The origin of the anomalous superconducting properties of MgB(2)

Generalized Elliott-Yafet theory of electron spin relaxation in metals: origin of the anomalous electron spin lifetime in MgB2

The temperature dependence of the electron-spin relaxation time in MgB2 is anomalous as it does not follow the resistivity above 150 K; it has a maximum around 400 K and decreases for higher temperatures. This violates the well established Elliot-Yafet theory of spin relaxation in metals. The anomaly occurs when the quasiparticle scattering rate (in energy units) is comparable to the energy difference between the conduction and a neighboring bands. The anomalous behavior is related to the unique band structure of MgB2 and the large electron-phonon coupling. The saturating spin relaxation is the spin transport analogue of the Ioffe-Regel criterion of electron transport.

Fully band-resolved scattering rate in MgB2 revealed by the nonlinear hall effect and magnetoresistance measurements

We have measured the normal state temperature dependence of the Hall effect and magnetoresistance in epitaxial MgB2 thin films with variable disorders characterized by the residual resistance ratio RRR ranging from 4.0 to 33.3. A strong nonlinearity of the Hall effect and magnetoresistance have been found in clean samples, and they decrease gradually with the increase of disorders or temperature. By fitting the data to the theoretical model based on the Boltzmann equation and ab initio calculations for a four-band system, for the first time, we derived the scattering rates of these four bands at different temperatures and magnitude of disorders. Our method provides a unique way to derive these important parameters in multiband systems.

Specific-heat evidence for two-gap superconductivity in the ternary-iron silicide Lu2Fe3Si5

We report low-temperature specific-heat studies on the single-crystalline ternary-iron silicide superconductor Lu(2)Fe(3)Si(5) with T(c)=6.1 K down to approximately T(c)/20. We confirm a reduced normalized jump in specific heat at T(c), and find that the specific heat divided by temperature C/T shows a sudden drop at approximately T(c)/5 and goes to zero with further decreasing temperature. These results indicate the presence of two distinct superconducting gaps in Lu(2)Fe(3)Si(5), similar to the typical two-gap superconductor MgB(2). We also report Hall coefficients, band structure calculations, and the anisotropy of upper critical fields for Lu(2)Fe(3)Si(5), which support the anisotropic multiband nature and reinforce the existence of two superconducting gaps in Lu(2)Fe(3)Si(5).

The chemical response of main-group extended solids to formal mixed valency: the case of LixBC

The introduction of mixed valency into extended main-group solids is discussed using the example of hole-doped LiBC, where a combination of experimental measurements and density functional theory calculations is used to understand the observed electronic properties in terms of deviation from the expected rigid-band electronic structure behaviour.

Observation of Leggett's collective mode in a multiband MgB2 superconductor

We report observation of Leggett's collective mode in a multiband MgB2 superconductor with Tc=39 K arising from the fluctuations in the relative phase between two superconducting condensates. The novel mode is observed by Raman spectroscopy at 9.4 meV in the fully symmetric scattering channel. The observed mode frequency is consistent with theoretical considerations based on first-principles computations.

Analysis of H(c2)(θ,T) for Mg(B(1-x)C(x))(2) single crystals by using the dirty two-gap model

To understand the effect of carbon doping on the superconductivity in MgB(2), we obtained the angle- and temperature-dependent upper critical fields [H(c2)(θ) and H(c2)(T)] for Mg(B(1-x)C(x))(2) single crystals (x = 0.06 and 0.1) from resistivity measurements while varying the temperature, the field, and the direction of the field. The detailed values of the diffusivity for two different directions for each σ-band and π-band were obtained to explain both the temperature- and the angle-dependent H(c2) by using the dirty-limit two-gap model. The induced impurity scattering of the σ-band and the π-band for both the ab-plane and the c-direction is studied.

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.

Anisotropy of the Sommerfeld coefficient in magnesium diboride single crystals

The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.

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.

Effect of magnetic impurities in a two-band superconductor: a point-contact study of mn-substituted single crystals

We present the first results of directional point-contact measurements in Mg1-xMnxB2 single crystals, with x up to 0.015 and bulk Tc down to 13.3 K. The order parameters Deltasigma and Deltapi were obtained by fitting the conductance curves with the two-band Blonder-Tinkham-Klapwijk model. BothDeltapi and Deltasigma decrease with the critical temperature of the junctions TAC, but remain clearly distinct up to the highest Mn content. Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the sigma band, as also confirmed by first-principles band-structure calculations.

Momentum-resolved electron-phonon interaction in lead determined by neutron resonance spin-echo spectroscopy

Neutron resonance spin-echo spectroscopy was used to monitor the temperature evolution of the linewidths of transverse acoustic phonons in lead across the superconducting transition temperature over an extended range of the Brillouin zone. For phonons with energies below the superconducting energy gap, a linewidth reduction of maximum amplitude was observed below . The electron-phonon contribution to the phonon lifetime extracted from these data is in satisfactory overall agreement with ab initio lattice-dynamical calculations, but significant deviations are found.

Large anisotropic normal-state magnetoresistance in clean MgB2 thin films

We report a large normal-state magnetoresistance with temperature-dependent anisotropy in very clean epitaxial MgB2 thin films (residual resistivity much smaller than 1 microOmega cm) grown by hybrid physical-chemical vapor deposition. The magnetoresistance shows a complex dependence on the orientation of the applied magnetic field, with a large magnetoresistance (Delta(rho)/(rho)0=136%) observed for the field H perpendicular ab plane. The angular dependence changes dramatically as the temperature is increased, and at high temperatures the magnetoresistance maximum changes to H||ab. We attribute the large magnetoresistance and the evolution of its angular dependence with temperature to the multiple bands with different Fermi surface topology in MgB2 and the relative scattering rates of the sigma and pi bands, which vary with temperature due to stronger electron-phonon coupling for the sigma bands.

Structure Determination of the 4d Metal Diborides: A Quantum Mechanical Study

Metal diborides (MB(2)) often have interesting thermal, mechanical, and superconducting properties. MgB(2) was put into focus some years ago for its high transition temperature (39 K) in combination with its simple AlB(2) structure. The boron structure in MB(2) is assumed to be dependent on the electron transfer from the nearby positioned metal atoms. An electronic and structural comparison has been performed here for various initially planar and puckered transition-metal borides, using quantum mechanical density functional theory (DFT) calculations under periodic boundary conditions. In comparison to MgB(2), the experimentally planar transition-metal diborides (ZrB(2), NbB(2), and MoB(2)) and the experimentally puckered ones (TcB(2), RuB(2), RhB(2), and PdB(2)) have been examined. The results indicate that the energetic stability generally follows the experimentally obtained results. The metals that are less electronegative than boron donate electrons to boron, which in turn induce planar boron structures (graphitic-like). The metals that prefer to be planar donate more than one electron, while the trend for metals which favor puckered B structures is that they donate less than one electron per metal atom. Two donated electrons per metal atom (or very close to) will result in the most stable AlB(2) structure.

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.

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%).

Role of the dopant in the superconductivity of diamond

We present an ab initio study of the recently discovered superconductivity of boron doped diamond within the framework of a phonon-mediated pairing mechanism. The role of the dopant, in substitutional position, is unconventional in that half of the coupling parameter lambda originates in strongly localized defect-related vibrational modes, yielding a very peaked Eliashberg alpha2F(omega) function. The electron-phonon coupling potential is found to be extremely large, and T(C) is limited by the low value of the density of states at the Fermi level. The effect of boron isotope substitution is explored.

Enhancement of the superconducting transition temperature of MgB2 by a strain-induced bond-stretching mode softening

We report a systematic increase of the superconducting transition temperature T(c) with a biaxial tensile strain in MgB2 films to well beyond the bulk value. The tensile strain increases with the MgB2 film thickness, caused primarily by the coalescence of initially nucleated discrete islands (the Volmer-Weber growth mode.) The T(c) increase was observed in epitaxial films on SiC and sapphire substrates, although the T(c) values were different for the two substrates due to different lattice parameters and thermal expansion coefficients. We identified, by first-principles calculations, the underlying mechanism for the T(c) increase to be the softening of the bond-stretching E(2g) phonon mode, and we confirmed this conclusion by Raman scattering measurements. The result suggests that the E(2g) phonon softening is a possible avenue to achieve even higher T(c) in MgB2-related material systems.

Kohn anomaly in MgB2 by inelastic X-ray scattering

We study phonons in MgB2 using inelastic x-ray scattering (1.6 and 6 meV resolution). We clearly observe the softening and broadening of the crucial E(2g) mode through the Kohn anomaly along GammaM, in excellent agreement with ab initio calculations. Low temperature measurements (just above and below T(c)) show negligible changes for the momentum transfers investigated and no change in the E(2g) mode at A between room temperature and 16 K. We report the presence of a longitudinal mode along GammaA near in energy to the E(2g) mode that is not predicted by theory.

Pair-breaking and superconducting state recovery dynamics in MgB2

We present studies of the photoexcited quasiparticle dynamics in MgB2 where, using femtosecond optical techniques, Cooper pair-breaking dynamics (PBD) have been temporally resolved for the first time. The PBD are strongly temperature and photoexcitation intensity dependent. Analysis of the PBD using the Rothwarf-Taylor equations suggests that the anomalous PBD arises from the fact that in MgB2 photoexcitation is initially followed by energy relaxation to high frequency phonons instead of, as commonly assumed, e-e thermalization. Furthermore, the bare quasiparticle recombination rate and the probability for pair breaking by phonons have been determined.

Mott transitions in multiorbital systems

Using the dynamical mean field theory it is shown that interorbital Coulomb interactions in nonisotropic multiorbital materials give rise to a single Mott transition. Nevertheless, narrow and wide subbands exhibit different excitation spectra in the metallic and insulating phases. The close analogy between "multigap" insulating behavior and multigap superconductivity is pointed out.

Time-resolved photoexcitation of the superconducting two-gap state in MgB2 thin films

Femtosecond pump-probe studies show that carrier dynamics in MgB2 films is governed by the sub-ps electron-phonon (e-ph) relaxation present at all temperatures, the few-ps e-ph process well pronounced below 70 K, and the sub-ns superconducting relaxation below T(c). The amplitude of the superconducting component versus temperature follows the superposition of the isotropic dirty gap and the three-dimensional pi gap dependences, closing at two different T(c) values. The time constant of the few-ps relaxation exhibits a double divergence at temperatures corresponding to the T(c)'s of the two gaps.

Definitive experimental evidence for two-band superconductivity in MgB2

The superconducting-gap of MgB2 has been studied by high-resolution angle-resolved photoemission spectroscopy. The results show that superconducting gaps with values of 5.5 and 2.2 meV open on the sigma band and the pi band, respectively, but both the gaps close at the bulk transition temperature, providing a definitive experimental evidence for the two-band superconductivity with strong interband pairing interaction in MgB2. The experiments validate the role of k-dependent electron-phonon coupling as the origin of multiple-gap superconductivity as well as the high transition temperature of MgB2.

Anomalous coherence peak in the microwave conductivity of c-axis oriented MgB2 thin films

The temperature dependence of the real part of the microwave complex conductivity at 17.9 GHz obtained from surface impedance measurements of two c-axis oriented MgB2 thin films reveals a pronounced maximum at a temperature around 0.6 times the critical temperature. Calculations in the frame of a two-band model based on Bardeen-Cooper-Schrieffer (BCS) theory suggest that this maximum corresponds to an anomalous coherence peak resembling the two-gap nature of MgB2. Our model assumes there is no interband impurity scattering and a weak interband pairing interaction, as suggested by band structure calculations. In addition, the observation of a coherence peak indicates that the pi band is in the dirty limit and dominates the total conductivity of our films.

Effects of two-band superconductivity on the flux-line lattice in magnesium diboride

We present neutron scattering from the flux line lattice (FLL) in MgB2. Between 0.5 and 0.9 T the FLL undergoes a 30 degrees reorientation, and simultaneously the scattered intensity falls sharply consistent with the weaker superconducting pi band being suppressed with increasing field. We speculate that the pi and sigma bands favor different FLL orientations, and that the reorientation is driven by the suppression of the pi band. When the c axis of the crystal is rotated 45 degrees to the applied field the penetration depth anisotropy could be measured, and rises both as a function of applied field and temperature.

Determination of the Fermi surface of MgB2 by the de Haas-van Alphen effect

We report measurements of the de Haas-van Alphen (dHvA) effect for single crystals of MgB2, in magnetic fields up to 32 T. In contrast to our earlier work, dHvA orbits from all four sheets of the Fermi surface were detected. Our results are in good overall agreement with calculations of the electronic structure and the electron-phonon mass enhancements of the various orbits, but there are some small quantitative discrepancies. In particular, systematic differences in the relative volumes of the Fermi-surface sheets and the magnitudes of the electron-phonon coupling constants could be large enough to affect detailed calculations of T(c) and other superconducting properties.

Fermi surface topology and the upper critical field in two-band superconductors: application to MgB2

Recent measurements of the anisotropy of the upper critical field B(c2) on MgB2 single crystals have shown a puzzling strong temperature dependence. Here, we present a calculation of the upper critical field based on a detailed modeling of band structure calculations that takes into account both the unusual Fermi surface topology and the two gap nature of the superconducting order parameter. Our results show that the strong temperature dependence of the B(c2) anisotropy can be understood as an interplay of the dominating gap on the sigma band, which possesses a small c-axis component of the Fermi velocity, with the induced superconductivity on the pi-band possessing a large c-axis component of the Fermi velocity. We provide analytic formulas for the anisotropy ratio at T=0 and T=T(c) and quantitatively predict the distortion of the vortex lattice based on our calculations.

c-Axis Raman scattering spectra of MgB2: observation of a dirty-limit gap in the pi bands

Raman scattering spectra from the ac face of thick MgB2 single crystals were measured in zz, xz, and xx polarizations. In zz and xz polarizations a threshold at around 29 cm(-1) forms in the below T(c) continuum but no pair-breaking peak is seen, in contrast to the sharp pair-breaking peak at around 100 cm(-1) in xx polarization. The zz and xz spectra are consistent with Raman scattering from a dirty superconductor while the sharp peak in the xx spectra argues for a clean system. Analysis of the spectra resolves this contradiction, placing the larger and smaller gap magnitudes in the sigma and pi bands and indicating that relatively strong impurity scattering is restricted to the pi bands.

Mixed state of a dirty two-band superconductor: application to MgB2

We investigate the vortex state in a two-band superconductor with strong intraband and weak interband electronic scattering rates. Coupled Usadel equations are solved numerically, and the distributions of the pair potentials and local densities of states are calculated for two bands at different values of magnetic fields. The existence of two distinct length scales corresponding to different bands is demonstrated. The results provide qualitative interpretation of recent scanning tunneling microscopy experiments on vortex structure imaging in MgB2.

The origin of multiple superconducting gaps in MgB2

Magnesium diboride, MgB2, has the highest transition temperature (T(c) = 39 K) of the known metallic superconductors. Whether the anomalously high T(c) can be described within the conventional BCS (Bardeen-Cooper-Schrieffer) framework has been debated. The key to understanding superconductivity lies with the 'superconducting energy gap' associated with the formation of the superconducting pairs. Recently, the existence of two kinds of superconducting gaps in MgB2 has been suggested by several experiments; this is in contrast to both conventional and high-T(c) superconductors. A clear demonstration of two gaps has not yet been made because the previous experiments lacked the ability to resolve the momentum of the superconducting electrons. Here we report direct experimental evidence for the two-band superconductivity in MgB2, by separately observing the superconducting gaps of the sigma and pi bands (as well as a surface band). The gaps have distinctly different sizes, which unambiguously establishes MgB2 as a two-gap superconductor.

Experimental evidence for anisotropic double-gap behavior in MgB2

The behavior of a type II superconductor in the presence of a magnetic field is governed by two characteristic length scales, the London penetration depth and the coherence length. We present magnetization measurements on MgB2 powder showing an anisotropy in the upper critical field and hence the coherence length of 6. Using the technique of small angle neutron scattering we show that this anisotropy is not mirrored in the London penetration depth, which is almost isotropic. This result can be explained by the superconductivity residing in two distinct electronic bands of the material, only one of which is highly anisotropic.

Superconductivity caused by the pairing of plutonium 5f Eelectrons in PuCoGa5

On the basis of electronic structure calculations we identify the superconductivity in the novel, high-temperature superconductor PuCoGa5 to be caused by the pairing of Pu 5f electrons. Assuming delocalized Pu 5f states, we compute theoretical crystallographic constants very near to the experimental ones, and the calculated specific heat coefficient compares reasonably to the measured coefficient. The theoretical Fermi surface is quasi-two-dimensional and the material appears to be close to a magnetic phase instability.

Heat conduction in the vortex state of NbSe2: evidence for multiband superconductivity

The thermal conductivity kappa of the layered s-wave superconductor NbSe2 was measured down to T(c)/100 throughout the vortex state. With increasing field, we identify two regimes: one with localized states at fields very near H(c1) and one with highly delocalized quasiparticle excitations at higher fields. The two associated length scales are naturally explained as multiband superconductivity, with distinct small and large superconducting gaps on different sheets of the Fermi surface. This behavior is compared to that of the multiband superconductor MgB2 and the conventional superconductor V3Si.

Phonon dispersion and lifetimes in MgB2

We measure phonon dispersion and linewidth in a single crystal of MgB2 along the Gamma-A, Gamma-M, and A-L directions using inelastic x-ray scattering. We use density functional theory to compute the effect of both electron-phonon coupling and anharmonicity on the linewidth, obtaining excellent agreement with experiment. Anomalous broadening of the E(2g) phonon mode is found all along Gamma-A. The dominant contribution to the linewidth is always the electron-phonon coupling.