Superconductivity of MgB2: covalent bonds driven metallic

New class of photocatalytic materials and a novel principle for efficient water splitting under infrared and visible light: MgB2 as unexpected example

Water splitting is unanimously recognized as environment friendly, potentially low cost and renewable energy solution based on the future hydrogen economy. Especially appealing is photocatalytic water splitting whereby a suitably chosen catalyst dramatically improves efficiency of the hydrogen production driven by direct sunlight and allows it to happen even at zero driving potential. Here, we suggest a new class of stable photocatalysts and the corresponding principle for catalytic water splitting in which infrared and visible light play the main role in producing the photocurrent and hydrogen. The new class of catalysts - ionic or covalent binary metals with layered graphite-like structures - effectively absorb visible and infrared light facilitating the reaction of water splitting, suppress the inverse reaction of ion recombination by separating ions due to internal electric fields existing near alternating layers, provide the sites for ion trapping of both polarities, and finally deliver the electrons and holes required to generate hydrogen and oxygen gases. As an example, we demonstrate conversion efficiency of ~27% at bias voltage V_bias = 0.5V for magnesium diboride working as a catalyst for photoinduced water splitting. We discuss its advantages over some existing materials and propose the underlying mechanism of photocatalytic water splitting by binary layered metals.

Spontaneous symmetry breaking in vortex systems with two repulsive lengthscales

Scanning Hall probe microscopy (SHPM) has been used to study vortex structures in thin epitaxial films of the superconductor MgB₂. Unusual vortex patterns observed in MgB₂ single crystals have previously been attributed to a competition between short-range repulsive and long-range attractive vortex-vortex interactions in this two band superconductor; the type 1.5 superconductivity scenario. Our films have much higher levels of disorder than bulk single crystals and therefore both superconducting condensates are expected to be pushed deep into the type 2 regime with purely repulsive vortex interactions. We observe broken symmetry vortex patterns at low fields in all samples after field-cooling from above T_c. These are consistent with those seen in systems with competing repulsions on disparate length scales, and remarkably similar structures are reproduced in dirty two band Ginzburg-Landau calculations, where the simulation parameters have been defined by experimental observations. This suggests that in our dirty MgB₂ films, the symmetry of the vortex structures is broken by the presence of vortex repulsions with two different lengthscales, originating from the two distinct superconducting condensates. This represents an entirely new mechanism for spontaneous symmetry breaking in systems of superconducting vortices, with important implications for pinning phenomena and high current density applications.

Phase Diagram and High-Temperature Superconductivity of Compressed Selenium Hydrides

Recent discovery of high-temperature superconductivity (Tc = 190 K) in sulfur hydrides at megabar pressures breaks the traditional belief on the Tc limit of 40 K for conventional superconductors, and opens up the doors in searching new high-temperature superconductors in compounds made up of light elements. Selenium is a sister and isoelectronic element of sulfur, with a larger atomic core and a weaker electronegativity. Whether selenium hydrides share similar high-temperature superconductivity remains elusive, but it is a subject of considerable interest. First-principles swarm structure predictions are performed in an effort to seek for energetically stable and metallic selenium hydrides at high pressures. We find the phase diagram of selenium hydrides is rather different from its sulfur analogy, which is indicated by the emergence of new phases and the change of relative stabilities. Three stable and metallic species with stoichiometries of HSe2, HSe and H3Se are identified above ~120 GPa and they all exhibit superconductive behaviors, of which the hydrogen-rich HSe and H3Se phases show high Tc in the range of 40-110 K. Our simulations established the high-temperature superconductive nature of selenium hydrides and provided useful route for experimental verification.

First-Principles Calculation of the Real-Space Order Parameter and Condensation Energy Density in Phonon-Mediated Superconductors

We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB2, CaC6 and hole-doped graphane.

Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system

A superconductor is a material that can conduct electricity without resistance below a superconducting transition temperature, Tc. The highest Tc that has been achieved to date is in the copper oxide system: 133 kelvin at ambient pressure and 164 kelvin at high pressures. As the nature of superconductivity in these materials is still not fully understood (they are not conventional superconductors), the prospects for achieving still higher transition temperatures by this route are not clear. In contrast, the Bardeen-Cooper-Schrieffer theory of conventional superconductivity gives a guide for achieving high Tc with no theoretical upper bound--all that is needed is a favourable combination of high-frequency phonons, strong electron-phonon coupling, and a high density of states. These conditions can in principle be fulfilled for metallic hydrogen and covalent compounds dominated by hydrogen, as hydrogen atoms provide the necessary high-frequency phonon modes as well as the strong electron-phonon coupling. Numerous calculations support this idea and have predicted transition temperatures in the range 50-235 kelvin for many hydrides, but only a moderate Tc of 17 kelvin has been observed experimentally. Here we investigate sulfur hydride, where a Tc of 80 kelvin has been predicted. We find that this system transforms to a metal at a pressure of approximately 90 gigapascals. On cooling, we see signatures of superconductivity: a sharp drop of the resistivity to zero and a decrease of the transition temperature with magnetic field, with magnetic susceptibility measurements confirming a Tc of 203 kelvin. Moreover, a pronounced isotope shift of Tc in sulfur deuteride is suggestive of an electron-phonon mechanism of superconductivity that is consistent with the Bardeen-Cooper-Schrieffer scenario. We argue that the phase responsible for high-Tc superconductivity in this system is likely to be H3S, formed from H2S by decomposition under pressure. These findings raise hope for the prospects for achieving room-temperature superconductivity in other hydrogen-based materials.

Electron-phonon coupling and its implication for the superconducting topological insulators

The recent observation of superconductivity in doped topological insulators has sparked a flurry of interest due to the prospect of realizing the long-sought topological superconductors. Yet the understanding of underlying pairing mechanism in these systems is far from complete. Here we investigate this problem by providing robust first-principles calculations of the role of electron-phonon coupling for the superconducting pairing in the prime candidate Cu_xBi₂Se₃. Our results show that electron-phonon scattering process in this system is dominated by zone center and boundary optical modes, with coexistence of phonon stiffening and softening. While the calculated electron-phonon coupling constant λ suggests that T_c from electron-phonon coupling is 2 orders smaller than the ones reported on bulk inhomogeneous samples, suggesting that superconductivity may not come from pure electron-phonon coupling. We discuss the possible enhancement of superconducting transition temperature by local inhomogeneity introduced by doping.

Phonon anomalies predict superconducting Tc for AlB2-type structures

The phonon anomaly, δ, calculated by ab initio DFT methods, indicates presence of superconductivity in Mg_0.5Ba_0.5B₂ and other AlB₂-type structures.

A first-principles study on the mechanical and thermodynamic properties of (Nb1−xTix)C complex carbides based on virtual crystal approximation

Tailoring the properties of complex carbides was achieved by component control, which enables it as a better candidate for specific application.

Deriving the electron-phonon spectral density of MgB2 from optical data, using maximum entropy techniques

We use maximum entropy techniques to extract an electron-phonon density from optical data for the normal state at T = 45 K of MgB2. Limiting the analysis to a range of phonon energies below 110 meV, which is sufficient for capturing all phonon structures, we find a spectral function that is in good agreement with that calculated for the quasi-two-dimensional σ-band. Extending the analysis to higher energies, up to 160 meV, we find no evidence for any additional contributions to the fluctuation spectrum, but find that the data can only be understood if the density of states is taken to decrease with increasing energy.

Pressure effects on the electronic structure and superconducting critical temperature of Li2B2

We present the structural, electronic and superconducting properties of Li2B2 under pressure within the framework of the density functional theory. The structural parameters, electronic band structure, phonon frequency of the E2g phonon mode and superconducting critical temperature Tc were calculated for pressures up to 20 GPa. We predicted that the superconducting critical temperature of Li2B2 is about 11 K and this decreases as pressure increases. We found that even though the lattice dynamics of the E2g phonon mode is similar to MgB2, the reduction of the σ-band density of states at Fermi level and the raising of the E2g phonon frequency with pressure were determinant to decrease λ and consequently Tc.

Phonon modes of MgB2: super-lattice structures and spectral response

Observed phonon modes of MgB₂ are equivalent to a lower symmetry super-lattice and may be linked to superconductivity via conservation of coherent acoustic energy.

Coherent phonon decay and the boron isotope effect for MgB2

DFT calculated phonon frequencies for a 2× super-lattice of MgB₂ isotopic forms with P6₃mc symmetry suggests coherent acoustic phonon decay may be an important contributor to superconductivity.

First-principles calculations on the effect of doping and biaxial tensile strain on electron-phonon coupling in graphene

Graphene has exhibited a wealth of fascinating properties, but is also known not to be a superconductor. Remarkably, we show that graphene can be made a conventional Bardeen-Cooper-Schrieffer superconductor by the combined effect of charge doping and tensile strain. While the effect of doping obviously enlarges the Fermi surface, the effect of strain profoundly increases the electron-phonon coupling. At the experimental accessible doping (~4×10(14) cm(-2)) and strain (~16%) levels, the superconducting critical temperature T(c) is estimated to be as high as ~30 K, the highest for a single-element material above the liquid hydrogen temperature.

Isotope and multiband effects in layered superconductors

In this review we consider three classes of superconductors, namely cuprate superconductors, MgB(2) and the new Fe based superconductors. All of these three systems are layered materials and multiband compounds. Their pairing mechanisms are under discussion with the exception of MgB(2), which is widely accepted to be a 'conventional' electron-phonon interaction mediated superconductor, but extending the Bardeen-Cooper-Schrieffer (BCS) theory to account for multiband effects. Cuprates and Fe based superconductors have higher superconducting transition temperatures and more complex structures. Superconductivity is doping dependent in these material classes unlike in MgB(2) which, as a pure compound, has the highest values of T(c) and a rapid suppression of superconductivity with doping takes place. In all three material classes isotope effects have been observed, including exotic ones in the cuprates, and controversial ones in the Fe based materials. Before the area of high-temperature superconductivity, isotope effects on T(c) were the signature for phonon mediated superconductivity-even when deviations from the BCS value to smaller values were observed. Since the discovery of high T(c) materials this is no longer evident since competing mechanisms might exist and other mediating pairing interactions are discussed which are of purely electronic origin. In this work we will compare the three different material classes and especially discuss the experimentally observed isotope effects of all three systems and present a rather general analysis of them. Furthermore, we will concentrate on multiband signatures which are not generally accepted in cuprates even though they are manifest in various experiments, the evidence for those in MgB(2), and indications for them in the Fe based compounds. Mostly we will consider experimental data, but when possible also discuss theoretical models which are suited to explain the data.

A first-principles prediction of two-dimensional superconductivity in pristine B₂C single layers

Based on first-principles lattice dynamics and electron-phonon coupling calculations, B(2)C sheets are predicted to be a two-dimensional (2D) phonon-mediated superconductors with a relatively high transition temperature (T(c)). The electron-phonon coupling parameter was calculated to be 0.92 and it is mainly contributed by low frequency out-of-plane phonon modes and electronic states with a π character. When the Coulomb pseudopotential, μ*, is set to 0.10, the estimated temperature, T(c), is 19.2 K. To the best of our knowledge, B(2)C is the first pristine 2D superconductor with a T(c) higher than the boiling point of liquid helium.

First-principles prediction of doped graphane as a high-temperature electron-phonon superconductor

We predict by first-principles calculations that p-doped graphane is an electron-phonon superconductor with a critical temperature above the boiling point of liquid nitrogen. The unique strength of the chemical bonds between carbon atoms and the large density of electronic states at the Fermi energy arising from the reduced dimensionality give rise to a giant Kohn anomaly in the optical phonon dispersions and push the superconducting critical temperature above 90 K. As evidence of graphane was recently reported, and doping of related materials such as graphene, diamond, and carbon nanostructures is well established, superconducting graphane may be feasible.

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB(2), such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg-Landau theory. We solve the corresponding nonlinear Ginzburg-Landau equations numerically exactly using an iterative method for arbitrary applied field H(c1) < H < H(c2), the Ginzburg-Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB(2) gives very good agreement.

Photoabsorption and photoemission of magnesium diboride at the Mg K edge

The Mg K edge photoabsorption spectrum and the B 1s, Mg 1s, Mg 2p and valence band photoemission spectra of polycrystalline magnesium diboride have been measured. The photoabsorption spectra of the diboride and the oxide, which is present as an impurity, were separated by measuring the Auger electron partial yield at electron energies characteristic of each phase. The spectra are consistent with published calculations of the density of unoccupied p symmetry states. Better agreement is obtained with calculations for the ground state of the system than with ones for the excited state. Valence band photoemission spectra were measured at photon energies corresponding to core resonances, but, within the signal to noise level of the spectra, no resonant enhancement was observed. This is consistent with the delocalized nature of the valence band.

Modeling of the phase evolution in Mg1-xAlxB2 (0 < x < 0.5) and its experimental signatures

Despite the chemical and structural simplicity of MgB(2), at 39 K this compound has the highest known superconducting transition temperature (T(c)) of any binary compound. Electron doping by substituting Al for Mg leads to decreasing T(c), and the observed concentration dependent rate of decrease has been proposed to arise from the nonideal character of MgB(2)-AlB(2) solid solutions, which derives from the existence of an ordered Mg(0.5)Al(0.5)B(2) compound. Heterogeneous nanoscale structure patterns in solid solutions have emerged as an important concept for complex materials, ranging from actinide alloys and oxides to high-temperature cuprate superconductors and manganite-based materials exhibiting colossal magnetoresistivity. In this work we investigate the formation of structural heterogeneities in Mg(1-x)Al(x)B(2), which take the form of nanoscale Al-Al and Al-Mg domains of different geometries and sizes, using molecular statics and Monte Carlo simulations, and in particular we study the corresponding signatures in diffraction experiments. In order to undertake this task, we first derive appropriate Mg-Al-B semiempirical potentials within the modified embedded atom method formalism. These potentials are also applied to explore the equilibrium Mg(1-x)Al(x)B(2) phase diagram for 0 < x < 0.5. Additionally, density functional theory calculations were utilized to study the influence of heterogeneities on the electronic structure and charge distribution in Mg(1-x)Al(x)B(2).

Multiband superconductivity in Pb, H under pressure and CaBeSi from ab initio calculations

Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which has received a lot of attention since the discovery of MgB(2), and show how it is possible to describe the superconducting properties of real materials on a fully ab initio basis.

Is LaFeAsO1-xFx an electron-phonon superconductor?

In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor LaFeAsO1-xFx using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant lambda=0.21 and logarithmic-averaged frequency omegaln=206 K give a maximum Tc of 0.8 K, using the standard Migdal-Eliashberg theory. For the F-doped compounds, we predict even smaller coupling constants. To reproduce the experimental Tc, a 5-6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.

Investigation of hole states near the Fermi level in Nb(1-)(x)Mg(x)B(2) by electron energy-loss spectroscopy and first-principles calculations

The fine structures of the electron energy-loss spectra (EELS) for the B-K edge have been examined in NbB(2) and superconducting Nb(0.75)Mg(0.25)B(2). The experimental results are analyzed based on the calculations of density functional theory (DFT) using the Wien2k code. The results of the EELS spectra and the angular decomposition of the density of states (DOS) reveal that both the B p(z) and B p(x)+p(y) states in NbB(2) have large weights at the Fermi energy due to intersheet covalent bonding with notable hybridization between the Nb 4d and B 2p states. This kind of hybridization also results in different core-hole behaviors for the B-K edge in two orthogonal crystallographic orientations. The best fit between experimental and theoretical data is achieved with consideration of the core-hole effect of the B 1s states, in particular for the q perpendicular c spectra. Analysis of the electronic structure of the Nb(1-)(x)Mg(x)B(2) superconductors suggests that confinement of the intersheet covalent bonding is likely to be favorable for the improvement of superconductivity in this kind of materials.

Theoretical indications of singular structural and electronic features of Laves-phase CaLi2 under pressure

In spite of the presence of ostensibly simple constituents, CaLi2 should be a very peculiar material under pressure. Its two 1-atmosphere polymorphs each undergo a structural bifurcation on densification to structures compressed or elongated in one lattice direction. A Hume-Rothery-type mechanism is proposed to account for the indicated lattice distortion. The narrowing of valence bands under pressure in this material, a large density of states at the Fermi level, and the expected high dynamical scales also hint at superconductivity.

From E2g to other modes: effects of pressure on electron-phonon interaction in MgB2

We study the effects of pressure on the electron-phonon interaction in MgB2 using density-functional-based methods. Our results show that the superconductivity in MgB2 vanishes by 100 GPa, and then reappears at higher pressures. In particular, we find a superconducting transition temperature Tc approximately 2 K for mu*=0.1 at a pressure of 137 GPa.

Low-energy charge-density excitations in MgB2: Striking interplay between single-particle and collective behavior for large momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.

Anisotropic drude response and the effect of anisotropic C substitution in

The in-plane and the out-of-plane optical spectra of small single crystals of Mg(B1-xCx)2 were directly determined by a microscope spectroscopy technique. Contrary to previous reports, the estimated plasma frequencies for both directions are quite consistent with the band calculation. A multi-Drude picture corresponding to a multiband system is necessary to explain the whole spectral profile. The spectral changes with the carbon substitution indicate a decrease of carrier concentration as well as an increase of scattering rate, particularly, in the sigma bands.

Chemical Control of Electronic Structure and Superconductivity in Layered Borides and Borocarbides: Understanding the Absence of Superconductivity in LixBC

The synthetic search for materials related to the 39 K superconductor MgB2 has been difficult. The most promising theoretical suggestion, hole doping of LiBC, does not lead to a new superconductor. We show here that a combination of density functional theory (DFT) calculations, materials synthesis, and structural characterization reveals the origin of the puzzling absence of superconductivity in Li1/2BC as a subtle change in the electronic structure driven by structural response to the introduction of holes. This indicates that the unique aspects of the electronic structure of MgB2 will be demanding to replicate in other systems.

Superconductivity and lattice instability in compressed lithium from Fermi surface hot spots

The highest superconducting temperature Tc observed in any elemental metal (Li with Tc approximately 18-20 K at pressure 35-48 GPa) is shown to arise from increasingly strong electron-phonon coupling concentrated along intersections of Kohn anomaly surfaces with the evolving Fermi surface. First-principles linear response calculations of the phonon spectrum and spectral function alpha2F(omega) reveal very strong Q- and phonon-polarization dependence of coupling strength, resulting in values of in the observed range. The sharp momentum dependence of the coupling even for the simple Li Fermi surface indicates more generally that a fine Q mesh is required for precise evaluation of lamda.

Inversion of two-band superconductivity at the critical electron doping of (Mg, Al)B2

Electron energy-loss spectroscopy (EELS) was combined with heat capacity measurements to probe changes of electronic structure and superconductivity in Mg(1-x)Al(x)B(2). A simultaneous decrease of EELS intensity from sigma-band hole states and the magnitude of the sigma gap was observed with increasing x, thus verifying that band filling results in the loss of strong superconductivity. These quantities extrapolated to zero at x approximately 0.33 as inferred from the unit cell volume. However, superconductivity was not quenched completely, but persisted with T(c) < 7 K up to about x approximately 55. Only the pi band had detectable density of states for 0.33 < or =x < or = 0.55, implying an inversion of the two-band hierarchy of MgB(2) in that regime. Since pi-band superconductivity is active in other materials such as intercalated graphite, implications for new materials with high T(c) are discussed.

Ab Initio Investigation of the Electronic and Geometric Structure of Magnesium Diboride, MgB2

Employing multireference variational (MRCI) and coupled cluster (CC) methods combined with quadruple-zeta quality correlation-consistent basis set, we have studied 36 states of the magnesium diboride (MgB(2)) molecule as well as 17 states of the experimentally unknown diatomic MgB. For all states of MgB(2), we report geometries, atomization energies, and dipole moments, while for the first 5 states, potential energy profiles have been also constructed. The ground state is formally of (1)A(1) V-shaped symmetry with an atomization energy of 108.1(109) kcal/mol at the MRCI(MRCI + Davidson correction) level. The first excited state ((3)B(1)) is less than 1 kcal/mol above the X(1)A(1) state, with the next state of linear Mg-B-B geometry (b(3)Sigma(-)) located 10 kcal/mol higher. In all states, bent or linear, the bonding is complicated and unconventional because of the extraordinary bonding agility of the boron atom(s).

Pressure induced effects on the Fermi surface of superconducting 2H-NbSe2

The pressure dependence of the critical temperature T(c) and upper critical field H(c2)(T) has been measured up to 19 GPa in the layered superconducting material 2H-NbSe2. T(c)(P) has a maximum at 10.5 GPa, well above the pressure for the suppression of the charge density wave (CDW) order. Using an effective two-band model to fit H(c2)(T), we obtain the pressure dependence of the anisotropy in the electron-phonon coupling and Fermi velocities, which reveals the peculiar interplay between CDW order, Fermi surface complexity, and superconductivity in this system.

Nonlocal screening, electron-phonon coupling, and phonon renormalization in metals

A method for calculating the phonon self-energy in metals arising from the coupling between phonons and electrons near the Fermi surface is developed. The essence of this scheme is the separation of the inter- and intraband parts of the electron polarizability. The intraband contribution provides extra screenings and is closely related to the electron-phonon coupling and phonon softening in metals. Applications of this scheme to phonons in MgB2 give excellent results when compared with experiments and previous theoretical work. In addition, both electron and hole dopings are found to reduce the renormalization effect of the E(2g) phonon mode, which indicates a weakened electron-phonon coupling in the doped systems.

Observation of interband pairing interaction in a two-band superconductor: MgB2

The recently discovered anisotropic superconductor MgB2 is the first of its kind showing the intriguing properties of two-band superconductivity. By tunneling experiments using thin film tunnel junctions, electron-coupled phonon spectra were determined showing that superconductivity in MgB2 is phonon mediated. In a further analysis, which involves first principles calculations, the strongest feature in these spectra could be traced back to the key quantity of two-band superconductivity, the interband pairing interaction. For the phonons, this interaction turns out quite selective. It involves mainly low-energy optical phonon modes, where the boron atoms move perpendicular to the boron planes.

Superconducting properties of MgB2 from first principles

Solid MgB(2) has rather interesting and technologically important properties, such as a very high superconducting transition temperature. Focusing on this compound, we report the first nontrivial application of a novel density-functional-type theory for superconductors, recently proposed by the authors. Without invoking any adjustable parameters, we obtain the transition temperature, the gaps, and the specific heat of MgB(2) in very good agreement with experiment. Moreover, our calculations show how the Coulomb interaction acts differently on sigma and pi states, thereby stabilizing the observed superconducting phase.

Band filling and interband scattering effects in MgB2: carbon versus aluminum doping

We argue, based on band structure calculations and the Eliashberg theory, that the observed decrease of T(c) of Al and C doped MgB2 samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant lambda by the variation of the density of states as a function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant pi gap as a function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant pi gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only.

Three-dimensional MgB2-type superconductivity in hole-doped diamond

We substantiate by numerical and analytical calculations that the recently discovered superconductivity below 4 K in 3% boron-doped diamond is caused by electron-phonon coupling of the same type as in MgB2, albeit in three dimensions. Holes at the top of the zone-centered, degenerate sigma-bonding valence-band couple strongly to the optical bond-stretching modes. The increase from two to three dimensions reduces the mode softening crucial for T(c) reaching 40 K in MgB2. Even if diamond had the same bare coupling constant as MgB2, which could be achieved with 10% doping, T(c) would be only 25 K. Superconductivity above 1 K in Si (Ge) requires hole doping beyond 5% (10%).