Electrodynamic response of Ba(Fe1-xRhx)2As2 across the s+- to s++ order parameter transition

TL;DR

This study investigates the electrodynamic response of Ba(Fe1-xRhx)2As2 superconductors to identify signatures of the transition from s+- to s++ order parameter symmetry induced by disorder, revealing peculiar surface resistance and conductivity behaviors.

Contribution

It provides the first analysis of electrodynamic properties across the s+- to s++ transition in iron-based superconductors, highlighting observable signatures of the order parameter change.

Findings

Surface resistance shows anomalies at the transition.

Normal conductivity exhibits distinctive behavior near the transition.

Electrodynamic response traces the order parameter transition.

Abstract

Most iron-based superconductors are characterized by the s+- symmetry of their order parameter, and are expected to go through a transition to the s++ state if enough disorder is introduced. We previously reported the observation of this transition in Ba(Fe1-xRhx)2As2 through a study of the disorder dependence of the critical temperature and low-temperature London penetration depth. In this paper we report on the analysis of the electrodynamic response of the same sample across the transition and we identify peculiarities in the behaviour of the surface resistance and normal conductivity, that can be considered as traces of the transition itself.

Tables

Table 1. Table 1: Normalized surface impedance values across the s ± to s ++ transition.

d.p.a.($\times {10}^{-3}$)	$R_s\left(10K\right)/R_s\left(T_c\right)$	$X_s\left(10K\right)/X_s\left(T_c\right)$
0	0.01	0.06
1.02	0.01	0.32
3.07	0.03	0.44
4.10	0.07	0.65
\hdashline 5.12	0.10	0.23
5.63	0.14	0.30
6.15	0.19	0.37
6.63	0.22	0.46

Full text

1 Introduction

Most iron-based superconductors (IBS), and in particular those of the 122 family, such as doped BaFe2As2, are characterized by a fully gapped pairing state with sign changing over different Fermi sheets: the s*±* state Chubukov2008 . These systems present multiple bands that cross the Fermi level and on which superconducting s-wave gaps open Stanev2008 . The relative sign of these gaps is opposite on hole and electron bands and coupling between them is provided mainly by antiferromagnetic spin fluctuations Mazin2008 .

Although direct experimental observations of the symmetry of the pairing state are extremely difficult to achieve, the s*±* state can be indisputably assigned through the identification of the disorder-driven transition to the s*++* sign-preserving state predicted by Efremov et al. Efremov2011 . In any multi-band superconductor, disorder causes the scattering of particles between different bands, that in turn drives the values of the gaps towards a common value Wang2013 . If in the pristine system the gaps have different sign, it is necessary for the system to reach a state in which all the gaps have the same sign in order for their values to converge: this is the s*±* to s*++* transition.

This behaviour was first observed by Schilling et al. Schilling2016 in thin films of Ba(Fe1-xCox)2As2 by extracting the value of the small gap from the coherence peak in the measured optical conductivity at increasing levels of disorder introduced via electron irradiation. In our previous work on this topic Ghigo2018prl , we identified the s*±* to s*++* transition in proton irradiated Ba(Fe1-xRhx)2As2 single crystals by observing one of its predicted hallmarks: a drop in the low-temperature value of the penetration depth. The experimental observation was validated by two-bands Eliashberg calculations that reproduced the experimental critical temperatures and superfluid densities, with the transition visible in the change of sign of the smallest gap at the expected disorder level. Those penetration depth and critical temperature measurements were carried out by means of a microwave resonator technique that also yields the normal conductivity $\sigma_{n}$ and surface impedance $Z_{s}$ as a function of temperature, below and above the critical temperature $T_{c}$ Ghigo2016ieee .

In this work we analyze the behaviour of $\sigma_{n}$ and $Z_{s}$ across the s*±* to s*++* transition and we identify peculiarities that can be considered as traces of the transition itself.

2 Experiment and results

The sample under investigation is the same optimally doped single crystal of Ba(Fe1-xRhx)2As2 studied in our previous work Ghigo2018prl . It was grown out of self flux using conventional high-temperature solution growth techniques Ni2008 ; Ni2009 , resulting in a doping level $x=0.068$ (determined by wavelength dispersive X-ray spectroscopy Hodovanets2012 ) and in a pristine critical temperature $T_{c}=23.5$ K. The critical temperature considered here is the temperature at which the penetration depth diverges, as reported in Ghigo2018prl . Disorder was introduced in the system in the form of point-like defects and small cascades via successive 3.5-MeV proton irradiation sessions. The amount of induced disorder was estimated as displacements per atom (d.p.a.) via Monte Carlo simulations with PHITS phits and SRIM srim codes.

Superconducting properties were characterized in the pristine state and after each irradiation session using a microwave resonator technique, already applied to IBS with different doping species, pristine Ghigo2017prb and irradiated Ghigo2017scirep . This technique consists in measuring the perturbations induced to the resonance of an YBa2Cu3O7-x coplanar waveguide resonator by coupling a small crystal to it. From the modifications in the resonance frequency and quality factor, and after a calibration procedure (explained in details in Ghigo2018sust and Ghigo2017prb ), the London penetration depth, normal conductivity and surface impedance as a function of temperature can be obtained.

Penetration depth data was used in Ghigo2018prl to identify the s*±* to s*++* transition. In the following, normal conductivity and surface impedance are analyzed.

Figure 1 shows the temperature dependence of the normal conductivity $\sigma_{n}$, normalized to its value at $T_{c}$, for all the levels of disorder analyzed. The sample in the pristine state shows a sharp increase of $\sigma_{n}$ below the critical temperature. When disorder is introduced, but the s*±* to s*++* transition has not yet occurred, the curves have a qualitatively different shape: the conductivity at low temperature is strongly suppressed and shows a clear and large peak at approximately 17 K. Surprisingly, when the s*++* state is reached, the conductivity curves become very similar to that of the pristine state, although with values that decrease with increasing disorder.

The surface impedance $Z_{s}=R_{s}+iX_{s}$ as a function of temperature is shown in Figure 2 for the pristine sample and after each irradiation dose. Both $R_{s}$ and $X_{s}$ are normalized to their values at $T_{c}$, above which $R_{s}=X_{s}$ as expected in the classical skin effect regime. When disorder increases, the real and imaginary parts of the impedance behave differently: at low temperature the normalized surface resistance shows a monotonic increase, whereas low temperature value of the surface reactance drops at the transition (see Table 2 for quantitative values). Moreover, in the s*++* state $X_{s}$ also develops a shoulder near $T=15$ K.