Electrical and Thermal Transport Properties of Layered Superconducting Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 Single Crystal

We have synthesized single crystals of iron-based superconducting Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 and performed extensive measurements on their transport properties. A remarkable difference in the behavior and a large anisotropy between in-plane and out-of-plane resistivity was observed. Disorder could explain the in-plane square-root temperature dependence resistivity, and interlayer incoherent scattering may contribute to the out-of-plane transport property. Along the ab plane, the estimated value of the coherence length is 15.5 Å. From measurements of the upper critical magnetic field Hc2 (T ≥ 20 K), we estimate Hc2(0) = 313 T. Thermal conductivity for Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 is relatively small, which can be accounted for by the disorder in the crystal and the low-charge carrier density as verified by the Hall effect.


Introduction
The Ca 10 (Pt n As 8 )(Fe 2 As 2 ) 5 (n = 3 or 4) system was first reported to exhibit superconductivity with a wide range of transition temperatures in 2011 [1][2][3]. After that, many studies have appeared in the past seven years [4][5][6][7][8]. Ca 10 (Pt 4 As 8 )(Fe 2 As 2 ) 5 has a layered structure consisting of superconducting FeAs layers separated by the spacer layers arranged as Ca-Pt 4 As 8 -Ca, which is shown in Figure 1a. This superconductor has been reported to crystallize in possible space groups including P4/n (tetragonal) [2,3], P2 1 /n (monoclinic) [7], and P1 (triclinic) [1,3]. The structure of the Pt 4 As 8 spacer layer is similar to a square lattice of As atoms, one fifth of the As atoms are replaced by substitutional Pt1 atoms [2], and the same amount of Pt2 atoms are interstitial, which leads to the displacement of As atoms from their ideal positions to form As dimers [2]. Because of the constraint from the As-As dimers and the FeAs sublattices, substitutional Pt1 atoms can sit in plane while the interstitial Pt2 atoms sit on the site either above or below the plane against Ca ions.
Most FeAs-based superconductors need doping to induce the superconductivity; Ca 10 (Pt 4 As 8 )(Fe 2 As 2 ) 5 allows doping on the Ca site or on the Fe site. In particular, Pt doping on the Fe site could bring faults and disorder into the crystal and also adjust the T c [2,5]. By studying its structure and physical properties, the origin of superconductivity may be elucidated. The interlayer distance of Ca 10 (Pt 4 As 8 )(Fe 2 As 2 ) 5 is reported to be~10.5 Å [2,3], which is larger than many other FeAs-based superconductors, and thus its properties are expected to be anisotropic. Figure 1c shows the X-ray diffraction spectrum for the as-grown thin, plate-like single crystal along the c-axis. Note that only (00l) peaks are observed and the pattern matches very well with that previously reported in [4]. A powder XRD spectrum is shown in Figure 1d. The result exhibits the peaks from diffractions not only (00l) planes but also (hkl) planes with nonzero h, k, l. X-ray structure determination confirms that the lattice parameters and angles for the sample are a = 8.7548(12) Å, b = 8.7642(10) Å, c = 10.69005(8) Å, and α = 94.674 (9) • , β = 104.396 (8) • , γ = 90.037(10) • , respectively, indicating our sample crystallizes in a triclinic structure with space group symmetry P1 at room temperature. No other impurities such as FeAs and PtAs 2 were observed in any X-ray spectrum. 10 20  The chemical composition was identified by the EDX measurement. A scanning electron microscope (SEM) image measured on the surface of the single crystal is shown in the Figure 2 inset. For each sample, five locations scattered on the surface were chosen for EDX measurement. An average of these scans was calculated. The results of the different samples are consistent with each other, implying homogenous growth was acquired throughout the batch. The average deviation is 3% for Ca, 5% for Pt, and 1% for Fe. The measured composition of the single crystals is Ca10Pt5.4Fe8.6As18, corresponding to a formula of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 if considering the Pt substitution effect.
The chemical composition was identified by the EDX measurement. A scanning electron microscope (SEM) image measured on the surface of the single crystal is shown in the Figure 2 inset. For each sample, five locations scattered on the surface were chosen for EDX measurement. An average of these scans was calculated. The results of the different samples are consistent with each other, implying homogenous growth was acquired throughout the batch. The average deviation is 3% for Ca, 5% for Pt, and 1% for Fe. The measured composition of the single crystals is Ca 10 Pt 5.4 Fe 8.6 As 18 , corresponding to a formula of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 if considering the Pt substitution effect.  Figure 3 displays the temperature dependence of the in-plane (ρab) and out-of-plane resistivity (ρc) of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 single crystals between 2 K and 300 K. The magnitude of ρab and its overall features are similar to the previous reports [2]. The normal-state ρab decreases with decreasing T ( > 0), showing a metallic behavior. It drops sharply at Tc_onset = ~34 K, reaching zero-resistivity state at 31.2 K. The transition width in temperature is less than 3 K, indicating that our sample has high quality and spatial homogeneity. The residual resistivity ratio (RRR) (300K)/ (Tc_onset) is 2.4. Relatively large Tc_onset and small RRR reflects the presence of Pt doping on the Fe site in FeAs layers as suggested in [1][2][3]. However, the out-of-plane resistivity ρc behaves strikingly different with ρab; it exhibits nearly independent T at higher temperatures and starts to increase with decreasing T ( < 0) below 200K, showing a nonmetallic behavior. It then goes through a sharp peak around 38 K before dropping to zero. The anisotropic property between ρab and c has not been noted in previous reports [1,2,4]. We acknowledge that this ρc-T profile is reproducible and it should be an intrinsic property of Ca10(Pt4As8)(Fe2−xPtxAs2)5. Due to the layered crystal structure of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5, the in-plane resistivity may be understood as a net resistivity of parallel connected resistors. A schematic of such a system is shown in Figure 4a. Here, we do not consider the resistance from the Ca layer because the FeAs and Pt4As8 layers are the main contributors of the electronic structure around the Fermi surface [9]. The net resistance (R) can be written as: Counts (Arbitary Unit)  Figure 3 displays the temperature dependence of the in-plane (ρ ab ) and out-of-plane resistivity (ρ c ) of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 single crystals between 2 K and 300 K. The magnitude of ρ ab and its overall features are similar to the previous reports [2]. The normal-state ρ ab decreases with decreasing T ( dρ ab dT > 0), showing a metallic behavior. It drops sharply at T c_onset =~34 K, reaching zero-resistivity state at 31.2 K. The transition width in temperature is less than 3 K, indicating that our sample has high quality and spatial homogeneity. The residual resistivity ratio (RRR) (300K)/ρ(T c_onset ) is 2.4. Relatively large T c_onset and small RRR reflects the presence of Pt doping on the Fe site in FeAs layers as suggested in [1][2][3]. However, the out-of-plane resistivity ρ c behaves strikingly different with ρ ab ; it exhibits nearly independent T at higher temperatures and starts to increase with decreasing T ( dρ c dT < 0) below 200K, showing a nonmetallic behavior. It then goes through a sharp peak around 38 K before dropping to zero. The anisotropic property between ρ ab and ρ c has not been noted in previous reports [1,2,4]. We acknowledge that this ρ c -T profile is reproducible and it should be an intrinsic property of Ca 10 (Pt 4 As 8 )(Fe 2−x Pt x As 2 ) 5 .  Figure 3 displays the temperature dependence of the in-plane (ρab) and out-of-plane resistivity (ρc) of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 single crystals between 2 K and 300 K. The magnitude of ρab and its overall features are similar to the previous reports [2]. The normal-state ρab decreases with decreasing T ( > 0), showing a metallic behavior. It drops sharply at Tc_onset = ~34 K, reaching zero-resistivity state at 31.2 K. The transition width in temperature is less than 3 K, indicating that our sample has high quality and spatial homogeneity. The residual resistivity ratio (RRR) (300K)/ (Tc_onset) is 2.4. Relatively large Tc_onset and small RRR reflects the presence of Pt doping on the Fe site in FeAs layers as suggested in [1][2][3]. However, the out-of-plane resistivity ρc behaves strikingly different with ρab; it exhibits nearly independent T at higher temperatures and starts to increase with decreasing T ( < 0) below 200K, showing a nonmetallic behavior. It then goes through a sharp peak around 38 K before dropping to zero. The anisotropic property between ρab and c has not been noted in previous reports [1,2,4]. We acknowledge that this ρc-T profile is reproducible and it should be an intrinsic property of Ca10(Pt4As8)(Fe2−xPtxAs2)5.  Due to the layered crystal structure of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5, the in-plane resistivity may be understood as a net resistivity of parallel connected resistors. A schematic of such a system is shown in Figure 4a. Here, we do not consider the resistance from the Ca layer because the FeAs and Pt4As8 layers are the main contributors of the electronic structure around the Fermi surface [9]. The net resistance (R) can be written as: Counts (Arbitary Unit) Due to the layered crystal structure of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 , the in-plane resistivity may be understood as a net resistivity of parallel connected resistors. A schematic of such a system is shown in Figure 4a. Here, we do not consider the resistance from the Ca layer because the FeAs and Pt 4 As 8 layers are the main contributors of the electronic structure around the Fermi surface [9]. The net resistance (R) can be written as: in which n is the number of Pt 4 As 8 -FeAs layers, and R FeAs and R Pt 4 As 8 are the resistance of the FeAs layer and Pt 4 As 8 layer, respectively. If the Pt 4 As 8 layer is semiconducting or insulating, it should have a much larger resistance than the FeAs layer. Then, the net resistance R should be dominated by the resistance of the Pt 4 As 8 layer and exhibit nonmetallic behavior. Yet, according to our results, the normal state ρ ab shows metallic behavior, indicating the spacer layer Pt 4 As 8 is metallic, which agrees with previous reports [2,4,9].
in which n is the number of Pt4As8-FeAs layers, and RFeAs and RPt4As8 are the resistance of the FeAs layer and Pt4As8 layer, respectively. If the Pt4As8 layer is semiconducting or insulating, it should have a much larger resistance than the FeAs layer. Then, the net resistance R should be dominated by the resistance of the Pt4As8 layer and exhibit nonmetallic behavior. Yet, according to our results, the normal state ρab shows metallic behavior, indicating the spacer layer Pt4As8 is metallic, which agrees with previous reports [2,4,9]. The normal state ρab of some traditional FeAs-based superconductors shows metallic behavior and may have linear dependence on temperature due to the inelastic scattering originating from electron-phonon interactions. In some cuprates, ρab has T 1.5 dependence, implying the Fermi-liquid behavior. Yet, the temperature dependence of the normal state ρab of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 is neither linear, quadratic temperature dependent, nor T 1.5 dependent, as observed in cuprates or other FeAs-based compounds [10]. The normal state ρab from 50 K to 300 K can be well fitted by = + √ with A = 0.079 ± 0.008 mΩ cm and B = 0.031 ± 0.003 mΩ cm K −1/2 . The red solid line in Figure 3a is the fit to the experimental data of the normal state ρab. All reported ρab for Ca10Pt4As8(Fe2As2)5 has the similar square-root temperature dependence regardless of Tc [1,2,4], and thus, it may be an intrinsic property to Ca10Pt4As8(Fe2As2)5.
The square-root temperature dependence of electrical resistivity is normally expected at low temperatures in disordered metals and degenerate semiconductors because of interference with scattering by impurities [11,12]. The studies on the Fermi surface of Ca10Pt4As8(Fe2As2)5 imply that the Pt4As8 layer contributes several electron pockets. Thus, there may be competition between the Pt4As8 layer and the negatively-charged FeAs layer for electrons, leading to possible Pt deficiency in the Pt4As8 layer and partial substitution of Fe by Pt in the Fe1-xPtxAs layer [3,5,13,14]. As a result, charge carriers in both the Pt4As8 and Fe1−xPtxAs layers could experience the effect of disorder, which may be the reason why the in-plane electrical resistivity has the square-root temperature dependence.
As shown in Figure 3b, ρc is much larger than ρab in the normal state. It can be understood with a schematic plot of the net resistance R = ( FeAs + Pt4As8) along the out-of-plane direction shown in Figure 4b. Different from the normal state ρc of some cuprates which can be described using the equation ρc = A/T + B × T exhibiting the non-Fermi liquid behavior, the nonmetallic normal state ρc of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 can be appropriately fitted using the equation = ′ + ′√ + ′ . The solid line in Figure 3b shows the fit of ρc from 90 K to 300 K. The fitting parameters are The normal state ρ ab of some traditional FeAs-based superconductors shows metallic behavior and may have linear dependence on temperature due to the inelastic scattering originating from electron-phonon interactions. In some cuprates, ρ ab has T 1.5 dependence, implying the Fermi-liquid behavior. Yet, the temperature dependence of the normal state ρ ab of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 is neither linear, quadratic temperature dependent, nor T 1.5 dependent, as observed in cuprates or other FeAs-based compounds [10]. The normal state ρ ab from 50 K to 300 K can be well fitted by T with A = 0.079 ± 0.008 mΩ cm and B = 0.031 ± 0.003 mΩ cm K −1/2 . The red solid line in Figure 3a is the fit to the experimental data of the normal state ρ ab . All reported ρ ab for Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 has the similar square-root temperature dependence regardless of T c [1,2,4], and thus, it may be an intrinsic property to Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 .
The square-root temperature dependence of electrical resistivity is normally expected at low temperatures in disordered metals and degenerate semiconductors because of interference with scattering by impurities [11,12]. The studies on the Fermi surface of Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 imply that the Pt 4 As 8 layer contributes several electron pockets. Thus, there may be competition between the Pt 4 As 8 layer and the negatively-charged FeAs layer for electrons, leading to possible Pt deficiency in the Pt 4 As 8 layer and partial substitution of Fe by Pt in the Fe 1−x Pt x As layer [3,5,13,14]. As a result, charge carriers in both the Pt 4 As 8 and Fe 1−x Pt x As layers could experience the effect of disorder, which may be the reason why the in-plane electrical resistivity has the square-root temperature dependence.
As shown in Figure 3b, ρ c is much larger than ρ ab in the normal state. It can be understood with a schematic plot of the net resistance R = n (R FeAs + R Pt 4 As 8 ) along the out-of-plane direction shown in Figure 4b. Different from the normal state ρ c of some cuprates which can be described using the equation ρ c = A/T + B × T exhibiting the non-Fermi liquid behavior, the nonmetallic normal state ρ c of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 can be appropriately fitted using the equation The solid line in Figure 3b shows the fit of ρ c from 90 K to 300 K. The fitting parameters are calculated as follows: A = 2.642 ± 0.009 mΩ cm, B = 0.308 ± 0.006 mΩ cm K −1/2 , and C = 667.7 ± 15 mΩ cm K.
The square-root temperature dependent component in ρ c is due to the in-plane scattering, which may be intrinsic as Anderson proposed for high-T c cuprates [15] or extrinsic due to a possible stacking fault [2]. The T −1 term can be attributed to interlayer incoherent scattering, similar to the properties of high-T c cuprates [15] and (Sr 4 V 2 O 6 )Fe 2 As 2 [16]. It implies the spacer layer Ca 10 Pt 4 As 8 is not superconducting in nature, so Josephson junctions are formed along the c-axis of Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 by stacking of the FeAs superconducting layer, the Ca 10 Pt 4 As 8 semiconducting layer, and the FeAs superconducting layer.
The resistivity anisotropy γ is calculated by γ = ρ c /ρ ab and it increases from~4.1 at 300 K to~7.9 around T c as displayed in Figure 5. The γ of Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 is larger than that of LaFeAsO 0.9 F 0.1 [17]. Relatively large anisotropy and a conspicuous difference in the behavior of ρ c and ρ ab suggests rgw strong 2D nature of electronic structures in Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 , which is rarely encountered in traditional Fe-based superconductors. The square-root temperature dependent component in ρc is due to the in-plane scattering, which may be intrinsic as Anderson proposed for high-Tc cuprates [15] or extrinsic due to a possible stacking fault [2]. The T −1 term can be attributed to interlayer incoherent scattering, similar to the properties of high-Tc cuprates [15] and (Sr4V2O6)Fe2As2 [16]. It implies the spacer layer Ca10Pt4As8 is not superconducting in nature, so Josephson junctions are formed along the c-axis of Ca10Pt4As8(Fe2As2)5 by stacking of the FeAs superconducting layer, the Ca10Pt4As8 semiconducting layer, and the FeAs superconducting layer.
The resistivity anisotropy is calculated by = ⁄ and it increases from ~4.1 at 300 K to ~7.9 around Tc as displayed in Figure 5. The γ of Ca10Pt4As8(Fe2As2)5 is larger than that of LaFeAsO0.9F0.1 [17]. Relatively large anisotropy and a conspicuous difference in the behavior of ρc and ρab suggests rgw strong 2D nature of electronic structures in Ca10Pt4As8(Fe2As2)5, which is rarely encountered in traditional Fe-based superconductors. The resistivity anisotropy (γ) in the superconducting state of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 was evaluated through resistivity measurements with an applied magnetic field H. Figure 6 shows the temperature dependence of ρab and ρc under H along both the c-axis and the ab plane.
In the case of I//ab and H//c-axis, it can be seen that the zero resistivity transition temperature (Tc0) decreases with the rising applied magnetic field accompanied by an increase in the transition width. The Tc0 is 18 K and the transition width ∆Tc is 16 K for H = 14 T, considering Tc_onset is 34 K. This type of superconducting transition broadening with increasing magnetic field (H) is rarely seen in Fe-based superconductors but very common in cuprates due to the presence of strong thermal vortices fluctuations [18].
Interestingly, the superconducting transition width ∆Tc does not change with an applied field when I//c and H//ab plane (Figure 6b) and H pushes both Tc_onset and Tc0 to the lower temperature by the same amount. This shift is also much smaller than that of ∆Tc for cases I//ab and H//c. The resistivity anisotropy (γ) in the superconducting state of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 was evaluated through resistivity measurements with an applied magnetic field H. Figure 6 shows the temperature dependence of ρ ab and ρ c under H along both the c-axis and the ab plane.
In the case of I//ab and H//c-axis, it can be seen that the zero resistivity transition temperature (T c0 ) decreases with the rising applied magnetic field accompanied by an increase in the transition width. The T c0 is 18 K and the transition width ∆T c is 16 K for H = 14 T, considering T c_onset is 34 K. This type of superconducting transition broadening with increasing magnetic field (H) is rarely seen in Fe-based superconductors but very common in cuprates due to the presence of strong thermal vortices fluctuations [18].
Interestingly, the superconducting transition width ∆T c does not change with an applied field when I//c and H//ab plane (Figure 6b) and H pushes both T c_onset and T c0 to the lower temperature by the same amount. This shift is also much smaller than that of ∆T c for cases I//ab and H//c. As shown in Figure 7, the c2 ( ) of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 was extracted by identifying the c( ) at which resistivity drops to 90% ρn, 50% ρn, and 10% ρn. ρn is the normal resistivity before superconducting transition, as indicated by dashed lines in Figure 6. is presented in Figure 8. ΓH taken at 90% resistivity drop reaches 8 near Tc, which is very close to the As shown in Figure 7, the H c2 (T) of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 was extracted by identifying the T c (H) at which resistivity drops to 90% ρ n , 50% ρ n , and 10% ρ n . ρ n is the normal resistivity before superconducting transition, as indicated by dashed lines in Figure 6. As shown in Figure 7, the c2 ( ) of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 was extracted by identifying the c( ) at which resistivity drops to 90% ρn, 50% ρn, and 10% ρn. ρn is the normal resistivity before superconducting transition, as indicated by dashed lines in Figure 6. The temperature dependence of the Hc2 anisotropy parameter = obtained from Figure 7 is presented in Figure 8. ΓH taken at 90% resistivity drop reaches 8 near Tc, which is very close to the  Figure 8. Γ H taken at 90% resistivity drop reaches 8 near T c , which is very close to the normal-state γ we obtained previously in the resistivity measurements. Γ H varies from 4 to 6 using a 50% criteria as compared to 122 type. For example, with Γ H =~2 for BaFe 2 As 2 [19,20], the H c2 anisotropy of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 is much larger.
It also can be noted from Figure 7b that H ab c2 (T) increases almost linearly with decreasing temperature, while H c c2 (T) exhibits an upward shape with a steep increase at low temperatures. This phenomena quite possibly originates from the multi-band effect such as in the NdFeAsO 0.7 F 0.3 and MgB 2 systems [21,22]. Thus, the positive curvature of H c c2 (T) reflects a multi-band nature in electrical structure for Ca 10 (Pt 4 As 8 )(Fe 2 As 2 ) 5 . normal-state we obtained previously in the resistivity measurements. ΓH varies from 4 to 6 using a 50% criteria as compared to 122 type. For example, with ΓH = ~2 for BaFe2As2 [19,20], the Hc2 anisotropy of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 is much larger. It also can be noted from Figure 7b that ( ) increases almost linearly with decreasing temperature, while ( ) exhibits an upward shape with a steep increase at low temperatures. This phenomena quite possibly originates from the multi-band effect such as in the NdFeAsO0.7F0.3 and MgB2 systems [21,22]. Thus, the positive curvature of ( ) reflects a multi-band nature in electrical structure for Ca10(Pt4As8)(Fe2As2)5. Upper critical field Hc2 is an important parameter for all superconductors especially in their practical applications. We estimated Hc2 at 0 K using the Werthamer-Helfand-Hohenberg (WHH) approximation [23]: The corresponding coherence lengths are calculated via the Ginburg Landau (GL) formula: where = 2.07 × 10 Wb. The obtained results are listed in Table 1. Although all derived values depend on how Hc2(T) is extracted, the large difference of and implies Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 exhibits a large anisotropy in its superconducting state. Furthermore, the values of ξc(0) derived from different criteria are all less than 10.69005(8) Å, i.e., the length of c-axis of the unit cell, suggesting that Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 meets the dimensional requirement of fabricating the intrinsic Josephson junctions (iJJs). Upper critical field H c2 is an important parameter for all superconductors especially in their practical applications. We estimated H c2 at 0 K using the Werthamer-Helfand-Hohenberg (WHH) approximation [23]: The corresponding coherence lengths are calculated via the Ginburg Landau (GL) formula: where ϕ 0 = 2.07 × 10 −15 Wb. The obtained results are listed in Table 1 implies Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 exhibits a large anisotropy in its superconducting state. Furthermore, the values of ξ c (0) derived from different criteria are all less than 10.69005(8) Å, i.e., the length of c-axis of the unit cell, suggesting that Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 meets the dimensional requirement of fabricating the intrinsic Josephson junctions (iJJs). Table 1. The upper critical field and coherence length of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 . For a normal metal with Fermi liquid behavior, the Hall coefficient (R H ) is independent of temperature. The situation is more complex if the material has multi-band or non-Fermi liquid behavior such as, for example, cuprates or heavy fermions. Their Hall coefficient exhibits strong temperature and doping dependencies. The H c c2 (T) curves show the multi-band nature of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 , so the Hall effect was measured by applying a magnetic field H⊥I//ab, and the data is presented in Figure 9. For a normal metal with Fermi liquid behavior, the Hall coefficient (RH) is independent of temperature. The situation is more complex if the material has multi-band or non-Fermi liquid behavior such as, for example, cuprates or heavy fermions. Their Hall coefficient exhibits strong temperature and doping dependencies. The ( ) curves show the multi-band nature of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5, so the Hall effect was measured by applying a magnetic field HI//ab, and the data is presented in Figure 9. The transverse RH remains negative at all temperatures above c, indicating that the charge carrier is dominated by electrons. The magnitude of RH increases with decreasing temperature, suggesting a multi-band and non-Fermi liquid behavior. Even though the doping in the FeAs layers is considered to be isovalent (i.e., Pt 2+ replaces Fe 2+ ) [2,5], it may still influence RH. Our H( ) is similar with previous reports [1,2], but it exhibits stronger temperature dependence, which suggests that the carrier concentration cannot be solely determined by the Pt concentration in this material.

Criteria in Determining
If a single band model is adopted, the corresponding carrier concentration (n) could be calculated with RH via n = −1/eRH. The temperature dependence of n is shown as the red line in Figure 9. Generally, n decreases monotonically with decreasing T. The calculated n is about 2.5 × 10 22 cm −3 at 300 K. It is comparable to other FeAs-based superconductors; for example, n of SrFe2As2 is about 1.52 × 10 22 cm −3 at 300 K [24]. The carrier concentration indicates that the normal state of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 behaves as a good metal. Before superconducting transition, the carrier concentration drops to 0.5 × 10 22 cm −3 ; however, it is still an order of magnitude larger than that of Ca10-3-8 (~10 21 between 2 K and 300 K) [2]. This is because the one extra Pt atom in the Pt4As8 intermediary layer exceeds the Zintl valence satisfaction requirement and introduces redundant electrons into the system, leading to enhanced metallicity and a relatively higher Tc.
A different method of probing conduction mechanism is provided by thermal conductivity. We measured the temperature dependence of thermal conductivity and the Seebeck coefficient for Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 from 2 K to 350 K, and the results are shown in Figure 10a.
The Seebeck coefficient (S) is negative at the measured temperature range above c, with a value of −25.5604 μV∕K at 300 K and a minimum value of −29.1343 μV∕K near 154 K resulting from a phonon-drag contribution. This confirms that the electron-type charge carrier dominates in Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5, which is consistent with the Hall effect measurement. Then, S starts to increase with decreasing temperature and reaches zero steeply at the superconducting transition temperature. In addition, the Seebeck curve shows no anomalous enhancements associated with the The transverse R H remains negative at all temperatures above T c , indicating that the charge carrier is dominated by electrons. The magnitude of R H increases with decreasing temperature, suggesting a multi-band and non-Fermi liquid behavior. Even though the doping in the FeAs layers is considered to be isovalent (i.e., Pt 2+ replaces Fe 2+ ) [2,5], it may still influence R H . Our R H (T) is similar with previous reports [1,2], but it exhibits stronger temperature dependence, which suggests that the carrier concentration cannot be solely determined by the Pt concentration in this material.
If a single band model is adopted, the corresponding carrier concentration (n) could be calculated with R H via n = −1/eR H . The temperature dependence of n is shown as the red line in Figure 9. Generally, n decreases monotonically with decreasing T. The calculated n is about 2.5 × 10 22 cm −3 at 300 K. It is comparable to other FeAs-based superconductors; for example, n of SrFe 2 As 2 is about 1.52 × 10 22 cm −3 at 300 K [24]. The carrier concentration indicates that the normal state of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 behaves as a good metal. Before superconducting transition, the carrier concentration drops to 0.5 × 10 22 cm −3 ; however, it is still an order of magnitude larger than that of Ca10-3-8 (~10 21 between 2 K and 300 K) [2]. This is because the one extra Pt atom in the Pt 4 As 8 intermediary layer exceeds the Zintl valence satisfaction requirement and introduces redundant electrons into the system, leading to enhanced metallicity and a relatively higher T c .
A different method of probing conduction mechanism is provided by thermal conductivity. We measured the temperature dependence of thermal conductivity and the Seebeck coefficient for Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 from 2 K to 350 K, and the results are shown in Figure 10a.
The Seebeck coefficient (S) is negative at the measured temperature range above T c , with a value of −25.5604 µV/K at 300 K and a minimum value of −29.1343 µV/K near 154 K resulting from a phonon-drag contribution. This confirms that the electron-type charge carrier dominates in Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 , which is consistent with the Hall effect measurement. Then, S starts to increase with decreasing temperature and reaches zero steeply at the superconducting transition temperature. In addition, the Seebeck curve shows no anomalous enhancements associated with the crystal structure or spin density wave (SDW) transitions widely observed in undoped compounds such as SmFeAsO and BaFe 2 As 2 [25,26], suggesting that there were no corresponding transitions in our sample at the temperatures measured.
Materials 2019, 12, 474 2 of 13 crystal structure or spin density wave (SDW) transitions widely observed in undoped compounds such as SmFeAsO and BaFe2As2 [25,26], suggesting that there were no corresponding transitions in our sample at the temperatures measured. With regard to the thermal conductivity (κ), it drops monotonously above c when temperature is lower than c, κ and decreases sharply with the opening of the superconducting gap. Before the drastic drop, κ first displays an abrupt increase with a bump feature upon entering the superconducting (SC) state, and a similar behavior is commonly observed in the cuprate superconductors, e.g., YBa2Cu3O7 [27] and Bi2Sr2CaCu2O8 [28]. The enhancement of κ below c reflects the increase of the phonon mean free path by the condensation of charge carriers. Phonons then cease to dissipate their momentum in collisions with such a condensate.
The electronic contribution to thermal conductivity ( ) above c could be evaluated by the Wiedemann-Franz law = ,where σ is the electrical conductivity of a metal and T is the temperature, L, known as the Lorenz number, which is equal to: = = 2.44 × 10 WΩK (4) in which e is elementary charge and kB is the Boltzmann constant. The calculated results are presented in Figure 10b.
It is worth noting that the κ value for Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 is smaller than that for LaFeAsO0.89F0.11 [29]. We know that the main scattering mechanisms for phonons in crystal are carriers and structural defects, and intrinsic phonon-phonon scattering only exists in clean materials. While in the Ca10(Pt4As8)(Fe2As2)5 system, both the off-centered Pt atoms in the Pt4As8 plane and the substitutional Pt atoms in the FeAs plane introduce disorder into the crystal, which causes phonons to be strongly scattered and the crystal lattice vibration to localize, resulting in the rather smaller thermal conductivity of Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5.

Conclusions
In conclusion, X-ray diffraction, resistivity, Hall effect, Seebeck coefficient, and thermal conductivity measurements were performed on high quality Ca10(Pt4As8)((Fe0.86Pt0.14)2As2)5 single crystals. We observed metallic in-plane resistivity but non-metallic out-of-plane resistivity for Ca10Pt4As8(Fe2As2)5. The anisotropic property is unusual, and its normal state resistivity exhibits a large anisotropy (~8) near Tc, making it one of the most anisotropic FeAs-based superconductors. The normal state in-plane resistivity has a square-root temperature dependence which is intrinsic to With regard to the thermal conductivity (κ), it drops monotonously above T c when temperature is lower than T c , κ and decreases sharply with the opening of the superconducting gap. Before the drastic drop, κ first displays an abrupt increase with a bump feature upon entering the superconducting (SC) state, and a similar behavior is commonly observed in the cuprate superconductors, e.g., YBa 2 Cu 3 O 7 [27] and Bi 2 Sr 2 CaCu 2 O 8 [28]. The enhancement of κ below T c reflects the increase of the phonon mean free path by the condensation of charge carriers. Phonons then cease to dissipate their momentum in collisions with such a condensate.
The electronic contribution to thermal conductivity (κ e ) above T c could be evaluated by the Wiedemann-Franz law κ el = σLT, where σ is the electrical conductivity of a metal and T is the temperature, L, known as the Lorenz number, which is equal to: k B e 2 = 2.44 × 10 −8 WΩK −2 (4) in which e is elementary charge and k B is the Boltzmann constant. The calculated results are presented in Figure 10b. κ el is smaller by about 5 orders of magnitude than κ as shown in Figure 10a. Thus, heat in Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 is mainly carried by phonons, and the electron contribution can be negligible. This is wholly different from the copper oxide superconductors. Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 is a relatively low-charge carrier density system. It is worth noting that the κ value for Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 is smaller than that for LaFeAsO 0.89 F 0.11 [29]. We know that the main scattering mechanisms for phonons in crystal are carriers and structural defects, and intrinsic phonon-phonon scattering only exists in clean materials. While in the Ca 10 (Pt 4 As 8 )(Fe 2 As 2 ) 5 system, both the off-centered Pt atoms in the Pt 4 As 8 plane and the substitutional Pt atoms in the FeAs plane introduce disorder into the crystal, which causes phonons to be strongly scattered and the crystal lattice vibration to localize, resulting in the rather smaller thermal conductivity of Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 .

Conclusions
In conclusion, X-ray diffraction, resistivity, Hall effect, Seebeck coefficient, and thermal conductivity measurements were performed on high quality Ca 10 (Pt 4 As 8 )((Fe 0.86 Pt 0.14 ) 2 As 2 ) 5 single crystals. We observed metallic in-plane resistivity but non-metallic out-of-plane resistivity for Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 . The anisotropic property is unusual, and its normal state resistivity exhibits a large anisotropy (~8) near T c , making it one of the most anisotropic FeAs-based superconductors. The normal state in-plane resistivity has a square-root temperature dependence which is intrinsic to Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 . The interlayer incoherent scattering contributes to the out-of-plane transport property. A large coherence length along the ab plane and upper critical field were observed. Disorder and low-charge carrier density in the crystal may account for the relatively small thermal conductivity. The layered structure and the relatively higher transition temperature with the large electrical transport anisotropy of Ca 10 Pt 4 As 8 (Fe 2 As 2 ) 5 implies it may be a new good candidate for and have potential application in the fabrication of high frequency microelectronic devices such as next generation intrinsic Josephson junctions (IJJs).