Received date: June 13, 2016; Accepted date: July 15, 2016; Published date: July 22, 2016
Citation: Muranaka T, Akimitsu J (2016) Superconductivity in Carbide Compounds. Chem Sci J 7:135. doi:10.4172/2150-3494.1000135
Copyright: © 2016 Muranaka T, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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The discovery of superconductivity in MgB2 and B-doped diamond has stimulated the search for new superconducting materials in similar systems containing light elements. In the framework of BCS theory, high frequency phonons induced in a network of light elements can yield a higher superconducting transition temperature (Tc). It shows that light element superconductors provide one of the most promising paths to a room-temperature superconductor taking account of the relationship electronic state and bonding state.
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The discovery of superconductivity in MgB2  and B-doped diamond  has stimulated the search for new superconducting materials in similar systems containing light elements. In the framework of BCS theory , high frequency phonons induced in a network of light elements can yield a higher superconducting transition temperature (Tc). These discoveries turned our attention towards new combinations of intermetallic compounds, and we discovered new superconductors in carbide systems, Y2C3  and B-doped SiC . In this paper, we review these superconductors.
Sesqui-carbides (R2C3: R=Y, La, Lu) such as Pu2C3, which crystallize as bcc structures without an inversion center, are reported to exhibit superconductivity at relatively high temperatures for intermetallic compounds, with Tc’s that depend on their carbon content [6-10]. The crystal structure of Y2C3 is shown in Figure 1. In this structure, Y atoms are aligned along the <111> direction and C atoms form C-C dimers.
In particular, Th substituted sesquicarbides of yttrium and lanthanum, (R2-xThx)C3, have attracted attention because their Tc’s are close to those of niobium-based A15-type superconductors. These materials showed superconductivity with a variable Tc, having a maximum at 17 K. So, we attempted to synthesize the sesquicarbide material under higher temperature and pressure conditions. With a high temperature and pressure synthesis at 1473~1873 K and 4~5.5 GPa, using cubic-anvil-type equipment, we found that Y2C3 had a maximum Tc of 18 K, as shown in Figure 2.
From a theoretical point of view, the band structure of Y2C3 shows that the hybridization of C-C dimer antibonding and the Y-4d characteristics are dominant at the Fermi level [11,12]. The electronic structure of YC2with C dimers suggests that the electronic structure could have substantial C-C antibonding character near the Fermi level . It has been reported that low-frequency metal atom vibrations have the largest electron-phonon coupling in Y2C3, while the contribution of high-frequency C-C stretching vibrations is comparatively small .
However, the mechanism of superconductivity in Y2C3 has not been well understood because of the difficulty involved in synthesizing stable, single-phase Y2C3 in air. We established a technique for synthesizing high-purity samples, and prepared samples having various Tc’s to investigate the mechanism of the variation of Tc in this system [14,15]. As shown in Figure 3, the magnetic susceptibility of Y2C3 decreased significantly at each Tc and the superconducting volume fraction of each Tc sample at lowest temperature in susceptibility measurements (1.8 K) was estimated to be approximately 40% in the field cooling process. The magnetization vs. magnetic field (M-H) curves exhibit typical type-II superconducting behavior.
The electronic specific heat (Cel) of each sample (11K material, 13K material, and 15K material) is shown in Figure 4. The total specific heat (C) is expressed by following formula;
The Cel is obtained by subtracting the lattice part of the specific heat (Cph) from the total specific heat (C), which is measured at zero field and 8T, respectively. In this case, an applied field cannot completely suppress superconductivity, and γT in the Cel term provides a minor contribution. So we used the normal-state entropy formula;
For determination of γ and ΘD (derived from where R=8.314J/(molK) and N=5) in an Sn/T vs. T2 plot. This method is useful for a superconductor, in which superconductivity cannot be completely suppressed by an applied magnetic field . The value of γ and ΘD of Y2C3 were calculated to be 4.7 mJ/molK2 and 540 K for the 11K material, 6.0 mJ/molK2 and 530 K for the 13K material, and 6.3 mJ/molK2 and 530 K for the 15K material, respectively. The fitting below Tc for each sample has revealed exp(-1/T)-dependence as predicted by BCS theory, rather than Tn-dependence as would an anisotropic superconductor. We estimated the superconducting gap parameters, 2Δ/kBTc, to be 3.6, 3.9, and 4.1 for 11, 13, and 15K materials, respectively. These facts suggest that the symmetry of the superconducting gap is an isotropic s-wave, and superconductivity in Y2C3 can be described as belonging to the strong coupling regime.
Figure 5 shows the temperature dependence of the specific heat of three samples under various magnetic fields. Tc decreases with increasing applied field and the μ0Hc2(0) was determined from the midpoint temperature of the jump at several applied fields, shown in Figure 6. The plots show a linear temperature dependence with the gradients dHc2/dT, and μ0Hc2(0) estimated to be about 22.7 T, 24.7 T, and 26.8 T, respectively, for the 11K, 13K, and 15K materials, from the relationship for type-II superconductors in the dirty limit;
and the coherence lengths, ξ, were determined to be 38, 36, and 35 Å, respectively, for the 11K, 13K, and 15K materials from following formula;
Table 1 lists the superconducting parameters of three phases of Y2C3 with various Tc’s. Y2C3 has a higher than Nb3Sn (Tc=18K, ΘD=230K) , being comparable to that of YNi2B2C (Tc=14K, ΘD=533K) . From relatively high ΘD, it is considered that the light element, Carbon, plays an important role in the superconductivity in Y2C3 and yields relatively high Tc. But Tc in Y2C3 is not related to ΘD as tabulated in Table 1.
Table 1: A summary of superconducting parameters of Y2C3.
Therefore we focus on the relationship between γ and Tc, the Tc of Y2C3 increases as γ increases. The γ value is given by , where is the density of states at the Fermi level. In BCS theory, Tc is given by , so it is considered that Tc in Y2C3 increases as increases. However, the γ value of Y2C3 is not very high in comparison with that of Nb3Sn, where γ=13 mJ/molK2 . So, we concluded that its high Debye temperature makes Tc relatively high despite its small Sommerfeld coefficient.
Nakane et al. looked for the causes of different Tc’s in Y2C3 structural properties, using neutron powder diffraction . As they reported, high-Tc (~15K) and low-Tc (~11K) phases involved a small difference in C-C dimer distance, 1.298(4) Å for 15K phase and 1.290(4) Å for 11K phase, while the lattice parameter was constant for all samples. Thus a change in C-C dimer distance may induce a change of the electronic state of the C-C dimer, resulting in an altered Tc in Y2C3.
Considering some other superconducting materials without an inversion center, CePt3Si and Li2Pt3B, their superconducting states are interesting because of the admixture of spin-singlet and spintriplet superconducting states that is induced by spin-orbit coupling [20,21]. Because Y2C3 does not have an inversion center in its crystal structure, the determination of the order parameter and the details of the superconducting gap structure are worth some attention.
In a 13C-NMR study of Y2C3 with a Tc =15.7 K at H=0 T, a clear decrease in 13C Knight Shift and an increase in the full width at half maximum (FWHM) of 13C-NMR spectra are observed below Tc , as shown in Figure 7 . It is suggested that the decrease of Knight Shift is due to a reduction of spin susceptibility associated with an onset of spin-singlet superconductivity in Y2C3, with the increase of FWHM possibly being due to an inhomogeneous distribution of vortex lattices.
Figure 8 shows the temperature dependence of 1/T1 in a magnetic field (H=9.85T). In the normal state, the plots obey the law: T1T=Constant. As shown in the inset of Figure 8, a tiny coherence peak is observed in (T1T)const/(T1T) just below Tc as in MgB2, indicating the opening of a full gap in the superconducting states of Y2C3. The temperature dependence of 1/T1 below Tc does not reveal a simple exponential term and seems to have small kink at around 5K.
Figure 9 shows the Arrhenius plot of (T1T)/(T1T)const vs. Tc/T, with Tc=12.2 K at H=9.85 T to help analyzing the details of the superconducting gap structure. The temperature dependence of (T1T)/ (T1T)const does not obey a simple power-law behavior such as T2- dependence. It seems that a large full gap opens in the high-temperature region, and low-lying quasiparticle excitations in the low-temperature region are dominated by the presence of a small full gap. The large and small superconducting gaps, 2Δ/kBTc, are estimated to be about 5 (T=5 K~Tc) and 2 (T<5 K), respectively. This behavior supporting multigap superconductivity in Y2C3 is not due to an extrinsic factor such as inhomogeneity of the samples, because 1/T1 is uniquely determined by the simple exponential curve of nuclear magnetization as shown in the inset of Figure 9.
This multigap behavior in Y2C3 is also detected by μSR measurements [23,24]. In the μSR study, muon spin relaxation rates of Y2C3 and La2C3 are reported. The crystal structure of La2C3 is a Pu2C3-type structure and its Tc’s are reported to be 6~13 K in different samples [9,25,26]. Therefore, an electronic structure similar to Y2C3’s is expected for La2C3, making La2C3 is a good candidate for comparative study with Y2C3. The specific heat measurement of La2C3 is reported to suggest single-gap superconductivity .
Figure 10 shows the temperature dependence of the muon spin relaxation rate for La2C3 and Y2C3. It is noted that plots of La2C3 reveal a deviation from single-gap BCS-type superconducting behavior, though in the case of Y2C3, no strong anomaly is observed in the muon spin relaxation. However, the temperature dependence below ~6 K (T/Tc<0.4) cannot be explained by a single-gap BCS picture. These temperature dependences can be understood from the double-gap structure in each compound by considering the Fermi surface of Y2C3 (three hole bands and one electron band) obtained by first-principles calculation .
Two superconducting gaps in Y2C3 and La2C3 can be realized by the differences in the density of states and Fermi velocities between hole and electron bands, so the temperature dependence of muon spin relaxation in each compound is affected by them. Taking the inter-band coupling strength, w, between the two compounds into account, the results after analyzing the difference in the temperature dependence of muon spin relaxation between Y2C3 and La2C3 by the two-gap model are listed in Table 2.
|Transverse field (kOe)||2.5||5.0|
|σν (0) (µs-1)||0.71(3)||0.48(2)|
|γ (0) (Å)||3800(100)||4600(100)|
|Δ1 (0) (meV)||2.7(1)||3.1(1)|
|Δ2 (0) (meV)||0.6(1)||0.7(3)|
Table 2: Superconducting parameters of Y2C3 and La2C3.
The solid lines in Figure 10 show the best-fit lines using a phenomenological double-gap model with s-wave symmetry [29,30]. The obtained difference in the relative weight, w, between two gaps might be connected with inter-band coupling. For La2C3, a simple model assuming two independent superconducting gaps, shown with a dashed line, is also tested, and a slightly better fit is obtained than the result in Table 2. This might suggest that the model may not necessarily be a good approximation for the case of weak inter-band coupling.
From the superconducting parameters of Y2C3 and La2C3 which are deduced from μSR measurements, the superconductivities in both compounds are described in the regime of strong electron-phonon coupling and s-wave symmetry, which is basically in good agreement with previous reports. However, in recent reports, the possibility of a nontrivial superconducting state in both compounds is pointed out. In the penetration depth, λ(T), and the upper critical field, μ0Hc2(T), of Y2C3 using a tunnel-diode-based resonant oscillation technique, λ(T) shows T-linear dependence at T<Tc indicating the existence of a superconducting gap with line nodes, and the μ0Hc2(T) presents a weak upturn at low temperature with a rather high value of about 29 T, which exceeds the weak-coupling Pauli limit . In 139La and 13C NMR of La2C3, 139La and 13C NMR shifts in the superconducting state do not differ from the normal state, and the 139La spin-lattice relaxation rate is strongly enhanced below Tc . These unconventional results can be attributed to the absence of inversion symmetry, which allows the possible mixture of spin-singlet and spin-triplet Cooper pairs in both compounds.
The superconductivity of doped semiconductors such as B-doped diamond in bulk  and films [33,34], and in B-doped Si  has stimulated renewed interest in the low-carrier-density superconductivity of doped semiconductors. In the case of B-doped diamond, experimental and theoretical research has sought to clarify whether its metallic nature arises from the holes at the top of the diamond valence band or from the boron impurity band formed above the valence band [36-47]. In particular, a higher-Tc is suggested, where bonds transform into bands by carrier-doping to a semiconductor [48-50].
In terms of structural features and physical properties, we focused on SiC, which has many stable polytypes including cubic zinc-blende, hexagonal and rhombohedral polytypes. As shown in Figure 11, in the cubic zinc-blende structure, labeled as 3C-SiC or β-SiC, Si and C occupy ordered sites in a diamond framework, and in hexagonal polytypes, nH-SiC, and rhombohedral polytypes, nR-SiC, generally referred to as α-SiC, nSi-C bilayers consisting of C and Si layers are stacked in a primitive unit cell.
Undoped SiC is a wide-band-gap semiconductor with a band gap of 2~3 eV depending on the crystal modification , and N, P, B, Al, etc. are lightly doped as donors or acceptors by ion implantation or thermal diffusion. When the dopant-induced carrier concentration increases, an insulator-to-metal transition occurs in semiconductors, and superconductivity has been induced in some semiconductors [52-55], in accord with theoretical predictions [56,57]. In SiC, the semiconductor-to-metal transition has been observed in n-type N-doped 4H-SiC with carrier concentrations above 1019 cm-3 without a superconducting transition .
In this situation, we succeeded in inducing type-I superconductivity in p-type boron-doped 3C-SiC with a carrier concentration of 1.06-1.91 × 1021 cm-3 , and after this report we confirmed a superconducting transition in B-doped 6H-SiC at a similar carrier concentration . The question arises whether SiC exhibits superconductivity with different dopant elements. In fact, p-type Al-doped 4H-SiC with an Al concentration of 8.7 × 1020 cm-3 showed metallic behaviors and a slight drop around 7 K in the temperature-dependence of sheet resistance . We note that this drop may indicate the onset of a superconducting transition, but a superconducting transition has not been confirmed. However, we did induce type-II superconductivity in p-type Al-doped 3C-SiC with a carrier concentration of 3.86-7.06 × 1020 cm-3 .
From typical PXRD patterns of B-doped 3C-SiC and 6H-SiC, the main phases in each sample were indexed as cubic zinc-blende 3C-SiC, and hexagonal 6H-SiC phases, respectively, as shown in Figure 12.
The refined lattice parameter of the major 3C-SiC phase increased after sintering, though only by ~0.1%, from 4.3575(3)Å to 4.3618(4) Å, and the refined lattice parameter, c, of the major 6H-SiC phase also increased after sintering by ~0.2%, from 15.06 Å to 15.09 Å. However, the refined lattice parameter, a, of 6H-SiC (in commercial 3.064 Å) did not change (within experimental accuracy). Because the atomic sizes of boron and carbon are comparable, but both are much smaller than silicon, the small changes in the lattice parameters suggest that boron substitutes at the carbon site in these samples. By means of the Hall effect at room temperature, the hole concentrations, n, were estimated to be ~1.91 × 1021 cm-3 for B-doped 3C-SiC and ~2.53 × 1020 cm-3 for B-doped 6H-SiC. The samples had much higher doping levels than those in previous reports [61-64]. The presence of liquid silicon in the sintering process may have helped boron diffusion and enhanced boron-substitution efficiency.
As shown in Figure 13, the magnetic susceptibility of B-doped 3C-SiC and 6H-SiC under a magnetic field of 1 Oe (zero field cooling process) significantly decreases at ~1.4 K, suggesting the occurrence of superconductivity with a superconducting volume fraction over 100% by the shielding effect.
Figure 14 shows magnetization vs. magnetic field (M-H) curves of B-doped 3C-SiC and 6H-SiC. These curves reveal type-I superconducting behavior. In both compounds, the onset field of magnetization shows a hysteresis about 30 Oe wide at the lowest temperature. Hysteresis during increasing and decreasing fields suggests that a 1st order transition under a finite magnetic field is occurring in both compounds, supporting type-I superconductivity. From the M-H curves, the critical field, Hc, is estimated to be about 100 Oe.
As shown in Figure 15, the electrical resistivity in B-doped 3C-SiC:B and 6H-SiC reveals metallic conductivity, reflecting the high carrierdoping level with residual resistivity ratios, RRR (ρ300K/ρ5K), of 11.4 and 4.7, respectively. B-doped 3C-SiC exhibits a much smaller resistivity, almost T-linear, but B-doped 6H-SiC exhibits a broad feature at around 150 K suggesting the weak localization of carriers or a contribution from non-metallic grain boundaries. The inset of Figure 15 shows an expanded view of the low-temperature data. The resistivities exhibit sharp drops at 1.5 K (B-doped 3C-SiC) and 1.4 K (B-doped 6H-SiC), corresponding to the Tc’s observed from the susceptibility.
To determine the phase diagram in the magnetic field-temperature (H-T) plane for both samples, the resistivities were measured by varying the temperature at different magnetic fields (T-scan shown in Figure 16), and varying the magnetic fields at different temperatures (H-scan shown in Figure 17). In the T-scan, only one transition was observed at Tc at zero field, while a large super cooling effect was observed in both SiC samples in finite fields. In the H-scan, hysteresis was also observed under 130 Oe in B-doped 3C-SiC and 100 Oe in B-doped 6H-SiC. The (i) in-field hysteresis, (ii) absence of hysteresis in a zero field, and (iii) very small value of the critical field, give strong evidence for type-I superconductivity in both SiC polytypes.
The H-T phase diagram determined from the resistivity data (T-scan and H-scan) is shown in Figure 18. Applying the conventional formula Hc(T)=Hc(0)[1-(T/Tc(0))α], the thermodynamic critical field, Hc(T), is estimated to be 132 ± 3 Oe with α~2.0 for B-doped 3C-SiC and 125 ± 5 Oe with α~ 1.6 for B-doped 6H-SiC in the warming plots. The same procedure applied to the cooling plots yields α ~ 1.6 in both SiC polytypes. This transition is identified as the upper limit of the intrinsic super cooling limit. The corresponding transition fields are denoted as Hsc (the subscript “sc” stands for super cooling) with an estimated Hsc(0)=102 ± 6 Oe for B-doped 3C-SiC and 94 ± 3 Oe for B-doped 6H-SiC, respectively.
Applying the Ginzburg-Landau (GL) theory of type-I superconductivity to these data, one can estimate an upper limit of the GL parameter κ from the difference of the critical fields obtained by a field-cooling run and a subsequent warming run [65,66]: .This formula yields κ ~ 0.32 for B-doped 3C-SiC and 0.31 for B-doped 6H-SiC, in agreement with the analysis of the Hall effect and the specific heat data [67,68]. This supports the type-I nature of superconductivity in B-doped SiC. Note that the value of κ is below 0.41, which is required in a model based on super cooling instead of superheating [66,69,70].
Table 3 lists basic normal-state parameters: Fermi wave number kF, effective mass m*, Fermi velocity vF, mean free path l; as well as superconducting state parameters: penetration depth λ, coherence length ξ and Ginzburg-Landau parameter κGL deduced from T-scan and H-scan in resistivity, Hall effect, and specific heat [67,68].
|n [cm-3]||1.91 × 1021||2.53 × 1020||1.80 × 1021||2.80 × 1021|
|Hc2(0) [Oe]||-||-||4.2 × 104||4 × 103|
|vF [m/s]||3.8 × 105||1.1 × 105||-||-|
Table 3: Age parameters of C. carpiofrom the Yamuna river, India.
For comparison, the previously reported parameters for B-doped diamond (C:B) and B-doped Si (Si:B) are added. The coherence lengths of B-doped 3C-SiC and 6H-SiC are compared with B-doped diamond and B-doped Si. Type-I superconductivity in B-doped SiC originates in these long coherence lengths.
However, it is not clear why SiC:B reveals type-I superconductivity in spite of the dirty limit (l << ξ). From SEM images of B-doped SiC samples (not shown in this paper), the maximum crystal grain size is about 5 μm, and in higher B-content samples (higher starting ratio), the crystal grain size tends to grow much larger. Crystal grain size growth is enhanced by adding Si and B during the synthesis process.
However, Tc in superconducting B-doped SiC samples does not change with the B-nominal composition. It is considered that the B-doping level in B-doped SiC has already reached the limiting level (a certain constant B/C ratio) in a solid state reaction. As a result, Tc does not change. Moreover, the mean free path l in B-doped SiC samples is reduced by grain boundary effects or un-reacted starting powder. Thus the mean free path l in B-doped SiC can be extended up to the clean limit (l >> ξ) in a high quality sample.
We have reviewed superconductivity in carbide compounds, whose Tc’s are unfortunately limited to the 10Kï½ž20K range. During the process in the developments of these superconductors, we focused on the high frequency phonon which was induced by light element. The maximum Tc in sesqui-carbides and wide band-gap semiconductors are 18K and 11K, respectively, at this stage. So, other routes have to be sought for development of new high-Tc superconductor. Recently, much attention has been paid to the new superconductor H3S (Tc 200K) under ultra-high pressure (200 GPa), which can be described by the BCS theory . This probably shows that light element superconductors provide one of the most promising paths to a room temperature superconductor taking account of the relationship electronic state and bonding state.
This work is supported by Grant-in-Aid from Ministry of Education, Culture, Sports, Science and Technology (MEXT) under No. 25000003, 26247057, and by JSPS KAKENHI Grant Number 15H05886 and partially by the Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers from Japan Society for the Promotion of Science.