Superconductivity of MgB2: covalent bonds driven metallic

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%).

Superconductivity in boron-doped diamond

Superconductivity of boron-doped diamond, reported recently at T(c)=4 K, is investigated exploiting its electronic and vibrational analogies to MgB2. The deformation potential of the hole states arising from the C-C bond-stretch mode is 60% larger than the corresponding quantity in MgB2 that drives its high T(c), leading to very large electron-phonon matrix elements. The calculated coupling strength lambda approximately 0.5 leads to T(c) in the 5-10 K range and makes phonon coupling the likely mechanism. Higher doping should increase T(c) somewhat, but the effects of three dimensionality primarily on the density of states keep doped diamond from having a T(c) closer to that of MgB2.

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.

Prediction of new phases of nitrogen at high pressure from first-principles simulations

A rich variety of competing phases is predicted for nitrogen at accessible pressures, including a new metallic chainlike phase very close in energy to the previously predicted cubic gauche phase, and other phases at slightly higher energies, e.g., one with N2 and N6 units. Large energy barriers between structures can account for recent observations of metastability, and we identify a low barrier transition path from the known epsilon phase to the chainlike metallic phase. In analogy to MgB2, the metal is anisotropic with multiple Fermi surfaces formed from pi and sigma states.

Investigation of the Electronic and Structural Properties of Potassium Hexaboride, KB6, by Transport, Magnetic Susceptibility, EPR, and NMR Measurements, Temperature-Dependent Crystal Structure Determination, and Electronic Band Structure Calculations

The electronic and structural properties of potassium hexaboride, KB(6), were examined by transport, magnetic susceptibility, EPR, and NMR measurements, temperature-dependent crystal structure determination, and electronic band structure calculations. The valence bands of KB(6) are partially empty, but the electrical resistivity of KB(6) reveals that it is not a normal metal. The magnetic susceptibility as well as EPR and NMR measurements show the presence of localized electrons in KB(6). The EPR spectra of KB(6) have two peaks, a broad ( approximately 320 G) and a narrow (less than approximately 27 G) line width, and the temperature-dependence of the magnetic susceptibility of KB(6) exhibits a strong hysteresis below 70 K. The temperature-dependent crystal structure determination of KB(6) shows the occurrence of an unusual variation in the unit cell parameter hence supporting that the hysteresis of the magnetic susceptibility is a bulk phenomenon. The line width DeltaH(pp) of the broad EPR signal is independent of temperature and EPR frequency. This finding indicates that the line broadening results from the dipole-dipole interaction, and the spins responsible for the broad EPR peak has the average distance of approximately 1.0 nm. To explain these apparently puzzling properties, we examined a probable mechanism of electron localization in KB(6) and its implications.

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.

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.

Synthesis and characteristion of Li(x)BC-hole doping does not induce superconductivity

The synthesis of Li(x)BC (x > 0.5) by high temperature Li deintercalation from LiBC is demonstrated by refinement of X-ray and neutron powder diffraction data--contrary to theoretical expectation no superconductivity above 2K is observed in these materials.

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.

Search for E(2g) phonon modes in MgB2 single crystals by point-contact spectroscopy

The electron-phonon interaction in magnesium diboride MgB2 single crystals is investigated by point-contact (PC) spectroscopy. For the first time the electron coupling with E(2g) phonon modes is resolved in the PC spectra. The correlation between intensity of the extremely broad E(2g) modes in the PC spectra and value of the superconducting gap is established. Our observations favor current theoretical models for electron-phonon mediated superconductivity in MgB2, and they better match the harmonic phonon model.

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.

Direct evidence for two-band superconductivity in MgB2 single crystals from directional point-contact spectroscopy in magnetic fields

We present the results of the first directional point-contact spectroscopy experiments in high-quality MgB2 single crystals. Because of the directionality of the current injection into the samples, the application of a magnetic field allowed us to separate the contributions of the sigma and pi bands to the total conductance of our point contacts. By using this technique, we were able to obtain the temperature dependency of each gap independent of the other. The consequent, strong reduction of the error on the value of the gap amplitude as a function of temperature allows a stricter test of the predictions of the two-band model for MgB2.

Percolative Superconductivity in Mg1-xB2

Our results from various transport experiments on Mg1-xB2 indicate a surprising effect associated with the presence of a Mg deficiency in MgB2: the phase separation between Mg-vacancy rich and Mg-vacancy poor phases. The Mg-vacancy poor phase is superconducting, but the insulating nature of the Mg-vacancy rich phase probably originates from the Anderson (disorder-induced) localization of itinerant carriers. Furthermore, electron diffraction measurements indicate that within vacancy-rich regions these defects tend to order with intriguing patterns. This electronic phase separation in Mg1-xB2 shows similar, but also distinct characteristics compared with that observed in La(2)CuO(4+delta).

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

Magnesium diboride differs from ordinary metallic superconductors in several important ways, including the failure of conventional models to predict accurately its unusually high transition temperature, the effects of isotope substitution on the critical transition temperature, and its anomalous specific heat. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the 'superconducting energy gap', should clarify why MgB(2) is different. Some early experimental studies have indicated that MgB(2) has multiple gaps, but past theoretical studies have not explained from first principles the origin of these gaps and their effects. Here we report an ab initio calculation of the superconducting gaps in MgB(2) and their effects on measurable quantities. An important feature is that the electronic states dominated by orbitals in the boron plane couple strongly to specific phonon modes, making pair formation favourable. This explains the high transition temperature, the anomalous structure in the specific heat, and the existence of multiple gaps in this material. Our analysis suggests comparable or higher transition temperatures may result in layered materials based on B, C and N with partially filled planar orbitals.

Unraveling the symmetry of the hole states near the Fermi level in the MgB2 superconductor

We use x-ray absorption spectroscopy (XAS) and electron energy loss spectroscopy (EELS) to study the fine structure at the K edge of boron in MgB(2). We observe in XAS a peak of width 0.7 eV at the edge threshold, signaling a narrow energy region with empty boron p states near the Fermi level. The changes in the near edge structure observed in EELS with direction of the momentum transfer imply that these states have p(x)p(y) symmetry. Our observations are consistent with electronic structure calculations indicating a narrow energy window of empty p(x)p(y) states that falls to zero at 0.8 eV above the Fermi level. The disappearance of the p(x)p(y) feature in EELS at grain boundaries suggests that this signature may become powerful in probing superconductivity at nanoscale.

Temperature and field dependence of the anisotropy of MgB2

The anisotropy gamma of the superconducting state of high quality single crystals of MgB2 was determined, using torque magnetometry with two different methods. The anisotropy of the upper critical field was found to be temperature dependent, decreasing from gamma approximately 6 at 15 K to 2.8 at 35 K. Reversible torque data near T(c) reveal a field dependent anisotropy, increasing nearly linearly from gamma approximately equal to 2 in zero field to 3.7 in 10 kOe. The unusual temperature dependence is a true bulk property and can be explained by nonlocal effects of anisotropic pairing and/or the k--> dependence of the effective mass tensor.

Electronic structure of MgB2 from angle-resolved photoemission spectroscopy

The first angle-resolved photoemission spectroscopy results from MgB2 single crystals are reported. Along the GammaK and GammaM directions, we observed three distinct dispersive features approaching the Fermi energy. These can be assigned to the theoretically predicted sigma (B 2p(x,y)) and pi (B 2p(z)) bands. In addition, a small parabolic-like band is detected around the Gamma point, which can be attributed to a surface-derived state. The overall agreement between our results and the band calculations suggests that the electronic structure of MgB2 is of a conventional nature, thus implying that electron correlations are weak and may be of little importance to superconductivity in this system.

Evidence for two-band superconductivity from break-junction tunneling on MgB2

Superconductor-insulator-superconductor tunnel junctions have been fabricated on MgB2 that display Josephson and quasiparticle currents. These junctions exhibit a gap magnitude, Delta approximately 2.5 meV, that is considerably smaller than the BCS value, but which clearly and reproducibly closes near the bulk T(c). In conjunction with fits of the conductance spectra, these results are interpreted as direct evidence of two-band superconductivity.

Prediction of high T(c) superconductivity in hole-doped LiBC

The layered lithium borocarbide LiBC, isovalent with and structurally similar to the superconductor MgB2, is an insulator due to the modulation within the hexagonal layers (BC vs B2). We show that hole doping of LiBC results in Fermi surfaces of B-C p sigma character that couple very strongly to B-C bond stretching modes, precisely the features that lead to superconductivity at T(c) approximately equal to 40 K in MgB2. Comparison of Li(0.5)BC with MgB2 indicates the former to be a prime candidate for electron-phonon coupled superconductivity at substantially higher temperature than in MgB2.

High T(c) superconductivity in MgB2 by nonadiabatic pairing

The evidence for the key role of the sigma bands in the electronic properties of MgB2 points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the sigma bands. We show that the nonadiabatic theory leads to a coherent interpretation of T(c) = 39 K and the boron isotope coefficient alphaB = 0.30 without invoking very large couplings and it naturally explains the role of the disorder on T(c). It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these types of compounds.

Superconducting gap in MgB(2): electronic Raman scattering measurements of single crystals

Polarization-resolved Raman scattering measurements were performed on MgB(2) single crystals to determine the magnitude, symmetry, and temperature dependence of the superconducting gap. A single sharp peak due to Cooper pair breaking appears in the electronic continuum below T(c), reaching a maximum Raman shift of 105 +/- 1 cm(-1) [2 Delta(0)/k(B)T(c) = 3.96 +/- 0.09] and showing up to 5 cm(-1) anisotropy between polarized and depolarized spectra. The temperature dependence of 2 Delta follows that predicted from BCS theory, while the anisotropy decreases with decreasing temperature. It is concluded that the Raman results are consistent with a slightly anisotropic s-wave gap in a conventional BCS superconductor.

Ab initio investigation of collective charge excitations in MgB2

A sharp collective charge excitation is predicted in MgB2 at approximately 2.5 eV for q perpendicular to the boron layers, based on an all-electron analysis of the dynamical density response within time-dependent density functional theory. This novel excitation, consisting of coherent charge fluctuation between Mg and B sheets, induces an abrupt plasma edge in the experimentally observable reflectivity. The existence of this mode reflects the unique electronic structure of MgB2 that is also responsible for strong electron-phonon coupling. By contrast, the acoustic plasmon, recently suggested to explain the high T(c), is not realized when realistic transition strengths are incorporated.

Optical properties of c-axis oriented superconducting MgB2 films

Temperature dependent optical conductivities and dc resistivity of c-axis oriented superconducting (T(c) = 39.6 K) MgB2 films (approximately 450 nm) have been measured. The normal state ab-plane optical conductivities can be described by the Drude model with a temperature independent Drude plasma frequency of omega(p,D) = 13 600+/-100 cm(-1) or 1.68+/-0.01 eV. The normal state resistivity is fitted by the Bloch-Grüneisen formula with an electron-phonon coupling constant lambda(tr) = 0.13+/-0.02. The optical conductivity spectra below T(c) of these films suggest that MgB2 is a multigap superconductor.

Implications of reflectance measurements on the mechanism for superconductivity in MgB2

Recent optical studies in c-axis oriented superconducting MgB2 films indicate that the electron-phonon coupling is weak. We reinforce this conclusion by examining the raw reflectance data; its frequency dependence is incompatible with strong electron-phonon scattering. This is further strengthened by analysis of the real part of the conductivity, and by the temperature dependence of the effective Drude scattering rate. Using a realistic electron-phonon spectral shape, we find lambda(tr) approximately 0.15. To the extent that lambda(tr) approximately lambda, this disagrees sharply with model calculations, and is far too low to provide the means for T(c) = 39 K. A simple model is constructed with coupling to a high frequency excitation, which is consistent with both the low frequency optical data and the high T(c).

Optical conductivity and penetration depth in MgB(2)

The complex conductivity of a MgB(2) film has been investigated in the frequency range 4<nu<30 cm(-1) and for temperatures 2.7<T<300 K. The overall temperature dependence of both components of the complex conductivity is reminiscent of BCS-type behavior, although a detailed analysis reveals a number of discrepancies. A peak in the temperature dependence of the real part of the conductivity is detected for frequencies below 9 cm(-1). The superconducting penetration depth follows a T(2) behavior at low temperatures.

High current-carrying capability in c-axis-oriented superconducting MgB2 thin films

In high-quality c-axis-oriented MgB2 thin films, we observed high critical current densities ( J(c)) of approximately 16 MA/cm(2) at 15 K under self-fields comparable to those of cuprate high-temperature superconductors. The extrapolated value of J(c) at 5 K was estimated to be approximately 40 MA/cm(2). For a magnetic field of 5 T, a J(c) of approximately 0.1 MA/cm(2) was detected at 15 K, suggesting that this compound would be a very promising candidate for practical applications at high temperature and lower power consumption. The vortex-glass phase is considered to be a possible explanation for the observed high current-carrying capability.

Specific heat of Mg11B2: evidence for a second energy gap

Measurements of the specific heat of Mg11B2 from 1 to 50 K, in magnetic fields to 9 T, give the Debye temperature, Theta = 1050 K, the coefficient of the normal-state electron contribution, gamma(n) = 2.6 mJ mol(-1) K-2, and a discontinuity in the zero-field specific heat of 133 mJ mol(-1) K-1 at T(c) = 38.7 K. The estimated value of the electron-phonon coupling parameter, lambda = 0.62, could account for the observed T(c) only if the important phonon frequencies are unusually high relative to Theta. At low T, there is a strongly field-dependent feature that suggests the existence of a second energy gap, about 4 times smaller than the major gap.

Giant anharmonicity and nonlinear electron-phonon coupling in MgB2: a combined first-principles calculation and neutron scattering study

First-principles calculations of the electronic band structure and lattice dynamics for the new superconductor MgB (2) are carried out and found to be in excellent agreement with our inelastic neutron scattering measurements. The numerical results reveal that the E(2g) in-plane boron phonons near the zone center are very anharmonic and strongly coupled to the planar B sigma bands near the Fermi level. This giant anharmonicity and nonlinear electron-phonon coupling is key to quantitatively explaining the observed high T(c) and boron isotope effect in MgB (2).

Phonon density of states in MgB2

We report inelastic neutron scattering measurements of the phonon density of states in Mg 11B2, which has a superconducting transition at 39.2 K. The acoustic phonons extend in energy to 36 meV, and there are highly dispersive optic branches peaking at 54, 78, 89, and 97 meV. A simple Born-von Kàrmàn model reproduces the mode energies, and provides an estimate of the electron-phonon coupling of lambda approximately 0.9. Furthermore, the estimated boron and magnesium contributions to the isotope effect are in qualitative agreement with experiment. The data confirm that a conventional phonon mechanism, with moderately strong electron-phonon coupling, can explain the observed superconductivity.

Phonon dispersion and electron-phonon coupling in MgB2 and AlB2

We present a first principles investigation of the lattice dynamics and electron-phonon coupling of the superconductor MgB2 and the isostructural AlB2 within the framework of density functional perturbation theory using a mixed-basis pseudopotential method. Complete phonon dispersion curves and Eliashberg functions alpha2F are calculated for both systems. The main differences are related to high frequency in-plane boron vibrations, which are strongly softened in MgB2 and exhibit an exceptionally strong electron-phonon coupling. We also report on Raman measurements, which support the theoretical findings. Implications for the superconducting transition temperature are briefly discussed.