Session N8: Focus Session: Novel superconductors V: Borides, Organics and Others

Engineering superconductors with ab initio methods: the example of LiB

The identification of novel crystal structures is a fundamental step for predicting new stable compounds in alloys. While performing ab initio data mining of intermetallic compounds [1], we discover a new family of layered metal borides [2], of which MgB$_2$ is one particular element (the new phases are called Metal Sandwich (MS)). Thermodynamic stability and electronic properties of these MS phases are investigated in details, leading to the prediction of a hypothetical novel superconductor MS-LiB [2,3]. Calculations show that the MS phases in the Li-B system exhibit electronic features similar to those of MgB$_2$ [2,3] and CaC$_6$ [4]. Although the predicted critical temperature of LiB is lower than that of MgB$_2$ (references [4] and [5] for MS2-LiB and MS1-LiB, respectively), the peculiarities of MS-LiB in terms of electronic structure, layer arrangements and doping capabilities allow a lot of freedom in the search for higher $T_c$ systems [5]. We acknowledge the San Diego Supercomputer Center for computational resources. \newline \newline [1] S. Curtarolo et al., Phys. Rev. Lett. {\bf 91}, 135503 (2003). \newline [2] A.N. Kolmogorov, S. Curtarolo, Phys. Rev. B {\bf 73}, 180501(R) (2006). \newline [3] A.N. Kolmogorov, S. Curtarolo, in press, Phys. Rev B {\bf 74} (2006), condmat/0607654. \newline [4] A.Y. Liu, I.I. Mazin, cond-mat/0610057. \newline [5] M. Calandra, A.N. Kolmogorov, S. Curtarolo, submitted (2006).   

Electronic structure of MS2-LiB under hydrostatic pressure.

Recently ab initio calculations have found that the Li-B phase equilibrium diagram has two new phases: MS1 and MS2 [A. Kolmogorov and S. Curtarolo, Phys. Rev. B \textbf{73}, 180501R (2006)]. These two phases are stable enough to compete against known phases. These lithium borides exhibit electronic features similar to those in magnesium diboride and they are expected to be superconductors. In this work, we have studied the structural and electronic properties of the MS2-LiB system under pressure. The calculations were performed using the SIESTA code, with the GGA exchange-correlation functional in the PBE form. We have used numerical atomic orbitals as the basis set for the valence wavefunctions employing a double $\zeta $-polarized basis. We present a detailed analysis of the band structure, Fermi surface, and orbital populations as a function of the hydrostatic pressure. In particular, we focus on the behavior of the $\sigma $- and $\pi $-bands derived from the boron $p$-states.   

Combining the advantages of superconducting MgB2 and CaC6 in one material: suggestions from first-principles calculations

We show that a recently predicted layered phase of lithium monoboride, Li$_2$B$_2$, combines the key mechanism for strong electron-phonon coupling in MgB$_2$ (i.e., interaction of covalent B $\sigma$ bands with B bond-stretching modes) with the dominant coupling mechanism in CaC$_6$ (i.e., interaction of free-electron-like interlayer states with soft intercalant modes). Yet, surprisingly, the electron-phonon coupling in Li$_{2}$B$_{2}$ is calculated to be weaker than in either MgB$_2$ or CaC$_6$. This is due to the accidental absence of B $\pi$ states at the Fermi level in Li$_{2} $B$_{2}$. In MgB$_2$, the $\pi$ electrons play an indirect but important role in strengthening the coupling of $\sigma$ electrons. We discuss the use of doping to restore $\pi$ electrons at the Fermi level, which would enhance the coupling and the superconducting $T_c$.   

The Structural and Physical Properties of the Vacancy Ordered LiBC Phases

The prediction of superconductivity on the hole doped LixBC system [1] has triggered to particular interest on the synthesis of non-stoichiometric LiBC compounds. However, isolation of a non-stoichiometric phase of the LiBC have not been succeed as a single phase, yet. All of the experimental studies exhibited non-superconductivity in the disordered Li$_{x}$BC phases. Contrary to the disordered Li$_{x}$BC phases synthesized in the literature [2], non-stoichiometric Li vacancy ordered phases were obtained in this work. Additionally, the structural analysis with Rietveld refinement in a series of samples identified the stages of the intercalation of Li between the BC layers. The effect of stoichiometry on the physical properties of ordered Li$_{x}$BC phase was investigated at low temperatures. [1] Rosner H.et al., PRL 88, 12, 2002. [2] Fogg A.M.et al.JACS,128, 10043, 2006.   

The Pressure Effect on the Electronic Structure of the Ordered LiBC

In this study, the effect of the higher pressures (0-100GPa) on the electronic structure was investigated for an ordered structure of Li$_{x}$BC phase. And also, the stoichiometric effect was examined by the first principles calculations in terms of the metallic behaviour for the range of 0 $\le $ x $\le $ 1. It was observed that the density of states near the Fermi level decreases depending on the pressure and the energy gap above the Fermi level contracts for the higher pressure values for especially Li$_{0.5}$BC compound predicted as a superconductor [1-3]. DOS is extremely sensitive to the Li stoichiometry and the unit cell volume. The pressure has the different effect on the electronic structure of Li$_{1.0}$BC system behaviour for the same pressure range by contrast with the nonstoichiometric LiBC. \newline [1] Rosner H.et al., PRL 88, 12, 2002. \newline [2] Singh P.P. et al., Solid State Comm., 124,25-28, 2002. \newline [3] Dewhurst J.K. et al., PRB 68, 020504(R), 2003.   

Mechanism of Superconductivity in Boron-Doped Diamond

The recent discovery of superconductivity in boron-doped diamond above liquid helium temperature has attracted considerable interest. Theoretical investigations indicate that the superconducting pairing in this material is of the conventional phonon-mediated type. However, the nature of the phonon mechanism involved and the role of the dopants are still controversial issues. In order to elucidate such issues we performed first-principles calculations of the electron-phonon interaction in boron-doped diamond, considering a virtual crystal model and a supercell model which explicitly includes the boron atoms. For each model we calculated the Eliashberg functions with high accuracy by sampling the corresponding Brillouin zone with a million of inequivalent $k$-points. We found that the localized vibrational modes associated with the boron atoms provide a significant contribution to the electron-phonon coupling strength and that superconductivity in diamond is crucially linked to the breaking of the lattice periodicity induced by the doping.   

Critical fields, vortex melting and the irreversibility line in quasi 2D organic superconductors.

We have measured the critical field and aspects of the vortex structure in anisotropic organic superconductors using pulsed and dc fields up to 50 and 45 T respectively and at temperatures down to 55 mK. In all cases we measured the penetration depth using the tunnel diode oscillator technique. When the sample is oriented with the conducting planes parallel to the applied magnetic field, we have found that the irreversibility line does not extrapolate to the high fields predicted by Mola et. al. [1] based on their measurements and the use of the Tinkham equation. We also find that many signatures of the vortex system, such as jumps, melting and hysteresis are absent in this parallel sample orientation. In addition, when using a pulsed field apparatus we have consistently measured lower critical fields than we find from the use of dc field apparatus. We assume this is due to a time constant associated with the vortices entering and leaving the sample, but not all of our data supports this claim. [1] M.M. Mola, S. Hill, J.S. Brooks, and J.S. Qualls, Phys. Rev. Lett. \textbf{86}, 2130 (2001).   

Unconventional Metallic States of the Superconducting Layered Organic Charge Transfer Salts

We show, by analyzing previously published nuclear magnetic resonance data, that there are large antiferromagnetic (AF) fluctuations above 50 K and a pseudogap below 50 K in the metallic state of $\kappa-$(ET)$_2$Cu[N(CN)$_2$]Br. We discuss the relationships between the metallic state, the AF Mott insulating state, and the unconventional superconducting state. The AF correlation length is found to be $3.5 \pm 2.5$ lattice constants at $T=50$ K; this places the material between the isotropic triangular lattice and the square lattice We show that the low temperature regime of the metallic state of $\kappa-$(ET)$_2$Cu[N(CN)$_2$]Br is not a renormalized Fermi liquid, as has been previously thought. We argue that a pseudogap is responsible for the loss of the density of states in the spin degrees of freedom, seen in NMR data, while that probes of the charge degrees of freedom have a Fermi liquid character in these materials. We compare and contrast our phenomenological description with the predictions of dynamical mean field theory (DMFT) and the resonating valence bond (RVB) theory. Similar spin fluctuations and pseudogap are also found in $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Cl, fully deuteratred $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br, and $\kappa$-(ET)$_2$Cu(NCS)$_2$ suggesting common physics in these salts.   

Specific heat study of the effect of cooling rate on the superconducting and normal states of $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br

It is well known that the $T_c$ of $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br is dependent on the rate it is cooled in the temperature range 80-60~K. One interpretation of this effect is that rapid cooling introduces disorder which suppresses $T_c$ because of its unconventional nature. Here we present a specific heat study of this effect in both hydrogenated and deuterated samples. We find that not only does $T_c$ depend on the cooling rate, but that the normal-state Sommerfeld coefficient, $\gamma$, is strongly suppressed (by up to a factor 2) with rapid cooling. The data indicate that rapid cooling induces macroscopic phase separation between an insulating and metallic / superconducting phase at low temperature. The field dependence of $\gamma$ for the deuterated sample is highly unusual. As the field is increased it initially increases in a conventional way then suddenly collapses to a small value. We interpret this as evidence for a field induced superconductor-insulator transition.   

Low temperature penetration depth of $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br

Several experimental results have suggested that the quasi-2D organic metal $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br is host to some form of unconventional superconductivity. The presence of gap nodes in the superconducting order parameter should be detectable through power law behavior in the penetration depth at low temperature. The most accurate measurements of the temperature dependent penetration depth to date show a fractional power law, $\lambda\propto T^{1.5}$. However, these measurements were not performed at sufficiently low temperatures to determine whether this was due to the combination of gap nodes and the effects of impurity scattering, or due to an intrinsic form of exotic pair excitation. Using a radio frequency (rf) tunnel diode technique in a dilution fridge we have extended these measurements to T~$\sim$ 75~mK ($\sim$0.006~$T_c$). Special care has been taken to eliminate heating effects at these temperatures due to the presence of the small applied rf field. Data at the lowest temperature are more consistent with a nodal state in the presence of impurities.   

Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors

We study the Mott transition, antiferromagnetism and superconductivity in layered organic conductors using Cellular Dynamical Mean Field Theory for the frustrated Hubbard model. A $d$-wave superconducting phase appears between an antiferromagnetic insulator and a metal for $t^{\prime }/t=0.3-0.7 $, or between a nonmagnetic Mott insulator (spin liquid) and a metal for $t^{\prime }/t\geq 0.8$, in agreement with experiments on layered organic conductors including $\kappa $-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$. These phases are separated by a strong first order transition. The phase diagram gives much insight into the mechanism for d-wave superconductivity. Two predictions are made. \newline \newline B. Kyung and A.-M.S. Tremblay, Phys. Rev. Lett. \textbf{97}, 046402 (2006)   

Comparative Studies of Quasi-One-Dimensional Superconductivity in Sc$_{5}$Ir$_{4}$Si$_{10}$ and Lu$_{5}$Ir$_{4}$Si$_{10}$

Compounds with a formula $R_{5}T_{4}X_{10}$ ($R$=Sc, Y, rare earth elements, $T$=Co, Ir, Rh, Os, $X$=Si, Ge) crystallize in Sc$_{5}$Co$_{4}$Si$_{10}$--type structure with Sc-Si chains running along the $c$-axis. Some of them show superconductivity with relatively high transition temperatures and coexistence of superconductivity and charge-density wave. We have grown high quality single crystals of Sc$_{5}$Ir$_{4}$Si$_{10 }$and Lu$_{5}$Ir$_{4}$Si$_{10}$ using the floating-zone method. Thus obtained crystals show superior properties compared with polycrystalline materials, such as higher $T_{c}$ and $H_{c2}$. Anisotropic superconducting properties in these crystals are studied in detail. The upper critical field shows clear anisotropy, with $H_{c2}^{c }>H_{c2}^{ab}$, consistent with the quasi-one-dimensional crystal structure. Both compounds have modest anisotropies with $\gamma (=H_{c2}^{c }$/$H_{c2}^{ab}$ )=2.3 for Sc$_{5}$Ir$_{4}$Si$_{10}$ and $\gamma $=1.6 for Lu$_{5}$Ir$_{4}$Si$_{10}$. Magnetic penetration depths in Sc$_{5}$Ir$_{4}$Si$_{10}$ ($\lambda _{c}$= 900 A and $\lambda _{ab}$ =2100 A) estimated from the magnetic field dependence of the equilibrium magnetization confirm quasi-one-dimensional nature of the superconducting state.