Scanning tunneling spectroscopy in MgB2

Multiband Superconductors: Two Characteristic Lengths for Each Contributing Condensate

The interference of multiple condensates coexisting in one system may lead to unconventional coherent behavior. This is expected when the spatial lengths of the condensates are essentially different. Traditionally, the characteristic spatial length of a superconducting condensate is associated with the gap function. However, the broader readership is more familiar with the concept of the Cooper-pair wave function. For conventional single-band superconductors, the gap function coincides with the center-of-mass Cooper-pair wave function up to the coupling constant, and the corresponding gap and wave function characteristic lengths are the same. Surprisingly, we find that in two-band superconductors, these lengths are the same only near the critical temperature. At lower temperatures, they can significantly deviate from each other, and the fundamental question of which of these lengths should be preferred when specifying the spatial scale of a band-dependent condensate in multiband superconducting materials arises.

Spectroscopic signature of two superconducting gaps and their unusual field dependence in RuB2

Recently RuB2was shown to be a possible two-gap, type-I superconductor. Temperature dependent heat capacity measurements revealed a two-gap superconducting ground state, while magnetic field dependent magnetization measurements indicated surprizing type-I superconductivity with a very low experimental critical field (Hc) ∼120 Oe. In this paper, we report direct spectroscopic evidence of two superconducting energy gaps in RuB2. We have measured scanning tunnelling spectra exhibiting signature of two gaps on different grains of polycrystalline RuB2, possibly originating from multiple bands. Analysis of the temperature dependent tunnelling spectra revealed that the gaps from different bands evolve differently with temperature before disappearing simultaneously at a singleTc. Interestingly, our experiments also reveal that the gaps in quasiparticle density of states survive up to magnetic fields much higher than the bulkHcand they evolve smoothly with field, unlike what is expected for a type-I superconductor, indicating the existence of a 'mixed state'.

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).

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.

Interband phase modes and nonequilibrium soliton structures in two-gap superconductors

We predict a new dynamic state in current-carrying superconductors with a multicomponent order parameter. If the current density J exceeds a critical value J(t), an interband breakdown caused by charge imbalance of nonequilibrium quasiparticles occurs. For J>J(t), the electric field penetrating from current leads gives rise to various static and dynamic soliton phase textures, and voltage oscillations similar to the nonstationary Josephson effect. We propose experiments to observe these effects which would probe the multicomponent nature of the superconducting order parameter.

Two-band superconductivity in MgB2

The study of the anisotropic superconductor MgB2 using a combination of scanning tunneling microscopy and spectroscopy reveals two distinct energy gaps at Delta(1)=2.3 meV and Delta(2)=7.1 meV at 4.2 K. Different spectral weights of the partial superconducting density of states are a reflection of different tunneling directions in this multiband system. Temperature evolution of the tunneling spectra follows the BCS scenario [Phys. Rev. Lett. 3, 552 (1959)]] with both gaps vanishing at the bulk T(c). The data confirm the importance of Fermi-surface sheet dependent superconductivity in MgB2 proposed in the multigap model by Liu et al. [Phys. Rev. Lett. 87, 087005 (2001)]].

Magneto-optical study of the superconducting gap of MgB(2) single crystals

We present magneto-optical reflectivity results in the basal plane of the hexagonal MgB(2). The data were collected on a mosaic of MgB(2) single crystals with T(c)=38 K from the ultraviolet down to the far infrared as a function of temperature and magnetic field oriented along the c axis. In the far infrared, there is a clear signature of the superconducting gap with a gap ratio 2 Delta/k(B)T(c) approximately 1.2, well below the weak-coupling value. The gap is suppressed in an external magnetic field, which is a function of temperature. We extract the upper critical field H(c2) along the c axis. The temperature dependence of H(c2) is compatible with the Helfand-Werthamer behavior.

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.

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.

Strong renormalization of phonon frequencies in Mg(1-x)Al(x)B2

The phonon spectrum of Mg(1-x)Al(x)B2 shows a strong dependence on the aluminum content x. This is experimentally demonstrated by both Raman and inelastic neutron scattering and theoretically predicted by first-principles calculations. The observed changes in the phonon spectrum are put into perspective with respect to the superconducting properties within this family of materials.

Evidence for a multiple superconducting gap in MgB(2) from high-resolution photoemission spectroscopy

We study the new binary intermetallic superconductor MgB(2) using high-resolution photoemission spectroscopy. The superconducting-state spectrum measured at 5.4 K shows a coherent peak with a shoulder structure, in sharp contrast to that expected from a simple isotropic-gap opening. The spectrum can be well reproduced using the weighted sum of two Dynes functions with the gap sizes of 1.7 and 5.6 meV. Temperature-dependent study shows that both gaps close at the bulk transition temperature. These results provide spectroscopic evidence for a multiple gap of MgB(2).

Two-gap state density in MgB(2): a true bulk property or a proximity effect?

We report on the temperature dependence of the quasiparticle density of states in the simple binary compound MgB(2) directly measured using scanning tunneling microscope (STM). To achieve high quality tunneling conditions, a small crystal of MgB(2) is used as a tip in the STM experiment. The "sample" is chosen to be a 2H- NbSe(2) single crystal presenting an atomically flat surface. At low temperature the tunneling conductance spectra show a gap at the Fermi energy followed by two well-pronounced conductance peaks on each side. They appear at voltages V(S) approximately +/-3.8 mV and V(L) approximately +/-7.8 mV. With rising temperature both peaks disappear at the T(C) of the bulk MgB(2), a behavior consistent with the model of two-gap superconductivity. The possibility of a particular proximity effect is also discussed.

Evidence for two superconducting energy gaps in MgB(2) by point-contact spectroscopy

Experimental support is found for the multiband model of the superconductivity in the recently discovered system MgB(2) with the transition temperature T(c) = 39 K. By means of Andreev reflection, evidence is obtained for two distinct superconducting energy gaps. The sizes of the two gaps ( Delta(S) = 2.8 meV and Delta(L) = 7 meV) are, respectively, smaller and larger than the expected weak coupling value. Because of the temperature smearing of the spectra the two gaps are hardly distinguishable at elevated temperatures, but when a magnetic field is applied the presence of two gaps can be demonstrated close to the bulk T(c) in the raw data.

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.

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.

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.

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.

The complex nature of superconductivity in MgB2 as revealed by the reduced total isotope effect

Magnesium diboride, MgB2, was recently observed to become superconducting at 39 K, which is the highest known transition temperature for a non-copper-oxide bulk material. Isotope-effect measurements, in which atoms are substituted by isotopes of different mass to systematically change the phonon frequencies, are one of the fundamental tests of the nature of the superconducting mechanism in a material. In a conventional Bardeen-Cooper-Schrieffer (BCS) superconductor, where the mechanism is mediated by electron-phonon coupling, the total isotope-effect coefficient (in this case, the sum of both the Mg and B coefficients) should be about 0.5. The boron isotope effect was previously shown to be large and that was sufficient to establish that MgB2 is a conventional superconductor, but the Mg effect has not hitherto been measured. Here we report the determination of the Mg isotope effect, which is small but measurable. The total reduced isotope-effect coefficient is 0.32, which is much lower than the value expected for a typical BCS superconductor. The low value could be due to complex materials properties, and would seem to require both a large electron-phonon coupling constant and a value of mu* (the repulsive electron-electron interaction) larger than found for most simple metals.