.

ABSTRACT

We report measurements of the specific heat of Ba$_{0.59}$K$_{0.41}$Fe$_{2}$As$_{2}$, an Fe-pnictide superconductor with $T_c$ = 36.9 K, for which there are suggestions of an unusual electron pairing mechanism. We use a new method of analysis of the data to derive the parameters characteristic of the electron contribution. It is based on comparisons of $α$-model expressions for the electron contribution with the total measured specific heat, which give the electron contribution directly. It obviates the need in the conventional analyses for an independent, necessarily approximate, determination of the lattice contribution, which is subtracted from the total specific heat to obtain the electron contribution. It eliminates the uncertainties and errors in the electron contribution that follow from the approximations in the determination of the lattice contribution. Our values of the parameters characteristic of the electron contribution differ significantly from those obtained in conventional analyses of specific-heat data for five similar hole-doped BaFe$_{2}$As$_{2}$ superconductors, which also differ significantly among themselves. They show that the electron density of states is comprised of contributions from two electron bands with superconducting-state energy gaps that differ by a factor 3.8, with 77$\%$ coming from the band with the larger gap. The variation of the specific heat with magnetic field is consistent with extended $s$-wave pairing, one of the theoretical predictions. The relation between the densities of states and the energy gaps in the two bands is not consistent with a theoretical model based on interband interactions alone. Comparison of the normal-state density of states with band-structure calculations shows an extraordinarily large effective mass enhancement, for which there is no precedent in similar materials and no theoretical explanation.

Motivation & Objective

• To develop a more accurate method for isolating the electron contribution in specific heat measurements of superconductors without relying on approximate lattice contribution subtraction.
• To resolve inconsistencies in electron parameter extraction from conventional analyses of similar hole-doped BaFe$_2$As$_2$ superconductors.
• To investigate the electronic structure and pairing symmetry in Ba$_{0.59}$K$_{0.41}$Fe$_2$As$_2$, particularly the presence of multiple superconducting gaps.
• To test the consistency of observed gap and density of states relationships with existing theoretical models based on interband interactions.

Proposed method

• The authors introduce an α-model-based analysis that compares theoretical expressions for the electron contribution directly to the total measured specific heat.
• This method bypasses the need for an independent, approximate determination of the lattice contribution, which is a major source of error in conventional analyses.
• The electron contribution is derived directly from fitting the α-model to the total specific heat data, minimizing systematic uncertainties.
• The analysis uses temperature- and magnetic field-dependent specific heat measurements to extract superconducting gap parameters and density of states.
• The method enables direct comparison between observed specific heat behavior and theoretical predictions for extended s-wave pairing.
• It allows for the identification of multiple electron bands with different energy gaps by fitting the data to a two-gap model.

Experimental results

Research questions

• RQ1 Can a new method for analyzing specific heat data eliminate the uncertainties associated with subtracting an approximate lattice contribution in superconducting materials?
• RQ2 What is the nature of the electron density of states in Ba$_{0.59}$K$_{0.41}$Fe$_2$As$_2$, and does it support multiple superconducting gaps?
• RQ3 Is the observed relationship between the density of states and energy gaps consistent with theoretical models based on interband interactions?
• RQ4 What is the origin of the extraordinarily large effective mass enhancement observed in the normal state, and how does it compare to band-structure calculations?
• RQ5 Does the magnetic field dependence of specific heat support extended s-wave pairing symmetry in this iron-based superconductor?

Key findings

• The new analysis method successfully isolates the electron contribution without relying on an approximate lattice subtraction, reducing systematic errors in parameter extraction.
• The electron density of states in Ba$_{0.59}$K$_{0.41}$Fe$_2$As$_2$ arises from two distinct electron bands with superconducting energy gaps differing by a factor of 3.8.
• Seventy-seven percent of the electron contribution to the density of states originates from the band with the larger energy gap.
• The magnetic field dependence of specific heat is consistent with extended s-wave pairing symmetry, supporting one of the theoretical predictions for this material.
• The observed relationship between the density of states and energy gaps in the two bands is inconsistent with theoretical models based solely on interband interactions.
• The normal-state density of states shows an extraordinarily large effective mass enhancement that has no precedent in similar materials and lacks a theoretical explanation.