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Universal Electrical Resistivity in Iron-Based High-Temperature Superconductors

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26 August 2026

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27 August 2026

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Abstract
Temperature-dependent electrical resistivity ρ(T) in cuprate, iron-based, and nickelate superconductors represents one of unresolved problems in modern solid-state physics, because of the high absolute value of ρ(T), which, in many cases, exceeds the Ioffe-Rigel criterion, and a large difference in the ρ(T) shape for samples with different doping. Here I show that the nearest neighbours parallel resistivity model (arXiv: 2607.23484) can well describe the in-plane resistivity ρab(T) in iron-based superconductors (IBS) of type 11, 111, 122, 1111, 1144 and 42214 in which the spin density wave phase or nematic order is suppressed by doping. The model is based on the postulate that ρab(T) is a sum of two parallel conduction channels, where one channel is described by the Bloch-Grüneisen equation and the other by the Arrhenius hopping equation. Consequently, the variety of ρab(T) in the IBS is explained as a variation of the Debye temperature ΘD and the hopping activation energy Ea. The derived Debye temperatures were used to estimate the electron-phonon coupling constant in the studied IBS.
Keywords: 
iron-based superconductors
;  
electrical resistivity
;  
the Bloch-Grüneisen equation
;  
the Arrhenius hopping equation
;  
the nearest neighbours parallel resistivity model
Subject: 
Physical Sciences  -   Condensed Matter Physics

I. Introduction

Iron-based superconductors (IBS) discovered by Hosono’s group two decades ago [1] represent perhaps the richest family of high-temperature superconductors (HTS) in phases, chemical and structural composition [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17], among other families of HTS [18,19,20,21,22,23]. The physical, chemical, and superconducting properties, phase transformations, spin density correlations in IBS and related compounds have been extensively studied since then [15,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61]. There are several ongoing projects for the development of manufacturing technology for the practical use of IBS [62,63,64,65,66,67,68,69].
Temperature-dependent electrical resistivity ρ T represents one of the most common measurements in the discovery and study of superconductors [70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95]. There are two commonly accepted approaches to analyzing ρ T data measured in the IBS, one of which is the second-order polynomial fitting [96,97,98,99,100,101]:
ρ T = ∑ i = 1 N ρ i T = ∑ i = 1 N A i × T i
where, i = 0,1 , 2 , and A i are free-fitting parameters. This approach has three main problems. First, it works only in a narrow temperature range well above Tc [102]. Second, the obtained parameters are highly dependent on the temperature range chosen for fitting. Third, the obtained parameters A i can change significantly (or even change sign) with a small change in the experimental ρ T curve.
The second common approach is the power-law fit [97,98,103,104]:
ρ T = ρ 0 + A × T n ,
where ρ 0 , A , and n are free-fitting parameters. First, it also works only in a narrow temperature range well above Tc [104]. Another problem with this approach is that the deduced parameters A have different physical units Ω m K − n , and therefore the interpretation and comparison of the deduced parameters for different samples are impossible. Other problems with this approach were discussed in Ref. [105].
In overall, Equations 1,2 are based on Matthiessen’s rule [106,107,108,109,110]:
ρ T = ∑ i = 1 N ρ i T ,
where ρ i T represents a direct summation contribution to the resistivity from the i-th dissipation mechanism. It should be noted, that the Matthiessen's rule relies on very little physical basis for single-phase metallic conductors (in particular for the in-plane resistivity of single crystals, ρ a b T ), because electric current flows through the entire cross-section of conductors in the normal state (this differs from the non-dissipative transport current flow in superconductors [63,64,65,66]), and, consequently, the contribution of each dissipation mechanism should be a sum of their conductivities:
ρ T = 1 ∑ i = 1 N 1 ρ i T ,
because each dissipation mechanism contributes as a resistance in the parallel electrical circuit.
This fundamental paradigm was taken into account in the parallel resistivity model [111,112,113]:
ρ T = 1 1 ρ s a t + 1 ρ B G = 1 1 ρ s a t + 1 ρ 0 + ρ D × T Θ D p × ∫ 0 Θ D T x p e x − 1 1 − e − x d x ,
where ρ s a t , ρ 0 , ρ D , Θ D are free fitting parameters, p = 5 for pure electron-phonon scattering mechanism (if the dominant dissipation mechanism is different, then p exhibits different values [114]); and ρ s a t is temperature-independent free-fitting parameters, which is related [111] to the Ioffe-Rigel [115] saturated resistivity, ρ 0 is the residual resistivity, ρ D is the resistivity constant, and Θ D is the Debye temperature.
This model (Equation 5) is used to deduce the Debye temperature Θ D in a wide range of low-temperature superconductors and hydride superconductors [116,117,118,119,120,121,122,123]. As it was clarified by Nowak et al. [124], Θ D deduced by Equation 5 should be designated as Θ D H T because it describes the phonon spectrum at high temperature range, above the transition temperature T ≳ 1.5 × T c . In addition to that, in many studies, the low-temperature Debye temperature Θ D L T is deduced from the low-temperature heat capacity data C p T [118,120,123,124,125,126,127]:
C p T = γ n × T + β 3 × T 3 + a 5 × T 5 ,
where γ n is the Sommerfeld coefficient, β 3 is the lattice specific heat coefficient, and a 5 is the correction term for phonon dispersion and anharmonicity. From the deduced β 3 value, the low-temperature Debye temperature is calculated via the formula [124]:
Θ D L T = 12 π 4 × N × R 5 × β 3 1 3 ,
where N is the number of atoms per formula unit (f.u.), and R = 8.31446 J m o l − 1 K − 1 is the universal gas constant.
There are always some differences between Θ D L T and Θ D H T because these two values are characteristic temperatures for different parts of the phonon spectrum.
It should be noted that (to the best of my knowledge) all reported in the literature values of the Debye temperature Θ D for iron-based superconductors represent the values of the Debye temperature at low temperatures Θ D L T [128,129]. In contrast, in this study, since the analysis is based on ρ T data equal to zero at T < T c , the derived Debye temperature values Θ D reported below must be assigned to Θ D H T .
There are very rare studies [130,131] where Equation 5 is applied for unconventional HTS. Some research groups utilize different reduced forms of Equation 5 [132]:
ρ T = 1 1 ρ s a t + 1 ρ 0 + A × T ,
or [133]:
ρ T = 1 1 ρ s a t + 1 ρ 0 + A × T 2 ,
or [134]
ρ T = 1 1 ρ s a t + 1 ρ 0 + A × T + B × T 2 ,
where ρ s a t , ρ 0 , A , and B are free-fitting parameters.
Shoemaker et al. [135] to approximate in-plane temperature-dependent resistivity ρ a b T in single crystal K0.85Fe1.9As2 proposed the following equation:
ρ T = 1 1 ρ m e t a l T   +   1 ρ s e m i c o n d u c t o r T = 1 1 ρ 0 + A × T n   +   1 ρ s a t × e E g 2 k B T ,
where ρ 0 , A , n , ρ s a t , and E g are free fitting parameters, E g is insulator activation energy, and k B = 1.3806 × 10 − 23   J K − 1 = 8.6173 × 10 − 5   e V K − 1 is the Boltzmann constant.
It should be noted that Equation 11 was used to analyze the ρ a b T data measured in other single crystals of iron chalcogenides [136,137].
The left side of Equation 11 is the exact main postulate on which a universal temperature-dependent model for the electrical resistivity of pure actinide metals has recently and independently been proposed [138]. Now, I must acknowledge that the postulate and primary idea for the model [138], which was named the nearest-neighbour hopping parallel resistivity model, had been proposed by Shoemaker et al. [135].
Since it is difficult to assume that pure elemental actinide metals can exhibit a semiconducting band, in [138], instead of ρ s e m i c o n d u c t o r T in the left-hand side of Equation 11, I used a more general assumption, according to which the temperature-independent saturation resistivity in the parallel resistivity model [111,112,113], ρ s a t , exhibits a temperature dependence that mathematically obeys the Arrhenius-Mott-Efros-Shklovskii type of law [139,140], however, the specific physical mechanism for which has not yet been established (it can be spin fluctuations):
1 ρ s a t → 1 ρ s a t × e E a k B T m ,
where E a is the activation energy for the hopping, and m is determined by the particular hopping mechanism. Also, in Ref. [138] exact formula for the ρ m e t a l T part was used:
1 ρ m e t a l T → 1 ρ 0 + ρ D × T Θ D p = 5 × ∫ 0 Θ D T x p = 5 e x − 1 1 − e − x d x .
The analysis of the ρ T of pure actinide metals [138] showed that m in Equation 12 can be taken equal to 1, and, thus, the analysis was performed by the following equation:
ρ T = 1 1 ρ s a t × e E a k B T   +   1 ρ 0 + ρ D × T Θ D p = 5 × ∫ 0 Θ D T x p = 5 e x − 1 1 − e − x d x .
As mentioned in [138], the condition p = 5 in Equation 14 means that the charge carriers exhibit an electron-phonon dissipation mechanism; if the dominant mechanism is different, p should have a different value [105,141].
Equation 14 allows to determine the Debye temperature Θ D H T besides the activation energy E a , while interpretations of the power-law exponent n and parameter A in Equation 11 are unknown.
It is important to note that Equations 11 and 14 have the same number of free fitting parameters, five. However, Equation 14 approximates the experimental ρ a b T data with much higher accuracy, which can be seen in Figure 1, where the ρ a b T data reported by Roslova et al. [137] for single crystal of iron chalcogenide (K1-xNax)yFe1.75Se2 (x=0.32; y = 0.95) are fitted with two Equations.
The analysis of in-plane temperature-dependent resistivity ρ a b T in iron-based superconductors (presented below) has shown that Equation 14 perfectly approximates the experimental data and that the deduced parameters are within the approximate range reported by independent experimental studies (in particular, the Debye temperature values).
Since the specific hopping mechanism for the second conduction channel is unknown, I continue to use the designation E a in Equation 14. However, if it were proven that the mechanism belongs to a pure semiconductor type (as it was assumed by Shoemaker et al. [135]), the deduced activation energy E a can be recalculated to the semiconducting gap energy E g :
E g = 2 × E a
It is also worth mentioning that the analysis presented here was carried out for high-temperature iron-based superconductors in which the formation of the spin-density wave phase is suppressed by chemical doping.
It should also be noted that since the IBS family is the largest among high-temperature superconductors (HTS), it is practically impossible to present results for all types of chemical doping or compressed IBS in a single paper. Therefore, the analysis is presented for typical chemical doping to demonstrate the universal applicability of the nearest-neighbours hopping parallel resistivity model (Equation 14) for analysing the in-plane electrical resistivity ρ a b T measured in single crystals of IBS phases 11, 111, 122, 1111, 1144, and 42214.

II. Data and Software

Because all IBSs are layered quasi-2D superconductors, thermodynamic fluctuations of the order parameter are significant in these superconductors [101,142,143]. Based on this, an excess in electrical conductivity appears in quasi-2D superconductors well above the transition temperature T c [101,144,145,146,147,148,149]. Since in this study the analysed experimental data are the temperature-dependent electrical resistivity ρ a b T , to avoid access to conductivity due to thermodynamic fluctuations of the superconducting order parameter, the experimental data ρ a b T were fitted with Equation 14 for the temperature range T ≳ 1.5 × T c , z e r o .
All analysed ρ a b T datasets were obtained by digitizing original experimental studies by using the ScanIt software [150], version 2.0.8.0. (Programming: Jasper van Baten, thanks to: Richard Baur). Data fits were performed in the Origin software [151], version 2021.

III. Results

3.1. Single crystals of the 1111-type

Iron-containing superconductors were discovered by Kamihara et al [1] in 2006 by observing superconductivity in LaFePO₄ [1]. The highest superconducting transition temperature is also observed for compounds in this 1111-type [24,68]. It is therefore natural to begin by presenting the results of the analysis obtained for compounds of this 1111-type.
Ma et al. [152] grew Ca(Fe1-xCox)AsF single crystals using the self-flux method and reported ρ a b T data for Ca(Fe1-xCox)AsF (x = 0.118) crystal, which has a zero resistance transition temperature T c , z e r o = 19   K [56,152]. The ρ a b T data for this single crystal are shown in Figure 2,a along with the fit using Equation 14. The deduced Debye temperature for this sample is relatively high Θ D H T = 599 ± 6   K .
Adamski et al. [53] grew NdFeAsO and NdFeAsO1-xFx single crystals in the NaCl/KCl flux at ambient pressure and reported the reduced temperature dependence of the resistivity ρ a b T ρ a b 300   K for three samples. The ρ a b T ρ a b 300   K data for NdFeAsO1-xFx (x=0.1) single crystal (which has a zero resistance transition temperature T c , z e r o = 40   K [53]) are shown in Figure 2,b along with the fit using Equation 14. The deduced Debye temperature for this sample is also relatively high Θ D H T = 449 ± 2   K .
Zhigadlo et al. [153] grew single crystals of PrFeAsO1-y using the cubic-anvil high-pressure and high-temperature technique, and reported ρ a b T data for the La0.87Sm0.13FeAs0.91P0.09O single crystal. The ρ a b T data for the crystal, which has a zero-resistance transition temperature T c , z e r o = 13.4   K [153]) are shown in Figure 2,c along with the fit using Equation 14. The deduced Debye temperature for this sample is relatively low Θ D H T = 243 ± 3   K .
However, it should be noted that this sample also has a relatively low superconducting transition temperature T c , z e r o = 13.4   K [153].
The derived primary parameters, Θ D H T and E a , as well as the experimental superconducting transition temperature T c , vary considerably for samples doped at different chemical sites. A detailed analysis of the derived parameters is presented in the Discussion section.

3.2. Pnictide single crystals of the 122-type

Rotter et al. [6,7] discovered high-temperature superconductivity in the (Ba1-xKx)Fe2As2 pnictide 122-type in 2008.
To demonstrate that the nearest-neighbours hopping parallel resistivity model can be used to deduce parameters for non-superconducting pnictide 122-type, in Figure 3,a I show the ρ a b T data for single crystal Ba(Fe0.95Cu0.05)2As2 reported by Rosa et al. [154] along with the fit using Equation 14. The single crystal was grown by the influx technique [155]. The deduced Debye temperature for this sample is Θ D H T = 420 ± 3   K .
Luo et al. [156] grew (Ba0.6K0.4)Fe2As2 single crystals by flux method using FeAs as flux. The ρ a b T data, along with the fit using Equation 14, for the crystal with zero resistance transition temperature T c , z e r o = 36   K [156], are shown in Figure 3,b. The deduced Debye temperature for this sample is Θ D H T = 306 ± 1   K .
Remarkably, the deduced Debye temperature for the single crystal with the same stoichiometry (Ba0.6K0.4)Fe2As2, grown and measured by an independent research group (Chen et al. [156] with T c , z e r o = 37   K ), is the same: Θ D H T = 305 ± 7   K (Figure 3,c). It is further worth noting that other parameters deduced for two crystals of (Ba0.6K0.4)Fe2As2 (for instance, ρ 0 and ρ D ) are also within the same approximate ranges (Figure 2,b,c,).

3.3. Chalcogenide single crystals of the 122-type

Guo et al. [5] discovered high-temperature superconductivity in the 122-chalcogenide-type single crystals KxFe2Se2 in 2010. This is a very rare study in the field of superconductivity, where high-temperature superconductivity was discovered through measurements performed on single crystals.
The first reported ρ a b T curve [6] for K0.78Fe1.70Se2 is shown in Figure 4,a along with the fit performed using Equation 14. The deduced Debye temperature for this sample is Θ D H T = 323 ± 2   K and the activation energy for the nearest-neighbours hopping conductivity E a = 43.4 ± 0.1 m e V . These values agree very well with the values deduced from the experimental curves ρ a b T measured in the single crystal K0.85Fe1.90Se2 studied by Shoemaker et al. [135] ( Θ D H T = 368 ± 6   K and E a = 43.8 ± 0.1 m e V (Figure 4,b)) and the single crystal K0.80Fe1.76Se2 studied by Hu et al. [158] ( Θ D H T = 357 ± 1   K and E a = 38.9 ± 0.1 m e V (Figure 4,c)). It should be pointed out that the absolute values of the ρ a b T reported by Shoemaker et al. [135] and Hu et al. [158] are different for more than one order of magnitude.
It should also be noted that the deduced:
E a = 43.8 ± 0.1 m e V
for the K0.85Fe1.90Se2 [135] also agrees well with the reported E g value by Shoemaker et al. [135], who fit the ρ a b T data with Equation 11:
E a = E g 2 = 41.5 m e V
In more details the deduced parameters are discussed in the Discussion section.

3.4. Single crystals of the 111-type

Wang et al. [8] discovered superconductivity in the LiFeAs compound (111-type) with Tc = 18 K. Two weeks later, Tapp et al. [159] confirmed the discovery, and several months later, Parker et al. [160] reported that another 111-type NaFeAs exhibits the same Tc = 18 K. There is a low-Tc member of the 111-type LiFeP [27], for which perfect single crystals were grown and studied by Kasahara et al. [161].
Morozov et al. [57] grew large LiFeAs single crystals with dimensions up to 12x12x0.3 mm3 using the self-flux technique and reported ρ a b T data for one sample with T c , z e r o = 15.5   K shown in Figure 5,a along with the fit using Equation 14. The deduced Debye temperature for this sample is Θ D H T = 298 ± 1   K .
The same research group reported other ρ a b T dataset [162] for different LiFeAs single crystal with T c , z e r o = 17   K , which is shown in Figure 5,b together with the fit using Equation 14. The deduced Debye temperature for that sample reported by Heyer et al. [162] is in the same range of values Θ D H T = 265 ± 1   K .
The analysis of independently reported ρ a b T data for sample FP1 grew by Rullier-Albenque et al. [101,163] is shown in Figure 5,c. Samples grew up by this group have very high residual resistivity ratios R R R = ρ a b T = 300   K ρ 0 ≅ 250 [101,163]. The deduced Debye temperature for FP1 is in the same range of values Θ D H T = 301 ± 1   K .
The Aslamazov-Larkin analysis [144] of ρ a b T near Tc performed by Rullier-Albenque et al. [101] for LiFeAs samples showed that this phase exhibits a high level of 2D fluctuations, and the excess conductivity appeared well above the transition temperature. Based on this, data fittings using Equation 14 for LiFeAs (in Figure 4) were performed for ρ a b T ≥ 2 × T c , z e r o .

3.5. Single crystals of the 1144-type

Iyo et al. [4] discovered superconductivity in the 1144-type of IBS. In particular, Iyo et al. [4] reported that ceramics of CaAFe4As4 (A = K, Rb, Cs) and SrAFe4As4 (A = Rb, Cs) exhibit 31   K ≤ T c , z e r o ≤ 37   K . There are interesting compounds of this 1144-type with europium AEuFe4As4 (A = Rb, Sc), in which superconductivity coexists with ferromagnetism at low temperatures [16,164].
Bao et al. [165] grew RbEuFe4As4 single crystals and reported ρ a b T data for a sample with T c , z e r o = 36.8   K . The dataset, together with the fit using Equation 14, is shown in Figure 6,a. The deduced Debye temperature for this sample is Θ D H T = 243 ± 2   K .
Bristow et al. [166] grew CaKFe4As4 single crystals and reported ρ a b T data for a sample S2 with T c , z e r o = 34.9   K . The dataset and the fit are shown in Figure 6,b. Primary deduced parameters for this sample are Θ D H T = 272 ± 1   K and E a = 25.3 ± 0.2 m e V . These parameters are practically the same as the parameters deduced by the analysis of the ρ a b T data reported for the CaKFe4As4 single crystal by an independent research group, Pyon et al. [167] with T c , z e r o = 35.3   K . The results of the analysis for data reported by Pyon et al. [167] is shown in Figure 6,c. It should also be noted that the absolute values of the ρ a b T in studies [166,167] differs by a factor of two.
This result can be served as evidence for the nearest-neighbours hopping parallel resistivity model reliability.
There are two main found differences between deduced parameters for RbEuFe4As4 and CaKFe4As4. One is that the E a in the RbEu-based crystal is nearly twice larger that the value in the CaK-based crystals, while the Debye temperature in the RbEu-based crystal is ~ 20% lower than this in the CaK-based counterparts.

3.6. Single crystal of the 42214-type

Katrych et al. [17,168] discovered superconductivity in the 42214-type of IBS compounds L4Fe2As2Te1-xO1-yFy (L=Pr, Sm, Gd) that exhibit the highest transition temperature T c , m a g n e t i z a t i o n ≅ 45   K measured by DC magnetization.
Pisoni et al. [132] grew Sm4Fe2As2Te0.72O2.8F1.2 single crystals at high temperature and high pressure employing a cubic-anvil system. The reported ρ a b T data for the sample with T c , z e r o = 31.3   K together with the fit using Equation 14, is shown in Figure 7. The deduced Debye temperature for this sample is Θ D H T = 330 ± 2   K .

3.7. Single crystals of the 11-type

Hsu et al. [9] discovered superconductivity in FeSe exhibiting T c , z e r o = 7   K at room pressure, and Medvedev et al. [169] showed that the transition temperature increases rapidly under pressure and reaches T c = 36.7   K at P = 8.9   G P a . Atomically thin epitaxial FeSe films have an even higher transition temperature [170,171,172,173].
Since bulk pure FeSe undergoes a structural nematic transition at T s ~ 90   K , the analysis of ρ a b T for this type of IBS is beyond the scope of the present study (and the analysis will be provided in a separate report), I have presented here the analysis for FeTe1-xSex single crystals, where this structural transition is suppressed, and the FeTe1-xSex compounds are also 11-type of IBS.
Pallecchi et al. [174] grew iron-excess Fe1+yTe1−xSex single crystals by the Bridgeman method. The ρ a b T data reported for the sample with T c , z e r o = 12   K and the composition of Fe1.013Te1-xSex (x=0.3) data shown in Figure 8,a together with the fit using Equation 14. The deduced Debye temperature for this sample is Θ D H T = 249 ± 12   K .
Liu et al. [175] grew Fe1+yTe1−xSex single crystals, and the ρ a b T data reported for the sample SC1 with T c , z e r o = 13.2   K and the measured average composition Fe1.03Te1-xSex (x=0.37) are shown in Figure 8,b together with the fit using Equation 14. The deduced Debye temperature for this sample is Θ D H T = 176 ± 9   K .
Sun et al. [176] grew Fe1+yTe1−xSex single crystals by the self-flux method [177], and the ρ a b T data reported for the sample with T c , z e r o = 14.2   K and the composition of FeTe1-xSex (x=0.43) are shown in Figure 8,c together with the fit using Equation 14. The deduced Debye temperature for this sample is Θ D H T = 172 ± 6   K .
It should be noted that despite the deduced Debye temperature varying in some range, 170   K ≤ Θ D H T ≤ 250   K , all analyzed Fe1+yTe1−xSex single crystals exhibit practically the same Arrhenius activation energy E a ≅ 40 m e V .

4. Discussion

Debye temperature Θ D values have been reported for virtually all IBS superconductors. However, in many reports the Θ D values were obtained by approximating the low-temperature heat capacity C p T data using Equation 6 and subsequent calculations based on the derived parameter β 3 using Equation 7.
However, as it was pointed out by McQueen et al. [127] and Tsurkan et al. [178] , this approach “…is generally only good up to  Θ D 50 … ” [127]. Considering that the ballpark value for Θ D in IBS is about Θ D = 250   K , the reported values for Θ D in IBS are to obey the inequality:
Θ D 50 ≅ 5   K ≪ T c ,
and thus, these values need to be designated as Θ D T ≅ 5   K ≡ Θ D L T (this clarification was also pointed out by Nowak et al. [124] in the case of high-entropy alloys).
In this study, the Debye temperatures Θ D H T were obtained from experimental data measured in the range:
1.5 × T c , z e r o ≲ T ≤ 300   K ,
and thus, the deduced Θ D H T values should be close to the values Θ D H T reported by the Mössbauer spectroscopy technique [179,180,181].
Since the temperature range indicated in Equation 18 is closer to and precedes the observed T c , the obtained Θ D H T values are more appropriate for testing the possibility of classical electron-phonon mechanisms for superconductivity in IBS (which may be assisted, enhanced, or operating in conjunction with other mechanisms). A possibility for the electron-phonon mediated superconductivity in IBS is under ongoing discussion since the discovery of these superconductors [182].
I calculated the electron-phonon coupling constant λ e − p h for all the superconductors studied (Table I) by using the following equations [116,183,184] (where it was assumed that μ * = 0.125 ):
T c , z e r o = Θ D H T 1.45 e − 1.04 × 1 + λ e − p h λ e − p h − μ * × 1 + 0.62 × λ e − p h × f 1 × f 2 *
f 1 = 1 + λ e − p h 2.46 1 + 3.8 μ * 3 / 2 1 / 3
f 2 * = 1 + 0.0241 − 0.0735 × μ * × λ e − p h 2
The obtained values of λ e − p h (Table I) show that the electron-phonon mechanism as the main mechanism of superconductivity in IBS can be considered as a possibility.

5. Conclusions

In this study, it is shown that the in-plane resistivity data ρ a b T in seven types of iron-based superconductors, namely, 11, 111, 122-pnictides, 122-chalcogenides, 1111, 1144 and 42214, are well described by the nearest-neighbor hopping parallel resistance model [138], the basic idea of which was proposed by Shoemaker et al. [135], and the complete physical equation for the temperature-dependent metallic conductivity channel was proposed in [138].
Table I. were used for calculations with the assumed μ * = 0.125 . Θ D is the Debye temperature, Θ E is the Einstein temperature.
Table I. were used for calculations with the assumed μ * = 0.125 . Θ D is the Debye temperature, Θ E is the Einstein temperature.
IBS type Chemical formula Observed T c , z e r o (K) Reported Θ D L T (K) Reported Θ D H T (K) Derived Θ D H T (K) λ e − p h

11		 Fe1.013Te1-xSex (x=0.3) [174] 12 [174] 174 185]
200 [127]
235 [178]
240 [179]		 285 [179]
Θ D , 1 H T = 127 [178]
Θ D , 2 H T = 235 [178]
Θ E H T = 315 [178]		 249 ± 12 0.94
Fe1.03Te1-xSex (x=0.37) [175] 13.2 [175] 176 ± 9 1.23
FeTe1-xSex (x=0.43) [176] 14.2 [176] 172 ± 6 1.32

111 		LiFeAs [57] 15.5 [57] 310 186]
300 [187]
290 for NaFeAs [188] 		298 ± 1 0.98
LiFeAs [162] 17 [162] 265 ± 1 1.11
LiFeAs [101,163] 17.5 [101] 301 ± 1 1.04

122 pnic-tides 		(Ba1-xKx)Fe2As2 (x=0.4) [156] 36 [156] 274 [189]
260 [190]
246 (x = 0.5) [191]
250 for La0.4Na0.6Fe2As2 [128]
292 for
CaFe2As2 [192] 		~ 292 for
CaFe2As2 [192]
306 ± 1 1.81
(Ba1-xKx)Fe2As2 (x=0.4) [157] 37 [157] 305 ± 7 1.86

122 chalco-genides 		K0.78Fe1.70Se2 [5] 27.2 [5] 212 [193]
197 [194] 		323 ± 2 1.34
K0.85Fe1.90Se2 [135] 25 [135] 368 ± 6 1.15
K0.80Fe1.76Se2 [158] 30.9 [158] 357 ± 1 1.37
(K1-xNax)yFe1.75Se2
(x=0.32; y = 0.95) [137]		 31.7 [137] 536 ± 1 1.05
1111 Ca(Fe1-xCox)AsF
(x = 0.118) [152]		 19 [152] 339 for SrFeAsF [195]
285 for PrFeAsO1-xFₓ [196]
316 for LaFeAsO0.9F0.1 [197]
323 for LaFeAsO [129]		 342 for SrFeAsF [198]
347 for SrFeAsF [198]
294 for PrFeAsO1-xFₓ [196]
355 [199] 		599 ± 6 0.78
NdFeAsO1-xFx (x=0.1) [53] 40 [53] 449 ± 2 1.40
La0.87Sm0.13FeAs0.91P0.09O [153] 13.4 [153] 243 ± 3 1.01
1144 RbEuFe4As4 [165] 36.8 [165] 391 [181] 243 ± 2 2.38
CaKFe4As4 [166] 34.9 [166] 272 ± 1 1.98
CaKFe4As4 [167] 35.5 [167] 277 ± 1 1.98
42214 Sm4Fe2As2Te0.72O2.8F1.2 31.3 330 ± 2 1.48

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgement

The work was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation for the IMP UB RAS. The author gratefully acknowledges the research funding from the Ministry of Science and Higher Education of the Russian Federation under the Ural Federal University Program of Development within the Priority-2030 Program.

Declaration of interests

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Preprints 230228 g001
Figure 1. Fits with (a) Equation 11 [135], and (b) Equation 14 [138] of the same ρ a b T data measured in 122-type chalcogenide single crystal (K1-xNax)yFe1.75Se2 (x=0.32; y = 0.95) (data reported by Roslova et al. [137]). (a) Equation of E g 2 = E a was used to calculate E a . Fit quality R-square (COD) = 0.9997. (b) Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 1. Fits with (a) Equation 11 [135], and (b) Equation 14 [138] of the same ρ a b T data measured in 122-type chalcogenide single crystal (K1-xNax)yFe1.75Se2 (x=0.32; y = 0.95) (data reported by Roslova et al. [137]). (a) Equation of E g 2 = E a was used to calculate E a . Fit quality R-square (COD) = 0.9997. (b) Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 2. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 1111-type single crystals of the IBS. (a) Ca(Fe1-xCox)AsF (x=0.118) (data reported by Ma et al. [152]). Fit quality R-square (COD) = 0.9979. (b) NdFeAsO1-xFx (x=0.1) (data reported by Adamski et al. [53]). Fit quality R = 0.9999. (c) La1-xSmxFeAs1-yPyO (x = 0.13, y = 0.09) (data reported by Zhigadlo et al. [153]). Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 2. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 1111-type single crystals of the IBS. (a) Ca(Fe1-xCox)AsF (x=0.118) (data reported by Ma et al. [152]). Fit quality R-square (COD) = 0.9979. (b) NdFeAsO1-xFx (x=0.1) (data reported by Adamski et al. [53]). Fit quality R = 0.9999. (c) La1-xSmxFeAs1-yPyO (x = 0.13, y = 0.09) (data reported by Zhigadlo et al. [153]). Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 3. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 122-type pnictide single crystals. (a) Ba(Fe1-xCux)2As2 (x = 0.05) (data reported by Rosa et al. [154]). Fit quality R-square (COD) = 0.9996. (b) (Ba1-xKx)Fe2As2 (x = 0.4) (data reported by Luo et al. [156]). Fit quality R = 0.9999. (c) (Ba1-xKx)Fe2As2 (x = 0.4) (data reported by Chen et al. [157]). Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 3. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 122-type pnictide single crystals. (a) Ba(Fe1-xCux)2As2 (x = 0.05) (data reported by Rosa et al. [154]). Fit quality R-square (COD) = 0.9996. (b) (Ba1-xKx)Fe2As2 (x = 0.4) (data reported by Luo et al. [156]). Fit quality R = 0.9999. (c) (Ba1-xKx)Fe2As2 (x = 0.4) (data reported by Chen et al. [157]). Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 4. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 122-type chalcogenide single crystals. (a) K0.78Fe1.70Se2 (data reported by Guo et al. [5]). Fit quality R-square (COD) = 0.9999. (b) K0.85Fe1.90Se2 (data reported by Shoemaker et al. [135]). Fit quality R = 0.9999. (c) K0.80Fe1.76Se2 (data reported by Hu et al. [158]). Fit quality R = 0.9998. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 4. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 122-type chalcogenide single crystals. (a) K0.78Fe1.70Se2 (data reported by Guo et al. [5]). Fit quality R-square (COD) = 0.9999. (b) K0.85Fe1.90Se2 (data reported by Shoemaker et al. [135]). Fit quality R = 0.9999. (c) K0.80Fe1.76Se2 (data reported by Hu et al. [158]). Fit quality R = 0.9998. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 5. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 111-type single crystals LiFeAs. (a) data reported by Morozov et al. [57]). Fit quality R-square (COD) = 0.9999. (b) Data reported by Heyer et al. [162]. Fit quality R = 0.9999. (c) Data reported by Rullier-Albenque et al. [101,163] for sample FP1. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 5. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 111-type single crystals LiFeAs. (a) data reported by Morozov et al. [57]). Fit quality R-square (COD) = 0.9999. (b) Data reported by Heyer et al. [162]. Fit quality R = 0.9999. (c) Data reported by Rullier-Albenque et al. [101,163] for sample FP1. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 6. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 1144-type single crystals. (a) Data for the RbEuFe4As4 single crystal reported by Bao et al. [165]). Fit quality R-square (COD) = 0.9999. (b) Data for the CaKFe4As4 single crystal (S2) reported by Bristow et al. [166]). Fit quality R = 0.9999. (c) Data for the CaKFe4As4 single crystal reported by Pyon et al. [167]. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 6. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 1144-type single crystals. (a) Data for the RbEuFe4As4 single crystal reported by Bao et al. [165]). Fit quality R-square (COD) = 0.9999. (b) Data for the CaKFe4As4 single crystal (S2) reported by Bristow et al. [166]). Fit quality R = 0.9999. (c) Data for the CaKFe4As4 single crystal reported by Pyon et al. [167]. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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Figure 7. Fit with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in the 42214-type single crystal. Data for the Sm4Fe2As2Te0.72O2.8F1.2 single crystal reported by Pisoni et al. [132]). Fit quality R-square (COD) = 0.9998. Deduced parameters are shown in the figure. The 95% confidence bands are shown by pink shadow areas.
Figure 7. Fit with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in the 42214-type single crystal. Data for the Sm4Fe2As2Te0.72O2.8F1.2 single crystal reported by Pisoni et al. [132]). Fit quality R-square (COD) = 0.9998. Deduced parameters are shown in the figure. The 95% confidence bands are shown by pink shadow areas.
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Figure 8. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 11-type single crystals. (a) Data for the Fe1.013Te1-xSex (x=0.3) single crystal reported by Pallecchi et al. [174]). Fit quality R-square (COD) = 0.9854. (b) Data for the Fe1.03Te1-xSex (x=0.37) single crystal reported by Liu et al. [166]). Fit quality R = 0.9999. (c) Data for the CaKFe4As4 single crystal reported by Pyon et al. [167]. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
Figure 8. Fits with the nearest-neighbor hopping parallel resistance model (Equation 14) of the ρ a b T data measured in 11-type single crystals. (a) Data for the Fe1.013Te1-xSex (x=0.3) single crystal reported by Pallecchi et al. [174]). Fit quality R-square (COD) = 0.9854. (b) Data for the Fe1.03Te1-xSex (x=0.37) single crystal reported by Liu et al. [166]). Fit quality R = 0.9999. (c) Data for the CaKFe4As4 single crystal reported by Pyon et al. [167]. Fit quality R = 0.9999. Deduced parameters are shown in each panel. The 95% confidence bands are shown by pink shadow areas.
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