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.     

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.     

Phonon density of states and phonon dispersion of superconducting MgB2

For the superconductor MgB2, we have calculated the phonon density of states (DOS), phonon dispersion and Eliashberg function throughout the Brillouin zone (BZ), using an empirical potential model. The calculated values are consistent with the theoretical and experimental values. The calculated results show our empirical potential model is available for MgB2.     

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.     

新型超导体二硼化镁(MgB_2)基础研究及其应用展望

文章简要介绍了新型超导体二硼化镁的发现、研究进展和应用前景 .理论和实验都已经证明 ,二硼化镁的超导电性来源于电声子耦合 ,可以用具有S -波对称性波函数的BCS图像来描述 .然而在二硼化镁超导体中 ,人们发现有两个超导能隙 ,一个在 6meV ,另外一个在 2meV左右 ,它们同时在超导转变温度处打开 ,这给超导机理研究带来了一些新的内容 .在混合态物理方面 ,人们发现超导与正常态的边界线 (上临界磁场Hc2 )与磁通融化线(不可逆线Hirr)之间有很大的间隙 ,即使在绝对零度时也是如此 ,作者提出这可能是由于双能隙的结果或磁通物质的量子融化 .在应用方面 ,最有可能把它做成超导磁体 ,利用闭路循环制冷机制冷在 2 0K左右使用 ,这样极有可能取代现在医学上使用的核磁共振成像的液氦温度超导磁体     

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.     

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.     

Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps

Density-functional calculations of the phonon spectrum and electron-phonon coupling in MgB (2) are presented. The E(2g) phonons, which involve in-plane B displacements, couple strongly to the p(x,y) electronic bands. The isotropic electron-phonon coupling constant is calculated to be about 0.8. Allowing for different order parameters in different bands, the superconducting lambda in the clean limit is calculated to be significantly larger. The E(2g) phonons are strongly anharmonic, and the nonlinear contribution to the coupling between the E(2g) modes and the p(x,y) bands is significant.     

MgB_2(001)面超导结构的电子浓度第一原理分析

采用密度范函理论计算了金属化合物MgB2(001)薄膜结构的电子能带结构和状态密度,计算的交换相关能分别采用LDA和GGA。规范保守赝势的计算结果表明,晶格常数与实验值误差在很小的范围内,分析了引起MgB2(001)面结构超导转变时电子浓度和偏态密度的变化情况,发现构成该超导体结构的成键有三种,着重从结构的电子浓度变化分析了其超导特性,六角蜂窝状结构中硼原子间相互作用为sp2杂化的共价键,镁原子和硼原子之间是离子键结合,镁原子层是金属键结合,镁原子的价电子部分转移到硼原子的pz轨道,部分电子为镁原子层共用。MgB2的超导机制为强烈的电子-声子耦合,为B原子间强烈的共价作用形成,是传统S波超导体。对Mg元素同一主族的其它硼化物进行布居分析,发现MgB2中Mg原子电子转移明显强于BeB2和CaB2,说明电子浓度是引起超导转变的一个重要因素。     

Specific heat and thermal conductivity in the mixed state of MgB2

The specific heat C and the electronic and phononic thermal conductivities kappa(e) and kappa(ph) are calculated in the mixed state for magnetic fields H near H(c2), including the effects of supercurrent flow and Andreev scattering. The resulting function C(H) is nearly linear while kappa(e)(H) exhibits an upward curvature near H(c2). The slopes decrease with impurity scattering which improves the agreement with the data on MgB2. The ratio of phonon relaxation times tau(n)/tau(s)=g(omega(0),H) for phonon energy omega(0) is smeared out around omega(0)=2Delta and tends to one for increasing H. This leads to a rapid reduction of kappa(ph)(H) in MgB2 for relatively small fields due to the rapid suppression of the smaller energy gap.     

Giant nonadiabatic effects in layer metals: raman spectra of intercalated graphite explained

The occurrence of nonadiabatic effects in the vibrational properties of metals has been predicted since the 1960s, but hardly confirmed experimentally. We report the first fully ab initio calculations of nonadiabatic frequencies of a number of conventional (hcp Ti and Mg) and layered metals (MgB2, CaC6, and other intercalated graphites). Nonadiabatic effects can be spectacularly large (up to 30% of the phonon frequencies) in both cases, but they can only be experimentally observed in the Raman spectra of layered compounds. In layered metals nonadiabatic effects are crucial to explaining the observed Raman shifts and linewidths. Moreover, we show that those quantities can be used to extract the electron momentum-relaxation time.     

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.     

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.     

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%).     

Josephson effect in MgB(2) break junctions

We present the first observation of the dc and ac Josephson effect in MgB(2) break junctions. The junctions, obtained at 4.2 K in high-quality, high-density polycrystalline metallic MgB(2) samples, show a nonhysteretic dc Josephson effect. By irradiating the junctions with microwaves we observe clear Shapiro steps spaced by the ideal Delta V value. The temperature dependence of the dc Josephson current and the dependence of the height of the steps on the microwave power are obtained. These results directly prove the existence of pairs with charge 2e in MgB(2) and give evidence of the superconductor-normal metal-superconductor weak link character of these junctions.     

Pressure-Stabilized New Phase of CaN_4

We propose a new CaN_4 high pressure structure with the P2_1/m space group.The P2_1/m-CaN_4 structure is constituted by the infinite armchair N-chain.The dynamical stability and mechanical stability are verified by the calculations of phonon dispersion curves and elastic constants.The enthalpy difference calculation shows that the P2_1/m phase is more stable than the reported P4_12_12 phase.The advantaged properties of P2_1/m-CaN_4,such as high nitrogen content(58.3%) and low polymerization pressure(18.3 GPa),allow it to be a potential high energy materlal.Band structure calculation shows that the P2_1/m-CaN_4 structure is a metallic phase.The nonpolar covalent single N-N bond is a sigma bond.The charge transfer between the Ca and N atoms results in an ionic bond interaction.     

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.     

原位法MgB_2-B_4C复相超导体合成及相含量调控研究

以B4C和Mg为原料合成的MgB2-B4C复相超导体具有高的临界电流密度(Jc)和高的超导转变温度(Tc),是一种有潜力的实用MgB2超导材料,其成相机理对复相MgB2超导体的相含量调控和磁通钉扎研究具有重要意义。结合经典烧结理论,研究了B4C-Mg真空固相烧结制备MgB2-B4C复相超导体的超导相形成和晶粒生长过程,给出了B4C-Mg的金斯特林格扩散模型和MgB2晶粒生长过程。通过选择B4C原料粒径,MgB2-B4C复相超导体超导相体积相含量在18%-88%范围可控。相含量88%的MgB2-B4C复相超导体临界转变温度达33.5K,转变宽度1.5K。10 K环境6T外场下电流密度可以达到1×104A/cm2,表明MgB2-B4C复相超导体具有良好的磁通钉扎行为。     

Theoretical investigation of planar square carbon allotrope and its hydrogenation

Using density functional theory we investigate a novel carbon allotrope 'SqC': a square planar material that can be more than tetracoordinated. Carbon atoms in this 2D square Bravais lattice form an unusual five-center four-electron bond with neighboring four carbon atoms (tetracoordination). Such an electron-deficient bonding leaves an empty orbital which enables penta- or hexa-coordinated carbon atom. Indeed, our simulations demonstrate such penta- and hexa-coordinated configurations upon partial and complete hydrogenation, respectively. Surprisingly, in all the forms SqC shows the metallic character. SqC has the binding energy of 6.7 eV and it also satisfies the Born stability criteria. Yet our phonon calculations show that it may only be considered as quasi-stable.     

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.