7 0 0 Carbon Based Superconductors 2 n a Reinhard K. Kremer∗, Jun Sung Kim, and Arndt Simon J 9 Max-Planck-Institut fu¨r Festk¨orperforschung, 2 ] Heisenbergstr.1, D-70569 Stuttgart, Germany n o (Dated: February 6, 2008) c - r Abstract p u s We review the characteristics of some carbon based novel superconductors which emerged in . t a the past two decades since the discovery of superconductivity in the high-T oxocuprates. In m c - particular, we summarize the properties of ternary layered carbide halides of the rare rarth metals d n withcompositionRE C X (RE=Y,La; X=Cl,Br,I)andoftherareearthdi-andsesquicarbides, o 2 2 2 c [ YC2, LaC2 and La2C3. Finally, we briefly discuss the properties of the recently discovered Ca and 1 Yb intercalated graphite superconductors, CaC and YbC . 6 6 v 2 0 PACS numbers: abc 7 1 0 7 0 / t a m - d n o c : v i X r a 1 I. INTRODUCTION The discovery of high-T superconductivity by Bednorz and Mu¨ller1 in 1986 marks the c beginning of a period of a vivid search for - chemically and physically partly extremely complex - new oxocuprates and for theoretical approaches to understand their puzzling properties, quite a few of which remained controversial even until today. The advent of this completely unexpected class of new superconductors also revived the interest in more conventional - ‘low-T ’ - superconductors. In due course, a number of new systems were c found, and already known superconductors were reinvestigated with improved and refined experimental and theoretical tools. These activities led to surprising new discoveries as that of the 40 K superconductor MgB by Nagamatsu et al.2 Apart from its T , MgB is 2 c 2 special primarily for two reasons: Compared e.g. to the high-T oxocuprates its crystal c structure is of remarkable simplicity allowing electronic and phononic structure calculations of high precision, and MgB is the first system for which multigap superconductivity has 2 independently been evidenced by several experimental techniques.3,4,5 Until the discovery of MgB , doped fullerenes had shown the highest T values after the 2 c high-T oxocuprates. With large enough quantities of purified C available,6 Hebard et al. c 60 prepared superconductors with a T of 18 K by doping polycrystalline C and C films c 60 60 with alkali metals.7 Subsequently, by adjusting the separation of the C molecules using a 60 proper composition of different alkali metals, T ’s up to ∼33 K were reached.8 c Superconductivity in doped fullerenes also redraw attention to carbon based supercon- ductors in general. Especially, binary and quasibinary transition metal carbides have a long history in showing T ’s which were among the highest found before the discovery of the c high-T oxocuprates.9 Later borocarbides of composition REM B C, with RE = Y or Lu c 2 2 and M = Ni or Pd, with T ’s up to 22 K attracted considerable interest.10,11 c Superconductivity in graphite intercalation compounds (GICs) is another early field of research which recently was revived. The discovery of superconducting GICs dates back to the pioneering work of Bernd Matthias’ group in the 1960’s, however, the T ’s of these c early GICs remained well below 1 K.12,13 Subsequently, the T ’s of alkali metal intercalated c GICs could be raised by intercalation under pressure with e.g. Li and Na, but T did not c significantly exceed the boiling point of liquid helium.14 It was not until recently that T of c the GICs could be significantly enhanced by intercalating divalent alkaline earth metals like 2 Ca and Yb.15 Finally, after graphite and C , diamond was also converted into a superconductor by 60 hole doping induced by a substitution of about 3% B into C sites. Ekimov et al. showed that such a boron-doped diamond is a bulk, type-II superconductor below T ∼4 K with c superconductivity surviving in a magnetic field up to H (0)≥3.5 T.16 c2 In our search for complex metal-rich rare earth halides we found a series of new super- conducting layered carbide halides of the rare earth metals with T ’s up to ∼10 K.17,18,19 c For a deeper understanding of the chemistry and physics of these we in turn reinvestigated also the properties of binary dicarbides and sesquicarbides of composition REC and RE C , 2 2 3 with R=Y,La. Superconductivity in binary carbides of rare earth metals had been an in- tensively investigated topic in the sixties and seventies of the last century. In this family of compounds T values peaked with (Y Th ) C at 17 K.20 c 0.7 0.3 2 3 Superconductivity in rare earth metal sesquicarbides recently regained considerable attention after the reports by Amano et al. and Nakane et al. about the successful synthesis of binary Y C under high pressure conditions (∼5 GPa).21,22 The reported T ’s reached 2 3 c 18 K and the upper critical field exceeded 30 T. In the following we will summarize some of the characteristic properties of the ternary layered rare earth metal carbide halides and the binary di- and sesquicarbides. We conclude with some remarks on our results on the recently discovered alkali earth GICs. II. SUPERCONDUCTIVITY IN RARE EARTH CARBIDE HALIDES AND RARE EARTH CARBIDES A. Ternary Layered Cabide Halides of the Rare Earth Metals The carbide halides of the rare earth metals, RE C X (X=Cl, Br, I and RE being a 2 2 2 rare-earth metal) crystallize with layered structures which contain double layers of close- packed metal atoms sandwiched by layers of halogen atoms to form X-RE-C -RE-X slabs 2 as elementary building blocks. These connect via van der Waals forces in stacks along the crystallographic c-axis. Different stacking sequences (1s and 3s stacking variants) have been found. The carbon atoms form C-C dumbbells which occupy the octahedral voids in the close-packed metal atom doublelayers (cf. Fig. 1).23,24 3 b a b a c c FIG. 1: (left) Crystal structure of Y C I (1s stacking variant) and (right) crystal structure of 2 2 2 Y C Br (3s stacking variant) projected along [010] with the unit cells outlined. C, Y, and (I,Br) 2 2 2 atoms are displayed with increasing size. Compounds containing the nonmagnetic rare-earth metals Y and La are superconductors (Fig. 2). The maximum T of 11.6 K which was achieved by adjusting the composition in c the quasi-ternary phases Y C (X,X’) .18 The variation of T (x) across the transition of the 2 2 2 c 3s and the 1s stacking variant indicating that superconductivity is essentially a property of the configuration of an individual X-RE-C -RE-X slab rather than of the stacking details 2 in the crystal structure. The transition temperatures of all known superconducting phases RE C X are compiled in Table I. 2 2 2 compound T (K) µ H (T) reference c 0 c2 Y C Cl 2.3 - 18 2 2 2 Y C Br 5.04 3 18,19,25 2 2 2 Y C I 10.04 12 18,25,26,27 2 2 2 Y C Br I 11.6 - 18 2 2 0.5 1.5 La C Br 7.03 - 28 2 2 2 La C I 1.72 - 28 2 2 2 TABLE I: Transition temperatures and upper critical fields, µ H , of the known superconducting 0 c2 phases RE C X (RE=Y, La; X=Cl, Br, I) 2 2 2 4 The heat capacity of Y C I shows a sharp anomaly, however with a jump height 2 2 2 ∆C (T )/γT ≈2 which is considerably larger than the value 1.43 expected from weak P C C coupling BCS theory.19,26 A fit of the heat capacity anomaly with the empirical α-model29 indicates strong coupling with 2∆(0)/k T ≈4.2, the superconducting gap being enhanced B C by about 20% over the BCS value, similar to the σ-gap in MgB 30. There is, however, no 2 indication from the temperature dependence of the heat capacity anomaly for a multiple gap scenario. Using approximate equations for strong coupling superconductors which re- late 2∆(0)/k T and ∆C (T )/γT to the logarithmic average over the phonon frequencies B C P C C ω 31,32 one estimates the typical phonon frequency range for Y C I to be ∼80-100cm−1. ln 2 2 2 In this range A modes have been discerned by Raman spectroscopy in which Y and halogen g atoms vibrate in-phase parallel and perpendicular to the layers.33,35 C stretching and tilting vibrations have considerably higher energies, and their role for electron-phonon coupling, particularly inthe case ofthe tilting modes, couldbeimportant.36 The electronic structure in close neighborhood to the Fermi energy, E , is characterized F by bands of low dispersion which are reminiscent of the quasimolecular character of the HOMO and LUMO orbitals of an isolated C-C dumbbell.35,37 These together with highly 12 0 3sstacking g) fc 11 1sstacking 3m/ 10 c-1 -20 9 (1 8 (cid:2)g-2 zfc (a) K) 7 ( Tc 6 0 g) fc 5 3m/ 4 c-1 3 -210 2 ( zfc (cid:2)g 1 YCBr Cl YCBr I (b) 2 2 2-z z 2 2 2-xx -2 0 0 2 4 6 8 10 2 1 0 1 2 T(K) z x FIG. 2: (left) field-cooled (fc) and zero field-cooled (zfc) magnetic susceptibilities of (a) Y C I 2 2 2 (after ref.[26]) and (b) La C Br (after ref.[28]). (right) T ’s of a series of quasiternary mixtures 2 2 2 c of Y C Br I and Y C Br Cl . Different stacking variants of the compounds are indicated by 2 2 2−x x 2 2 2−z z different symbols (after ref.[18]). 5 dispersive bands establish a flat/steep band scenario which in our view is a prerequisite of superconductivity in a more general sense.34 The low-dispersive bands give rise to two peaks in the electronic density of states, DOS, each about 100 meV above and below the Fermi energy which enclose a ‘pseudogap’ at E .35,37 Deviations from the linear temperature dependence of the Korringa relaxation of F 13C nuclei probed by 13C NMR are a clear manifestation for the proposed structure in the DOS close to E .38 F The electronic structure and the dispersion of the bands in the vicinity of E is very F sensitive to slight structural variations and can be very effectively tuned e.g. by hydrostatic pressure to increase the DOS and maximize T .39 When hydrostatic pressure is applied to c Y C I T increases, and a maximum of about 11.7 K is reached at 2 GPa, similar to the 2 2 2 c maximum T found in the quasi-ternary mixtures.27,39,40 The increase of T with pressure c c Y C I and also La C Br is remarkable and parallels the findings in observed for the Hg 2 2 2 2 2 2 based oxocuprates but also for fcc-La for which similar values for the relative increase 1/T ·dT /dP, have been detected.41,42 c c 2.0 ) v e / s e at 1.5 t P (GPa) s 0 1 2 ( 12 S O 0.00 GPa D 1.0 11 T (K)c 00..1742 GGPPaa 1.77 GPa 3.3 GPa 10 -100 -50 0 50 100 Energy (meV) FIG. 3: Electronic density of states, DOS, of Y C I in the close vicinity to E . The inset shows 2 2 2 F the pressure dependence of T of Y C I . The dotted line is a guide to the eye (after ref. [39,40]). c 2 2 2 6 B. Binary Dicarbides and Sesquicarbides of the Rare Earth Metals YC crystallizes with the body centered tetragonal CaC structure type (Fig. 4) with 2 2 C-C dumbbells centering Y metal atom octahedra which are slightly elongated along [001].43 YC had been found to be a superconductor with a T ∼3.88 K.44 Proper heat treatment 2 c of stoichiometric YC samples results in superconductors with a sharp transition and onset 2 T ’s up to 4.02(5)K , somewhat increased over those previously reported.45,46 LaC shows a c 2 T of about 1.6 K.44 c FIG. 4: Crystal structure of YC along [0 1 0]. Y and C atoms are drawn with decreasing size. An 2 Y-C -Y doublelayer as found in the ternary carbide halides of the rare earths metals, RE C X 2 2 2 2 (RE=Y, La; X=Cl, Br, I), is highlighted in dark grey. Heat capacity measurements (Fig.5) nicely reveal the anomaly at the transition to super- conductivity which follows closely the BCS weak-coupling predictions but already indicate significantly decreased critical fields as compared to those of the layered carbide halides.25 Electronic structure calculations for YC reveal strongly dispersive bands in planes per- 2 pendicular to the c-direction originating from Y dx2−y2 orbitals and also strongly dispersive bands in the c-direction emerging from combinations of Y d , d , and C p , p orbitals.45 xz yz x y As a consequence the electronic density of states close to the Fermi level is to a large extent featureless with a slight positive slope. Doping with Th or Ca (10% to 20%) decreases T .45 c As compared to the layered yttrium carbide halides, the critical fields of YC (<0.1 T, cf. 2 7 8 6 4 2 0 2 4 6 8 10 12 14 16 18 20 T2(K2) FIG.5: Superconductinganomalyintheheatcapacity ofYC2 (Bext=0,◦). Thenormalstate△has been reached by applying an exernal field of 0.4 T (after ref.[45]). The (red) solid line represents a fit to the predictions of the BCS theory with a slight smearing of T being included. c Fig.6 and Table I) are reduced by up to two orders of magnitude . The significant difference in the upper critical fields between the layered carbide halides and the dicarbides as well as the marked increase in the anisotropy of the coherence lengths (ξ /ξ ≈ 5,25) supports k ⊥ Ginzburg’s suggestion that from the point of view of possibilities to enhance T promis- c ing materials are layered materials and dielectric-metal-dielectric sandwich structures.47,48 In fact, by comparing the crystal structures of the dicarbides and the carbide halides of the rare earths (Figs. 1 and 4) one realizes that the R-C -R doublelayers carrying the su- 2 perconductivity in the ternary carbide halides can be considered as sections of the three dimensional structure of the dicarbides which are sandwiched by dielectric halogen layers. In this respect, the dicarbides and the carbide halides of the rare earth metals are interesting examples to test Ginzburg’s conjecture. La C (like Y C ) crystallizes with the cubic Pu C structure in the space group I43d 2 3 2 3 2 3 8 60 T) 40 m ( 2 Hc 30 (cid:2)0 20 T) 20 m ( J 10 - 0 0 10 20 30 40 50 (cid:3)H(mT) 0 0 0.0 0.5 1.0 T/T c FIG. 6: Upper critical field, µ H , determined from the isothermal magnetization measured of a 0 c2 spherical sample of YC . The inset displays the isothermal magnetizations measured at constant 2 temperatures of 2K, 2.2K, ..., 3.8K, 4K, in decreasing order (after ref.[25]). which belongs to the tetrahedral crystallographic class T with no center of symmetry.49 The d structure contains C–C dumbbells in a distorted dodecahedral coordination (‘bisphenoid’) formed by 8 La atoms (cf. Fig. 7). For a more detailed discussion of the problems of C deficiency and the problem of the aniostropy of the thermal ellipsoids of the C atoms see ref. [57]. A recent study of the crystal structure up to high pressures could not detect any structural phase transitions up to 30 GPa.50 In non-centrosymmetric systems with significant spin-orbit coupling superconducting or- der parameters of different parity can be mixed. A recent system which attracted particular interest in this respect, is the heavy fermion superconductor CePt Si which shows uncon- 3 ventional properties, as e.g. antiferromagnetism and superconductivity at T ∼2.2 K and T N c ∼ 0.75 K, respectively, and an upper critical field which considerably exceeds the paramag- netic limit.51 With no 4f electrons present and the high atomic mass of La (as compared to Y) La C is therefore an interesting system to study the effects of non-centrosymmetry on 2 3 superconductivity. Possible multi-gap superconductivity is another interesting issue which has been proposed for Th doped Y C and La C .63 Recently, Harada et al. from 13C NMR 2 3 2 3 measurements reported multi-gap superconductivity for Y C .64 2 3 Incontrast toY C which requires high-pressure synthesis methods21,22, samples ofLa C 2 3 2 3 9 b a c FIG. 7: Crystal structure of La C projected along [111] (after ref. [46]. (left) Unit cell with 2 3 La atoms indicated by the large spheres. (right) La atom environment of a C-C dumbbell. The thermal ellipsoids of the C atoms are shown. are readily accessible by arc-melting of the constituents. Early on, La C was reported to 2 3 have a T of ∼ 11 K.52,53,54 Subsequently, it has been shown that these samples were not c stoichiometric, as anticipated, but exhibit a range of homogeneity from 45.2% to 60.2% atom-% carbon content.46,55,56 Investigations of a series of samples La C with 0.3 ≥ δ ≥ 0 2 3−δ indicate a separation into two superconducting phases with rather sharp T ’s of ∼ 6 K and c 13.3-13.4 K (Fig. 8). The high T values are attributed to stoichiometric La C , viz. c 2 3 negligible C deficiency, which was assured individually for the samples by neutron powder diffraction.26,57,59 Our electronic structure calculations show a splitting of the bands near E indicating F that the spin degeneracy is lifted due to a sizable spin-orbit coupling in addition to the non- centrosymmetry in the structure.59 However, the band splitting in La C is much smaller 2 3 than those found for other non-centrosymmetric superconductors like CePt Si, Li Pt B or 3 2 3 Cd Re O .60,61,62 For Li Pd B, another non-centrosymetric superconductor, where the band 2 2 7 2 3 splitting iscomparablewiththatofLa C ,conventional BCStypebehaviorwithanisotropic 2 3 10