High-Temperature Superconductivity in Boron-Doped Q‑Carbon Anagh Bhaumik,† Ritesh Sachan,†,‡ and Jagdish Narayan*,† †
Department of Materials Science and Engineering, Centennial Campus, North Carolina State University, Raleigh, North Carolina 27695-7907, United States ‡ Materials Science Division, Army Research Office, Research Triangle Park, North Carolina 27709, United States S Supporting Information *
ABSTRACT: We report high-temperature superconductivity in B-doped amorphous quenched carbon (Q-carbon). This phase is formed after nanosecond laser melting of Bdoped amorphous carbon films in a super-undercooled state and followed by rapid quenching. Magnetic susceptibility measurements show the characteristics of type-II Bardeen− Cooper−Schrieffer superconductivity with a superconducting transition temperature (Tc) of 36.0 ± 0.5 K for 17.0 ± 1.0 atom % boron concentration. This value is significantly higher than the best experimentally reported Tc of 11 K for crystalline B-doped diamond. We argue that the quenching from metallic carbon liquid leads to a stronger electron−phonon coupling due to close packing of carbon atoms with higher density of states at the Fermi level. With these results, we propose that the non-equilibrium undercooling-assisted synthesis method can be used to fabricate highly doped materials that provide greatly enhanced superconducting properties. KEYWORDS: superconductivity, quenched carbon, Raman spectroscopy, electron energy loss spectroscopy, secondary ion mass spectroscopy
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Since the thermodynamic solubility limit for (substitutional) B in diamond is 2.0%, higher concentrations can be attained only by highly non-equilibrium techniques. It should be mentioned that substitutional boron atoms generate hole carrier concentration which enhances superconductivity. On the other hand, interstitial boron atoms in diamond lattice donate three electrons which adversely affect superconductivity by compensating holes and reducing carrier concentration. Similarly, atomic hydrogen atoms create B−H complexes which neutralize holes and reduce Tc. High-temperature and pressure (equilibrium) synthesis of B-doped diamond leads to Tc of 4 K.1 The increases in Tc have been achieved by non-equilibrium MPCVD (microwave plasma-enhanced chemical vapor deposition) synthesis of B-doped diamond, where the nonequilibrium aspect is derived from the energetics of plasma beyond equilibrium energy (kBT) of the CVD process. The highest Tc of 11 K has been achieved for B concentration of 5.0% in (111) MPCVD films.2 The (111)-oriented B-doped diamond films exhibited a Tc higher than that of the (100) thin films.2,3 This was due to the higher lattice expansion resulting
uperconductivity in diamond and carbon-related materials has generated extraordinary theoretical and experimental interest. Superconductivity in boron-doped diamond is well-established with observed Tc ranging from 4 to 11 K with increasing boron concentration in substitutional lattice sites of diamond.1−3 With the increase in hole concentration, strong attractive interactions are induced which cause an increase in Tc. From electron−phonon coupling calculations in B-doped diamond over a wide range of boron concentrations, Moussa and Cohen predicted Tc of over 55 K for substitutional B concentrations in the range of 20−30%.4 These calculations did not take into account electron anisotropy and phonon anharmonicity in improving the accuracy of electron−phonon coupling; nevertheless, they provide an important guide for the synthesis of materials with increasing boron concentrations by non-equilibrium techniques. It should be mentioned that B concentration beyond which boron starts clustering to form dimers is the upper limit for obtaining the highest Tc. The bonding and antibonding states in B dimers are made of symmetric and antisymmetric combinations of the bound state in B. The symmetric and antisymmetric states lie deeper in the band gap and above the isolated B energy level, respectively.5 These energy states do not contribute to the density of states at the Fermi level, thereby reducing the value of Tc. © 2017 American Chemical Society
Received: February 23, 2017 Accepted: April 27, 2017 Published: April 27, 2017 5351
DOI: 10.1021/acsnano.7b01294 ACS Nano 2017, 11, 5351−5357
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ACS Nano from unrelaxed strains in (111) B-doped diamond, thereby giving rise to higher density of states, which cause an increase in Tc onset from 6.3 K [in (100) B-doped diamond] to 11.4 K.2 Another motivation for superconductivity in amorphous Qcarbon and crystalline diamond was derived from superconductivity in pure single crystals of Bi with Tc of 0.53 mK,6 compared to Tc of 6.8 K in amorphous bismuth.7,8 Recently, we reported major breakthroughs in the direct conversion of amorphous carbon into Q-carbon or diamond, hBN into Q-BN or c-BN, and pure and N-doped carbon into pure and N-doped diamond, where diamond is in the form of single-crystal nanodiamonds, nanoneedles, microneedles, and thin films.9−12 In this work, we have used a non-equilibrium method based upon melting by a nanosecond laser of amorphous B-doped carbon films in a super-undercooled state and quenching subsequently to form B-doped singlecrystal diamond or Q-carbon. In this process, B-doped diamond and Q-carbon are formed without the presence of hydrogen, which reduces Tc by forming B−H complexes.4 In addition, defects can be controlled, and much higher concentrations of boron can be achieved by rapid quenching from melt via solute trapping. The Q-carbon has an amorphous structure with over 85% sp3 bonding and the other 15% with sp2 bonding. The molten carbon is metallic, which can be packed closely and quenched into a structure at an undercooling higher than that needed to form diamond. We have achieved Tc of 36.0 ± 0.5 K in B-doped Q-carbon and Tc of 25.0 ± 0.5 K for B-doped diamond with a similar boron concentration of 17.0 ± 1.0 atom %.
RESULTS AND DISCUSSION Figure 1a,b represents the time-of-flight secondary ion mass spectrometry (TOF-SIMS) of as-deposited B−C and B-doped Q-carbon thin films, respectively. The concentration and profile of C in the as-deposited films are periodic with alternating B and C layers. There is a considerable change in the B profile after the pulsed laser annealing (PLA) technique. After laser annealing, the B concentration becomes quite uniform throughout the deposited layer, indicating the melting of all the carbon layer. This large B redistribution after laser annealing can be used to estimate the boron diffusion coefficient in molten carbon during the PLA process, which is completed in ∼200 ns. Using the 2D diffusion equation, the diffusivity coefficient is calculated as ∼2 × 10−04 cm2/s. This high value is typical of diffusivity in liquid, and it demonstrates melting of carbon and laser-assisted, liquid-phase diffusivity of B while converting amorphous carbon into Q-carbon. This rapid melting and quenching are crucial for the emergence of superconductivity in this material. The SIMS spectra rule out the presence of any impurity elements in the as-deposited and laser-annealed thin films. Figure 2a depicts a field-emission scanning electron microscopy (FESEM) image of B-doped Qcarbon thin film. The filamentary structure is formed due to interfacial instability during the super-undercooling process by nanosecond ArF laser. Formation of nano- and microdiamonds is observed occasionally at the triple junctions. Figure 2b shows the cross-sectional high-angle annular dark-field (HAADF) image of the formed B-doped Q-carbon on the c-sapphire substrate. The elemental maps of B and C (Figure 2d,e), obtained by electron energy loss spectroscopy (EELS), clearly demonstrate the homogeneous distribution of B in Q-carbon throughout the analyzed region (boxed region in Figure 2c). A representative acquired EELS spectrum is presented in Figure
Figure 1. (a) SIMS profiles of as-deposited boron and carbon layers with the inset showing a schematic of the alternating layers of amorphous carbon and boron deposited on c-sapphire using pulsed laser deposition technique; (b) pulse laser-annealed (B-doped Qcarbon) thin films.
2b, showing the K-edges of B and C. The spectrum contains the characteristic π* and σ* peaks associated with the K-edge of B and C, which indicates the presence of C and B bonded in both sp3- and sp2-hybridized state. The EELS quantification13 estimates the average B concentration to be 17 ± 1 atom % in the Q-carbon. Figure S1 represents the HAADF image of Bdoped Q-carbon and X-ray EDS elemental mapping of B, Al, and C, whose concentrations are consistent with EELS. The Xray diffraction results (Figure S2) showed the Q-carbon structure as amorphous, consistent with high-resolution transmission electron microscopy (TEM) and HAADF. Figure 3a shows unpolarized Raman spectra of B-doped Qcarbon using a 532 nm wavelength laser as the excitation source. The spectra can be deconvoluted into three Ramanactive vibrational modes centered at 1105, 1322, and 1567 cm−1. The first peak corresponds to the sp2 bonding, whereas the second and third peaks represent sp3-bonded carbon and graphitic phase (G peak), respectively. The sp3 fractions calculated in the superconducting thin films of B-doped Qcarbon (Figure 3a) vary from 0.83 to 0.86, consistent with 5352
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Figure 2. (a) High-resolution FESEM image showing filamentary structures of B-doped Q-carbon, with the inset showing disconnected filamentary structures of B-doped Q-carbon (indicated by white arrows) formed due to interfacial instability; (b) EELS spectrum revealing characteristic K-edges of B and C with estimated 17 ± 1 atom % of B; (c) cross-sectional high-angle annular dark-field image of the formed B-doped Q-carbon on the csapphire substrate; (d) B-EELS mapping; and (e) C-EELS mapping. The scale bars shown in (d,e) correspond to 10 nm.
earlier Q-carbon results.10 The sp3-bonded C atoms play an important role in high-temperature superconductivity. The substitution of sp3-bonded C by B atoms creates a positively charged hole that facilitates the Cooper pair formation below the superconducting transition temperature. Due to the presence of quantum mechanical interference between the zone-center Raman-active optical phonon mode and the continuum of electronic states created by B atoms, there occurs an asymmetry and red shift of the diamond peak in the B-doped Q-carbon thin films. In the case of B-doped polycrystalline diamond samples, there are vibrational modes between 500 and 1225 cm−1 that are due to maxima in the phonon density of states.14 The presence of these peaks in the B-doped diamond thin film suggests distortion and isolated disorder in the diamond lattice. Reports also indicate that these peaks originate from the local vibrational mode of B pairs present in the interstitial sites.15 High-resolution Raman spectroscopy of B-doped Q-carbon thin films shows the absence of these peaks. This suggests that B is located in the electrically active sites of Q-carbon. The low intensity of the G peak indicates less graphitization in B-doped Q-carbon samples. Figure 3b depicts XPS spectra of as-deposited and B-doped Qcarbon thin films. There is an increase in C/O ratio after laser annealing. The absence of any impurity peaks in the survey scan and in the X-ray diffraction (Figure S2) of B-doped Q-carbon shows that the samples are impurity-free, consistent with SIMS data. Deconvolution of the high-resolution XPS scan in the range of 188−196 eV gives rise to two peaks. The two peaks are centered at 188.5 and 192 eV, which are attributed to B 1s and B−O electronic states, respectively.16 The magnetization versus temperature plots in zero-fieldcooled (ZFC) and field-cooled (FC) conditions are shown in Figure 4a at 100 Oe applied magnetic fields for Q-carbon doped with 17.0 ± 1.0 atom % boron. From these measurements, the Tc for B-doped Q-carbon was estimated
Figure 3. (a) Raman spectroscopy of B-doped Q-carbon thin films showing 84.3% sp3; (b) XPS survey scan of B−C and B-doped Qcarbon thin films. The inset in (b) illustrates high-resolution XPS scan showing the presence of B−O and B 1s peaks.
to be 36.0 ± 0.5 K. The Tc for crystalline diamond doped with the same boron concentration was found to be lower at 25.0 ± 0.5 K (Figure S3). Our results on B-doped Q-carbon and diamond follow the characteristics of superconductivity in bismuth, where Tc for amorphous bismuth is 6.8 K,7 compared to 53 mK for bismuth single crystal.7 This trend in bismuth has been correlated with enhanced electron−phonon coupling and higher density of states at the Fermi energy in amorphous Bi compared to single-crystal Bi.8 There is a large difference in the magnetic moment between the ZFC and FC curves, indicating the presence of large flux pinning forces in the material. This results in the trapping of magnetic flux in the FC condition. The transition temperature is shifted to lower values after application of magnetic field, suggesting inhomogeneous superconductivity in the B-doped Q-carbon thin films. The magnetic susceptibilities (χ) of B-doped Q-carbon samples are calculated as ∼−0.02 and ∼−0.09 emu·cc−1Oe−1 for FC and ZFC (at 5 K) conditions, respectively. The ZFC and FC magnetizations indicate the flux exclusion and flux expulsion, respectively, in the B-doped Q-carbon samples. The ZFC magnetic susceptibility (−4πχ) represents the shielding fraction in a superconducting material. A complete shielding (4πχ < −1) is observed in the B-doped Q-carbon samples that indicates a high-quality superconducting phase. A complete 5353
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curve with the Y axis is 5.40 T. The Ginzburg−Landau coherence length (εL) can be calculated using the formula εL = [Φ0/2πHc2(0)]0.5. Using the value of Hc2(0) as 5.40 T, εL is calculated as 79 Å. The value of penetration depth (λd) can also be found using the equation Hc1(0) = (Φ0/4πλ2d)ln(λd/εL). The value of λd is calculated as 82.3 Å. The Ginzburg−Landau parameter (k) is determined to be 1.04 (>1/20.5), thereby showing that B-doped Q-carbon is a type-II superconductor.20 The zero-temperature energy gap (Δ(0)) in B-doped Q-carbon is calculated as 5.52 meV. The value of the exponent (n) is determined using the power law:
Hc(T ) Hc(0)
=1−
n
( ). T Tc
21
From
the Hc2(T) data fitting, the value of n is derived as 2.11 for the case of Hc2(T), which is consistent with Bardeen−Cooper− Schrieffer (BCS) formalism. There is a downward curvature near 0 K in the case of Hc1(T), which can be explained by the increased contribution from Hc1σ(T) as compared to Hc1π(T).21 Detailed theoretical modeling of the superconductivity in Bdoped Q-carbon and diamond is in process and will be reported elsewhere.22 The critical current density (Jc) is determined ⎡ 20ΔM ⎤ using the Bean formula: Jc = ⎢ 2 w ⎥, where ΔM is the ⎣ tw (l − 3 ) ⎦ difference in magnetization values (+M and −M) at a particular magnetic field, and t, w, and l are the thickness, width, and length of the sample, respectively. The value of Jc (0 Oe) at 2 K is calculated as 11.36 × 1010 A/cm2, which is quite large compared to that of B-doped diamond. The large value of Jc (0 Oe) in B-doped Q-carbon is due to its small dimension. Large value of Jc (0 Oe) also indicates flux-melting in this material. The Tc for phonon-mediated superconductivity can be calculated using the McMillan formula:23 ω
Tc =
log
1.2
(
1.04(1 + λ)
)
exp − λ − μ*(1 + 0.62λ) , where ⟨ω⟩log is the logarith-
mic average of phonon frequencies, μ* is the screened Coulomb pseudopotential, and λ is the measure of average electron−phonon coupling. Using the value of ⟨ω⟩log and Tc as 67.4 meV23 and 36.4 K, respectively, the calculated value of λ is 0.797, which is consistent with theoretical calculations with Moussa and Cohen for B-doped diamond.4 This is indicative of moderate electron−phonon coupling in B-doped Q-carbon. This can be explained by the relation between λ, the density of states at the Fermi energy (N(0)), ionic mass (M), average square of electron−phonon matrix element (⟨I2⟩), and the characteristic phonon frequency averaged over the phonon spectrum (⟨ω2⟩). The average electron−phonon coupling parameter is related to the above variables by the following equation: λ = (N(0)⟨I2⟩)/(M⟨ω2⟩). Hall effect measurements indicate a composite carrier concentration of ∼1022 cm−3 in Bdoped Q-carbon samples. This indicates a substantial value of N(0) in these films. The ionic mass is also quite low, but the moderate value of λ in B-doped Q-carbon is due to the presence of strong covalent bonds (stronger than diamond), thereby dramatically increasing the value of ⟨ω2⟩. In the Bdoped Q-carbon thin films, all the valence states are of σ electronic states with stronger electron−phonon coupling as compared to that with B-doped diamond. The presence of substitutional disorder can quench Tc in B-doped diamond by opening a gap in the valence states. The value of Tc rises monotonically by increasing the B concentration (in the substitutional sites) in diamond. To date, the highest value of Tc achieved in diamond/5% B thin film synthesized using the
Figure 4. (a) Magnetic moment vs temperature plots of B-doped Qcarbon thin film showing Tc = 36.0 ± 0.5 K. Inset in (a) depicts M− H loops at a constant temperature below Tc. (b) Upper critical field and lower critical field in B-doped Q-carbon thin films along with the WHH curve. The inset in (b) depicts an enlarged view of the lower critical field in B-doped Q-carbon thin films.
shielding is also reported in Fe-based high-temperature superconductors.17,18 The superconducting volume fraction (Meissner fraction) is calculated from the FC curve at low applied magnetic field (H < Hc1). The superconducting volume fraction is calculated to be ∼25%, without considering the demagnetization enhancement factor. The inset in Figure 4a depicts the “butterfly hysteresis” at different temperatures (below Tc). The value of Hc1(T) and Hc2(T) were calculated from the hysteresis loops. The magnetic field value for the highest point in the negative magnetic moment (4th quadrant) in the hysteresis loop corresponds to Hc1(T). The value of Hc2(T) was determined as the field from which M(H) deviated first from the background (X axis).19 The Hc2(T) seems to vary at a faster rate than predicted by the Werthamer−Helfand− Hohenberg (WHH) model. According to the WHH model, the value of Hc2(0) is calculated using Hc2(0) = −0.69(dHc2/dT)Tc, where dHc2/dT denotes the slope at Tc. Solving this equation yields the value of Hc2(0) as 6.94 T, which is also shown in Figure 4b. In B-doped Q-carbon thin films, the value of Hc2(0) as calculated from the intersection of the extrapolated trend 5354
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ACS Nano plasma-enhanced CVD technique is 11 K.24 At higher B concentrations, B-doped diamond enters into the dirty type-II superconductor regime where scattering of Bloch states by impurities does not play an important role. The results from the temperature-dependent resistivity measurements of B-doped Q-carbon thin films are shown in Figure 5. It depicts the onset of Tc (Tc,on) at 37.8 K and Tc,off
Figure 5. Temperature-dependent (normalized) resistivity measurements of B-doped Q-carbon thin films showing the onset temperature of superconducting transition temperature at 37.8 K. The inset depicts the enlarged view of the superconducting transition showing the transition width to be 1.5 K. Figure 6. (a) Electronic Raman spectra of B-doped Q-carbon, Bdoped diamond,28 as-deposited B−C, and c-sapphire substrate. (b) Energy-level schematic diagram of B acceptor states in B-doped Qcarbon (green band) and B-doped diamond. The sapphire peak in (a) is indicated by *.
(zero-resistivity condition) at 35.5 K. The sharper superconducting transition in B-doped Q-carbon indicates the presence of a high-quality superconducting phase. The transition width (ΔT) is calculated as 1.5 K and is shown in the inset of Figure 5. This transition width is comparable to that in high-temperature superconductors25,26 and is considerably broader than observed in single-crystal superconductors (∼10−4 K).27 The broadening in the transition width is possibly due to the amorphous nature of B-doped Q-carbon. The electronic Raman spectra of B-doped Q-carbon, B-doped diamond,28 asdeposited B−C, and c-sapphire substrate are shown in Figure 6a. Our results show a distinct shallow acceptor energy level at 33.3 meV in B-doped amorphous Q-carbon, as compared to 37.0 meV in B-doped crystalline diamond.28 It has already been shown that at low B concentrations (
