Superconductivity in highly disordered dense carbon disulfide

Superconductivity in highly disordered dense carbon disulfide Ranga P. Diasa, Choong-Shik Yooa,1, Viktor V. Struzhkinb, Minseob Kima, Takaki Muramatsub, Takahiro Matsuokac, Yasuo Ohishic, and Stanislav Sinogeikind a Departments of Physics and Chemistry, Institute for Shock Physics, Washington State University, Pullman, WA 99164; bGeophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015; cJapan Synchrotron Radiation Research Institute, Sayo, Hyogo 679-5198, Japan; and dHigh Pressure Collaborative Access Team, Geophysical Laboratory, Carnegie Institution of Washington, Argonne, IL 60439

Edited by Roald Hoffmann, Cornell University, Ithaca, NY, and approved June 3, 2013 (received for review March 18, 2013)

High pressure plays an increasingly important role in both understanding superconductivity and the development of new superconducting materials. New superconductors were found in metallic and metal oxide systems at high pressure. However, because of the filled close-shell configuration, the superconductivity in molecular systems has been limited to charge-transferred salts and metal-doped carbon species with relatively low superconducting transition temperatures. Here, we report the low-temperature superconducting phase observed in diamagnetic carbon disulfide under high pressure. The superconductivity arises from a highly disordered extended state (CS4 phase or phase III[CS4]) at ∼6.2 K over a broad pressure range from 50 to 172 GPa. Based on the X-ray scattering data, we suggest that the local structural change from a tetrahedral to an octahedral configuration is responsible for the observed superconductivity.

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extended solids magnetic ordering metallization nonconventional superconductors non-Fermi liquids

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ighly compressed low-Z molecular solids become extended solids in 3D network structures of polymeric and/or metallic states, as found in their periodic high-Z counterparts (1, 2). A relevant question is then, if these extended forms of simple molecular solids can give rise to novel properties such as superconductivity and magnetism, as often found in sp/spd-elemental metals and metallic alloys at low temperatures (3, 4). The theoretical prediction of high-temperature (possibly 300 K) superconductivity in metallic hydrogen at high pressure is stimulating in this regard (5), yet the superconductivity in simple molecular solids has only been observed in paramagnetic oxygen at TC = ∼0.6 K above 100 GPa (6). Recently, we have reported that carbon disulfide undergoes a series of pressure-induced transformations from a transparent molecular solid (Cmca, depicted as phase I) at 2 GPa, to a black polymer of (–S–(C=S)–)p with three-folded carbon atoms bonded to sulfur atoms (CS3 phase or phase II[CS3], signifying the threefold carbon coordination in the bracket) at 10 GPa and then to a highly reflective polymer with four-folded carbons (CS4 phase or III[CS4]) above 40–50 GPa (2). Although highly disordered, phase III[CS4] exhibits a remarkable electrical conductivity of ∼5 μΩ m at ambient temperatures similar to that of an elemental metal (rather than an organic polymer or a polymeric metal) (7). The resistivity ∼5 μΩ m of phase III[CS4] is close to that of elemental metals, such as titanium (0.42 μΩ m), europium (0.94 μΩ m), and intermetallic alloys, such as Nichrome (1.1 μΩ m), Pt/Pd (0.4 μΩ m), rather than organic metals. In the present study, we further show that the phase III[CS4] undergoes a magnetic ordering transition below ∼42 K and enters a superconducting state at ∼6.2 K, both observed over a large pressure range from 50 to 172 GPa (the maximum pressure studied) and exhibits the characteristics of a correlated intermetallic “molecular” alloy. The present results are summarized in the phase diagram of carbon disulfide (Fig. 1). 11720–11724 | PNAS | July 16, 2013 | vol. 110 | no. 29

Experiments The present study was based on a number of experiments with over two dozen samples, all providing a consistent and reproducible set of electrical resistance, susceptibility, and X-ray scattering data. The liquid CS2 sample (99.99% from Sigma-Aldrich) was loaded onto a membrane-driven diamondanvil cell (mDAC) using 1/3-carat–type Ia diamond anvils with a 0.18-mm culet. The mDAC sample was then mounted in a vibration-free close-cycle cryostat (Cold-Edge Tech) for simultaneous Raman and electrical resistance measurements down to 5 K at 100-GPa pressures. We used a four-probe method to measure the electrical resistance. The electrical resistivity was then calculated through Van der Pauw’s equation 7, exp[−πLRA/ρ] + exp [−πLRB/ρ] = 1, where RA = VA/IA and RB = VB/IB represent the measured resistances between two coupled electrodes (Fig. S1), and ρ and L represent the resistivity and measured thickness of sample, respectively (8). We estimated the uncertainty no more than 10% for resistivity. For magnetic susceptibility measurements, we used a highly sensitive modulation technique capable of separating the spurious background signal from the sample signal using a Be–Cu DAC (Fig. S2) (9). Our background signal appeared to be that of paramagnetic, which can be interpolated with a smooth polynomial function in the range of the superconducting transition. The total signal can be represented as the complex variable U = AT eiφ T and the interpolated background as B = AB eiφ B ; our signal is then S = AS eiφ S = U − B, the difference of two complex variables. Angle-resolved X-ray scattering data were collected at low temperatures to 9 K, using microfocused (∼10 × 10 μm) monochromatic synchrotron X-rays at both 1 High Pressure Collaborating Access Team (HPCAT) beamlines (λ = 0.3982 Å) at the Advanced Photon Source and BL10XU (λ = 0.4136 Å) at the Super Photon Ring (SPring)-8 in Japan. The X-ray scattering intensities were recorded on high-resolution 2D image plates over a large 2θ range between 0 and 40° and then converted to 1D profiles using the Fit2D program (10). To investigate structure in the amorphous phase, pair distribution function (PDF) analysis was performed using PDFGetX2 (11). The background X-ray scattering was also measured from an empty cell after the experiments and was subtracted from the data to obtain the S(Q) (Fig. S3).

Results and Discussion Evidence for superconductivity in carbon disulfide is found in both the electrical resistance and magnetic susceptibility data (Fig. 2) obtained from a large number of experiments with over two dozen samples (SI Text). The superconducting transition, for example, is clearly recognized at the onset of the sharp resistance drop at 4.91 K at 60 GPa in Fig. 2A. The transition temperature TC increases to 6.01 K at 90 GPa at a rate of +32 mK/GPa and to 6.23 K at 140 GPa at +4.2 mK/GPa, then decreases to 5.82 K at 172 GPa (Fig. 2B). The resistance drop is nearly 60% within 0.1° of the transition. This is a very sharp drop, considering the disordered nature of this material and compared with other

Author contributions: C.-S.Y. designed research; R.P.D., C.-S.Y., M.K., T. Muramatsu, and T. Matsuoka performed research; C.-S.Y., V.V.S., Y.O., and S.S. contributed new reagents/ analytic tools; R.P.D., C.-S.Y., and M.K. analyzed data; and R.P.D. and C.-S.Y. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1

To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1305129110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1305129110

Fig. 1. (A) Pressure–temperature phase diagram for carbon disulfide, showing the superconducting transition at TC, the magnetic ordering transition at TN, and local structure change from a tetrahedral to an octahedral configuration (see Inset for structure). The pressure dependence of the TC was determined from both the resistance (open circles) and magnetic susceptibility (open squares) (Fig. 2), whereas that of the TN was determined from the temperature dependence of resistivity (Fig. 3). (B) Expanded view of the TC as a function of pressure to 180 GPa, indicating a discontinuity ∼100 GPa.

The superconducting transition is also apparent from the abrupt change in magnetic susceptibility at the onset of TC (Fig. 2B), as measured by an alternating-current method (9). The TC is seen at the onset of the susceptibility signal on the hightemperature side, where the magnetic flux completely enters the sample. Both the magnetic susceptibility and the electrical resistance data yield the consistent TC of around 6 K (Fig. 1). For a phonon-mediating superconductor with small Coulomb repulsion (16), the superconducting temperature can be approximated by TC = (θD/1.45) exp(−1.04(1+λ)/λ), where θD is the Debye temperature and λ is the electron–phonon coupling CHEMISTRY

superconducting transitions in organic superconductors (12) and pure elemental solids at high pressures (13, 14). It is not uncommon to observe a small residual resistance (0.4–0.7 Ω) in the superconducting state, likely arising from the contact resistance between the Pt electrical lead and the CS2 sample. Interestingly, the sample resistance at 48 GPa increases slightly below 6 K, showing the typical behavior of disordered metals in the presence of weak localization effects (15). The temperature-dependent resistance of low-pressure phases II[CS3] and III[CS4] below 48 GPa (Fig. S4), on the other hand, shows a gradual transition from an insulator to a metal.

Fig. 2. (A) Temperature-dependent electric resistance of carbon disulfide at high pressures, showing magnetic and superconducting transitions at several pressures that occur around 40 K (TN) and 6 K (TC), respectively. (Inset) Expanded view into the low-temperature region ( ∼6.6 (see the solid lines in Fig. S4B). Instead, it follows the 1/T1/4 dependence (see the lines in Fig. S4C), consistent with a variable range hopping (VRH) model of a Mott insulator (5). Its metallic nature is retained up to 202 GPa, the highest pressure studied at ambient temperature. The persistent electrical resistivity anomaly near 45 K in Fig. 4A may provide insight into the interplay between magnetic ordering and superconductivity. Fig. S5 plots the magnitude of the resistivity anomaly δρ as a function of pressure. Fig. S5, Inset shows that the δρ is obtained by extrapolating the temperature dependences above and below the transition to TN and evaluating the difference in the resultant electrical resistivity. The plot clearly shows a noticeable difference in δρ between the nonsuperconducting state at 48 GPa and the superconducting state at 60 GPa. The quantity δρ in the superconducting state steadily decreases with pressure to ∼100 GPa, above which it drops abruptly and then decreases again steadily above 120 GPa. This behavior can be understood in terms of decrease of the fraction of gapped Fermi surface spins, which reduces the number of available states into which quasiparticles can scatter. Thus, it results in the reduction in δρ as observed. This result is then consistent with the fact that the superconductivity and antiferromagnetism is mutually exclusive. Furthermore, the spin transition with an abrupt drop in δρ occurs at the onset of the local structural change and the electron-correlation change from the Fermi-liquid to non-Fermi-liquid transition, all at around 100 GPa. Therefore, these results seem to indicate that CS2 indeed undergoes a magnetic ordering transition before the superconducting state. 4. Qiu X, Thompson JS, Billinge JL (2004) PDFgetX2: A GUI-driven program to obtain the pair distribution function from X-ray powder diffraction data. J Appl Cryst 37:678. 5. Sage MH, Blake GR, Palstra TTM (2008) Insulator-to-metal transition in (R,Ca) VO3.. Phys Rev B 77:155121-1–8.

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Fig. S1. Thickness of the sample as a function of pressure during compression and decompression. (Inset) ρ(T) and R(T) at 70 GPa showing the similar systematic behavior as a function of temperature. Microphotographs of reflective CS2 samples at 28 and 55 GPa showing the experimental setup for four-probe electrical resistance measurements and the metallic reflectivity of CS2 samples above 55 GPa similar to those of Pt probes.

Dias et al. www.pnas.org/cgi/content/short/1305129110

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Fig. S2. (A) Amplitude of measured superconducting signal from CS2 at 50 GPa, overlapped with the background. (Inset) Background-subtracted signal using information for both signal amplitude and phase (B). See text for details. (B) Phase of total measured signal and background from CS2 at 50 GPa. (Inset) Critical component of Be–Cu DAC to measure the magnetic susceptibility signal by the modulation technique using signal coil (1), compensating coil (2), and excitation coil (3).


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Fig. S3. (A) CS2 sample (black), background (red) and background subtracted (blue) X-ray scattering patterns showing the analysis procedure to get the S(Q) in B. Background X-ray scattering was also measured from an empty cell after the experiments and the S(Q) data were Fourier transformed to obtain the G(r), as shown in Fig. 4.

Fig. S4. (A) Temperature-dependent electrical resistance of carbon disulfide at 24, 30, 37, and 43 GPa on a logarithmic scale, showing a transition from insulator to semiconductor to semimetal. (B) ln(ρ) against 1000/T (Arrhenius plot), showing the linearity indication above 150 K. (C) ln(ρ) against 1/T1/4 (VRH mechanism), showing the linearity indication at low temperatures in dashed lines.


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Fig. S5. Magnitude of the resistivity anomaly δρ plotted as a function of pressure, showing a competing effect of magnetic ordering and superconductivity in dense carbon disulfide. (Inset) δρ is defined by extrapolating the temperature dependences above and below the transition to TN and evaluating the difference in the resultant electrical resistivity.

Table S1. Measured and calculated (in parentheses) peak positions of pair distances at various temperatures and pressures

r1 (C1–S1) r2 (S1–S1) r3 (S1–S2) r4 (S1–S3) r5 (S1–S4) r6 (S1–S5) Density, g/cm3

Td 125 K at 63 GPa

Oh 40 K at 63 GPa

Td 58 GPa at 300 K

Oh 100 GPa at 300 K

1.67 (1.69) 2.85 (2.76) 4.20 (3.90) 5.14 (4.77) 6.28 (6.16) 6.97 (7.29) 4.93

2.14 (2.09) 3.03 (2.96) 4.16 (4.18) 5.13 (5.12) 6.15 (5.91) 7.10 (6.61) 4.90

1.68 (1.73) 2.80 (2.82) 4.58 (4.00) 5.43 (4.89) 6.67 (6.32) 7.34 (7.48) 4.25

1.91 (1.71) 2.70 (2.79) 3.84 (3.95) 4.71 (4.83) 5.73 (5.58) 6.80 (6.84) 4.75

Td and Oh represent, respectively, tetrahedral and octahedral local configurations. Only the first-nearest carbon and sulfur atoms are counted for the pair distance calculation because of the weak scattering contribution of carbon by electron diffusion under high coordination numbers.


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