Superconductivity in Carbide Compounds

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. each Tc sample at lowest temperature in susceptibility measurements (1.8 K) was estimated to be approximately 40% in the fi eld cooling process. Th e magnetization vs. magnetic fi eld (M-H) curves exhibit typical type-II superconducting behavior. Th e electronic specifi c heat (Cel) of each sample (11K material, 13K material, and 15K material) is shown in Figure 4. Th e total specifi c heat (C) is expressed by following formula; 3 5 el ph C C C T T T         (1) Th e Cel is obtained by subtracting the lattice part of the specifi c heat (Cph) from the total specifi c heat (C), which is measured at zero fi eld and 8T, respectively. In this case, an applied fi eld cannot completely suppress superconductivity, and γT in the Cel term provides a minor contribution. So we used the normal-state entropy formula; 3 5 1 1 3 5 n S T T T       (2) For determination of γ and ΘD (derived from 4 ( 3) (12 / 5) , D N R      where R=8.314J/(molK) and N=5) in an Sn/T vs. T2 plot. Th is method is useful for a superconductor, in which superconductivity cannot be completely suppressed by an applied magnetic fi eld [16]. Th e 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. Th e fi tting 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. Th ese 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 specifi c heat of three samples under various magnetic fi elds. Tc decreases with increasing applied fi eld and the μ0Hc2(0) was determined from the midpoint temperature of the jump at several applied fi elds, shown in Page 2 of 10 Citation: Muranaka T, Akimitsu J (2016) Superconductivity in Carbide Compounds. Chem Sci J 7: 135. doi: 10.4172/2150-3494.1000135 Volume 7 • Issue 3 • 1000135 Chem Sci J, an open access journal ISSN: 2150-3494 Figure 6. Th e 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;     0 c2 c2 c 0 0.69 / H dH dT T      (3) and the coherence lengths, , were determined to be 38, 36, and 35 Å, respectively, for the 11K, 13K, and 15K materials from following formula;   2 0 c2 0 0 ~ / H    (4) 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) [17], being comparable to that of YNi2B2C (Tc=14K, ΘD=533K) [18]. 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. Th erefore we focus on the relationship between γ and Tc, the Tc of Y2C3 increases as γ increases. Th e γ value is given by   2 2 B / 3, k D F     where   D F  is the density of states at the Fermi level. In BCS theory, Tc is given by     B c D 0 1.13 1/ k T exp V D F      , so it is considered that Tc in Y2C3 increases as   D F  increases. However, the γ value of Y2C3 is not very high in comparison with that of Nb3Sn, where γ=13 mJ/molK2 [17]. So, we concluded that its high Debye temperature makes Tc relatively high despite its small Sommerfeld coeffi cient. Nakane et al. looked for the causes of diff erent Tc’s in Y2C3 structural properties, using neutron powder diff raction [19]. As they reported, high-Tc (~15K) and low-Tc (~11K) phases involved a small diff erence 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. Th us 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 [22]. 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. Tc [K] 11.6 13.9 15.2  [mJ/molK2] 4.7 6.0 6.3 D [K] 540 530 530 μ0Hc2(0) [T] 22.7 24.7 26.8 2/kBTc 3.6 3.9 4.1  [Å] 38 36 35 Table 1: A summary of superconducting parameters of Y2C3. 0.2


Introduction
Th e discovery of superconductivity in MgB 2 [1] and B-doped diamond [2] has stimulated the search for new superconducting materials in similar systems containing light elements. In the framework of BCS theory [3], high frequency phonons induced in a network of light elements can yield a higher superconducting transition temperature (T c ). Th ese discoveries turned our attention towards new combinations of intermetallic compounds, and we discovered new superconductors in carbide systems, Y 2 C 3 [4] and B-doped SiC [5]. In this paper, we review these superconductors.

Superconductivity in Y 2 C 3
Sesqui-carbides (R 2 C 3 : R=Y, La, Lu) such as Pu 2 C 3 , which crystallize as bcc structures without an inversion center, are reported to exhibit superconductivity at relatively high temperatures for intermetallic compounds, with T c 's that depend on their carbon content [6][7][8][9][10]. Th e crystal structure of Y 2 C 3 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, (R 2-x Th x )C 3 , have attracted attention because their T c 's are close to those of niobium-based A15-type superconductors. Th ese materials showed superconductivity with a variable T c , 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 Y 2 C 3 had a maximum T c of 18 K, as shown in Figure 2.
From a theoretical point of view, the band structure of Y 2 C 3 shows that the hybridization of C-C dimer antibonding and the Y-4d characteristics are dominant at the Fermi level [11,12]. Th e electronic structure of YC 2 with C dimers suggests that the electronic structure could have substantial C-C antibonding character near the Fermi level [12]. It has been reported that low-frequency metal atom vibrations have the largest electron-phonon coupling in Y 2 C 3 , while the contribution of high-frequency C-C stretching vibrations is comparatively small [13].
However, the mechanism of superconductivity in Y 2 C 3 has not been well understood because of the diffi culty involved in synthesizing stable, single-phase Y 2 C 3 in air. We established a technique for synthesizing high-purity samples, and prepared samples having various T c 's to investigate the mechanism of the variation of T c in this system [14,15]. As shown in Figure 3, the magnetic susceptibility of Y 2 C 3 decreased signifi cantly at each T c and the superconducting volume fraction of each T c sample at lowest temperature in susceptibility measurements (1.8 K) was estimated to be approximately 40% in the fi eld cooling process. Th e magnetization vs. magnetic fi eld (M-H) curves exhibit typical type-II superconducting behavior.
Th e electronic specifi c heat (C el ) of each sample (11K material, 13K material, and 15K material) is shown in Figure 4. Th e total specifi c heat (C) is expressed by following formula; 3 5 el ph Th e C el is obtained by subtracting the lattice part of the specifi c heat (C ph ) from the total specifi c heat (C), which is measured at zero fi eld and 8T, respectively. In this case, an applied fi eld cannot completely suppress superconductivity, and γT in the C el term provides a minor contribution. So we used the normal-state entropy formula; where R=8.314J/(molK) and N=5) in an S n /T vs. T 2 plot. Th is method is useful for a superconductor, in which superconductivity cannot be completely suppressed by an applied magnetic fi eld [16]. Th e value of γ and Θ D of Y 2 C 3 were calculated to be 4.7 mJ/molK 2 and 540 K for the 11K material, 6.0 mJ/molK 2 and 530 K for the 13K material, and 6.3 mJ/ molK 2 and 530 K for the 15K material, respectively. Th e fi tting below T c for each sample has revealed exp(-1/T)-dependence as predicted by BCS theory, rather than T n -dependence as would an anisotropic superconductor. We estimated the superconducting gap parameters, 2Δ/k B T c , to be 3.6, 3.9, and 4.1 for 11, 13, and 15K materials, respectively. Th ese facts suggest that the symmetry of the superconducting gap is an isotropic s-wave, and superconductivity in Y 2 C 3 can be described as belonging to the strong coupling regime. Figure 5 shows the temperature dependence of the specifi c heat of three samples under various magnetic fi elds. T c decreases with increasing applied fi eld and the μ 0 H c2 (0) was determined from the midpoint temperature of the jump at several applied fi elds, shown in Figure 6. Th e plots show a linear temperature dependence with the gradients dH c2 /dT, and μ 0 H c2 (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, , 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 Y 2 C 3 with various T c 's. Y 2 C 3 has a higher than Nb 3 Sn (T c =18K, Θ D =230K) [17], being comparable to that of YNi 2 B 2 C (T c =14K, Θ D =533K) [18]. From relatively high Θ D , it is considered that the light element, Carbon, plays an important role in the superconductivity in Y 2 C 3 and yields relatively high T c . But T c in Y 2 C 3 is not related to Θ D as tabulated in Table 1.
Th erefore we focus on the relationship between γ and T c , the T c of Y 2 C 3 increases as γ increases. Th e γ value is given by  is the density of states at the Fermi level. In BCS theory, T c is given by increases. However, the γ value of Y 2 C 3 is not very high in comparison with that of Nb 3 Sn, where γ=13 mJ/molK 2 [17]. So, we concluded that its high Debye temperature makes T c relatively high despite its small Sommerfeld coeffi cient.
Nakane et al. looked for the causes of diff erent T c 's in Y 2 C 3 structural properties, using neutron powder diff raction [19]. As they reported, high-T c (~15K) and low-T c (~11K) phases involved a small diff erence 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. Th us a change in C-C dimer distance may induce a change of the electronic state of the C-C dimer, resulting in an altered T c in Y 2 C 3 .
Considering some other superconducting materials without an inversion center, CePt 3 Si and Li 2 Pt 3 B, 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 Y 2 C 3 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 13 C-NMR study of Y 2 C 3 with a T c =15.7 K at H=0 T, a clear decrease in 13 C Knight Shift and an increase in the full width at half maximum (FWHM) of 13 C-NMR spectra are observed below T c , as shown in Figure 7 [22]. 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 Y 2 C 3 , with the increase of FWHM possibly being due to an inhomogeneous distribution of vortex lattices.   Zero-field cooling process    region are dominated by the presence of a small full gap. Th e large and small superconducting gaps, 2Δ/k B T c , are estimated to be about 5 (T=5 K~T c ) and 2 (T<5 K), respectively. Th is behavior supporting multigap superconductivity in Y 2 C 3 is not due to an extrinsic factor such as inhomogeneity of the samples, because 1/T 1 is uniquely determined by the simple exponential curve of nuclear magnetization as shown in the inset of Figure 9.
Th is multigap behavior in Y 2 C 3 is also detected by μSR measurements [23,24]. In the μSR study, muon spin relaxation rates of Y 2 C 3 and La 2 C 3 are reported. Th e crystal structure of La 2 C 3 is a Pu 2 C 3 -type structure and its T c 's are reported to be 6~13 K in diff erent samples [9,25,26]. Th erefore, an electronic structure similar to Y 2 C 3 's is expected for La 2 C 3 , making La 2 C 3 is a good candidate for comparative study with Y 2 C 3 . Th e specifi c heat measurement of La 2 C 3 is reported to suggest single-gap superconductivity [27]. Figure 10 shows the temperature dependence of the muon spin relaxation rate for La 2 C 3 and Y 2 C 3 . It is noted that plots of La 2 C 3 reveal a deviation from single-gap BCS-type superconducting behavior, though in the case of Y 2 C 3 , no strong anomaly is observed in the muon spin relaxation. However, the temperature dependence below ~6 K (T/T c <0.4) cannot be explained by a single-gap BCS picture. Th ese temperature dependences can be understood from the double-gap structure in each compound by considering the Fermi surface of Y 2 C 3 (three hole bands and one electron band) obtained by fi rst-principles calculation [28].
Two superconducting gaps in Y 2 C 3 and La 2 C 3 can be realized by the diff erences 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 aff ected by them. Taking the inter-band Figure 8 shows the temperature dependence of 1/T 1 in a magnetic fi eld (H=9.85T). In the normal state, the plots obey the law: T 1 T=Constant. As shown in the inset of Figure 8, a tiny coherence peak is observed in (T 1 T) const /(T 1 T) just below T c as in MgB 2 , indicating the opening of a full gap in the superconducting states of Y 2 C 3 . Th e temperature dependence of 1/T 1 below T c does not reveal a simple exponential term and seems to have small kink at around 5K. Figure 9 shows the Arrhenius plot of (T 1 T)/(T 1 T) const vs. T c /T, with T c =12.2 K at H=9.85 T to help analyzing the details of the superconducting gap structure. Th e temperature dependence of (T 1 T)/ (T 1 T) const does not obey a simple power-law behavior such as T 2dependence. It seems that a large full gap opens in the high-temperature region, and low-lying quasiparticle excitations in the low-temperature coupling strength, w, between the two compounds into account, the results aft er analyzing the diff erence in the temperature dependence of muon spin relaxation between Y 2 C 3 and La 2 C 3 by the two-gap model are listed in Table 2.
Th e solid lines in Figure 10 show the best-fi t lines using a phenomenological double-gap model with s-wave symmetry [29,30]. Th e obtained diff erence in the relative weight, w, between two gaps might be connected with inter-band coupling. For La 2 C 3 , a simple model assuming two independent superconducting gaps, shown with a dashed line, is also tested, and a slightly better fi t is obtained than the result in Table 2. Th is 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 Y 2 C 3 and La 2 C 3 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 fi eld, μ 0 H c2 (T), of Y 2 C 3 using a tunnel-diode-based resonant oscillation technique, λ(T) shows T-linear dependence at T<T c indicating the existence of a superconducting gap with line nodes, and the μ 0 H c2 (T) presents a weak upturn at low temperature with a rather high value of about 29 T, which exceeds the weak-coupling Pauli limit [31]. In 139 La and 13 C NMR of La 2 C 3 , 139 La and 13 C NMR shift s in the superconducting state do not diff er from the normal state, and the 139 La spin-lattice relaxation rate is strongly enhanced below T c [32]. Th ese 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.

Superconductivity in Boron-Doped Sic
Th e superconductivity of doped semiconductors such as B-doped diamond in bulk [2] and fi lms [33,34], and in B-doped Si [35] 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][37][38][39][40][41][42][43][44][45][46][47]. In particular, a higher-T c is suggested, where bonds transform into bands by carrier-doping to a semiconductor [48][49][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 modifi cation [51], and N, P, B, Al, etc. are lightly doped as donors or acceptors by ion implantation or thermal diff usion. When the dopant-induced carrier concentration increases, an insulator-to-metal transition occurs in semiconductors, and superconductivity has been induced in some semiconductors    [52][53][54][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 10 19 cm -3 without a superconducting transition [58].
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 × 10 21 cm -3 [5], and aft er this report we confi rmed a superconducting transition in B-doped 6H-SiC at a similar carrier concentration [59]. Th e question arises whether SiC exhibits superconductivity with diff erent dopant elements. In fact, p-type Al-doped 4H-SiC with an Al concentration of 8.7 × 10 20 cm -3 showed metallic behaviors and a slight drop around 7 K in the temperature-dependence of sheet resistance [60]. We note that this drop may indicate the onset of a superconducting transition, but a superconducting transition has not been confi rmed. However, we did induce type-II superconductivity in p-type Al-doped 3C-SiC with a carrier concentration of 3.86-7.06 × 10 20 cm -3 [59].
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.
Th e refi ned lattice parameter of the major 3C-SiC phase increased aft er sintering, though only by ~0.1%, from 4.3575(3)Å to 4.3618(4) Å, and the refi ned lattice parameter, c, of the major 6H-SiC phase also increased aft er sintering by ~0.2%, from 15.06 Å to 15.09 Å. However, the refi ned 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 eff ect at room temperature, the hole concentrations, n, were estimated to be ~1.91 × 10 21 cm -3 for B-doped 3C-SiC and ~2.53 × 10 20 cm -3 for B-doped 6H-SiC. Th e samples had much higher doping levels than those in previous reports [61][62][63][64]. Th e presence of liquid silicon in the sintering process may have helped boron diff usion and enhanced boron-substitution effi ciency.
As shown in Figure 13, the magnetic susceptibility of B-doped 3C-SiC and 6H-SiC under a magnetic fi eld of 1 Oe (zero fi eld cooling process) signifi cantly decreases at ~1.4 K, suggesting the occurrence of superconductivity with a superconducting volume fraction over 100% by the shielding eff ect. Figure 14 shows magnetization vs. magnetic fi eld (M-H) curves of B-doped 3C-SiC and 6H-SiC. Th ese curves reveal type-I superconducting behavior. In both compounds, the onset fi eld of magnetization shows a hysteresis about 30 Oe wide at the lowest temperature. Hysteresis during increasing and decreasing fi elds suggests that a 1st order transition under a fi nite magnetic fi eld is occurring in both compounds, supporting type-I superconductivity. From the M-H curves, the critical fi eld, H c , 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, refl ecting the high carrierdoping level with residual resistivity ratios, RRR (ρ 300K /ρ 5K ), 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. Th e inset of Figure 15 shows an expanded view of the low-temperature data. Th e resistivities exhibit sharp drops at 1.5 K (B-doped 3C-SiC) and 1.4 K (B-doped 6H-SiC), corresponding to the T c 's observed from the susceptibility.   To determine the phase diagram in the magnetic fi eld-temperature (H-T) plane for both samples, the resistivities were measured by varying the temperature at diff erent magnetic fi elds (T-scan shown in Figure  16), and varying the magnetic fi elds at diff erent temperatures (H-scan shown in Figure 17). In the T-scan, only one transition was observed at T c at zero fi eld, while a large super cooling eff ect was observed in both SiC samples in fi nite fi elds. In the H-scan, hysteresis was also observed under 130 Oe in B-doped 3C-SiC and 100 Oe in B-doped 6H-SiC. Th e (i) in-fi eld hysteresis, (ii) absence of hysteresis in a zero fi eld, and (iii) very small value of the critical fi eld, give strong evidence for type-I superconductivity in both SiC polytypes.
Th e H-T phase diagram determined from the resistivity data (T-scan and H-scan) is shown in Figure 18. Applying the conventional  0)) α ], the thermodynamic critical fi eld, H c (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. Th e same procedure applied to the cooling plots yields α ~ 1.6 in both SiC polytypes. Th is transition is identifi ed as the upper limit of the intrinsic super cooling limit. Th e corresponding transition fi elds are denoted as H sc (the subscript "sc" stands for super cooling) with an estimated H sc (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 diff erence of the critical fi elds obtained by a fi eld-cooling run and a subsequent warming run [65,66]: Th is 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 eff ect and the specifi c heat data [67,68]. Th is 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 k F , eff ective mass m * , Fermi velocity v F , mean free path l; as well as superconducting state parameters: penetration depth λ, coherence length ξ and Ginzburg-Landau parameter κ GL deduced from T-scan and H-scan in resistivity, Hall eff ect, and specifi c heat [67,68]. 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, T c 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, T c does not change. Moreover, the mean free path l in B-doped SiC samples is reduced by grain boundary eff ects or un-reacted starting powder. Th us the mean free path l in B-doped SiC can be extended up to the clean limit (l >> ξ) in a high quality sample.

Conclusion
We have reviewed superconductivity in carbide compounds, whose T c 's are unfortunately limited to the 10K~20K range. During the process in the developments of these superconductors, we focused on the high frequency phonon which was induced by light element. Th e maximum T c 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-T c superconductor. Recently, much attention has been paid to the new superconductor H 3 S (T c  200K) under ultra-high pressure (200  GPa), which can be described by the BCS theory [71]. Th is 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.