Specific heat of single crystal MgB2: a two-band superconductor with two different anisotropies

The Influence of Electroluminescent Inhomogeneous Phase Addition on Enhancing MgB2 Superconducting Performance and Magnetic Flux Pinning

As a highly regarded superconducting material with a concise layered structure, MgB2 has attracted significant scientific attention and holds vast potential for applications. However, its limited current-carrying capacity under high magnetic fields has greatly hindered its practical use. To address this issue, we have enhanced the superconducting performance of MgB2 by incorporating inhomogeneous phase nanostructures of p-n junctions with electroluminescent properties. Through temperature-dependent measurements of magnetization, electronic specific heat, and Hall coefficient under various magnetic fields, we have confirmed the crucial role of inhomogeneous phase electroluminescent nanostructures in improving the properties of MgB2. Experimental results demonstrate that the introduction of electroluminescent inhomogeneous phases effectively enhances the superconducting performance of MgB2. Moreover, by controlling the size of the electroluminescent inhomogeneous phases and optimizing grain connectivity, density, and microstructural uniformity, we can further improve the critical temperature (TC) and flux-pinning capability of MgB2 superconducting materials. Comprehensive studies on the physical properties of MgB2 superconducting structures added with p-n junction electroluminescent inhomogeneous phases also confirm the general effectiveness of electroluminescent inhomogeneous phases in enhancing the performance of superconducting materials.

Multiple gaps revealed by low temperature specific heat in the 1111-type CaFe0.88Co0.12AsF single crystals

Low-temperature specific heat (SH) is measured on the 1111-type CaFe_0.88 Co_0.12AsF single crystals under different magnetic fields. A clear SH jump with the height [Formula: see text] mJ mol^-1 K^-2 is observed at the superconducting transition temperature T _c . The electronic SH coefficient [Formula: see text] increases linearly with the field below 5 T and a kink is observed around 5 T, indicating a multi-gap feature in the present system. Such a sign is also reflected in the T _c   -  B data. A detailed analysis shows that this behavior can be interpreted in terms of a two-gap scenario with the ratio [Formula: see text]-4.5.

Superconducting gap structure of FeSe

The microscopic mechanism governing the zero-resistance flow of current in some iron-based, high-temperature superconducting materials is not well understood up to now. A central issue concerning the investigation of these materials is their superconducting gap symmetry and structure. Here we present a combined study of low-temperature specific heat and scanning tunnelling microscopy measurements on single crystalline FeSe. The results reveal the existence of at least two superconducting gaps which can be represented by a phenomenological two-band model. The analysis of the specific heat suggests significant anisotropy in the gap magnitude with deep gap minima. The tunneling spectra display an overall "U"-shaped gap close to the Fermi level away as well as on top of twin boundaries. These results are compatible with the anisotropic nodeless models describing superconductivity in FeSe.

Enhanced quasiparticle heat conduction in the multigap superconductor Lu2Fe3Si5

Thermal transport measurements have been made on the Fe-based superconductor Lu2Fe3Si5 (T(c) ∼ 6  K) down to a very low temperature T(c)/120. The field and temperature dependences of the thermal conductivity confirm the multigap superconductivity with fully opened gaps on the whole Fermi surfaces. In comparison to MgB2, Lu2Fe3Si5 reveals a remarkably enhanced quasiparticle heat conduction in the mixed state. The results can be interpreted as a consequence of the unequal weight of the Fe 3d-electron character among the distinct bands.

Multiband superconductivity in the Chevrel phases SnMo6S8 and PbMo6S8

Sub-Kelvin scanning tunneling spectroscopy in the Chevrel phases SnMo6S8 and PbMo6S8 reveals two distinct superconducting gaps with Δ1=3 meV, Δ2∼1.0 meV and Δ1=3.1 meV, Δ2∼1.4 meV, respectively. The gap distribution is strongly anisotropic, with Δ2 predominantly seen when scanning across unit-cell steps on the (001) sample surface. The spectra are well fitted by an anisotropic two-band BCS s-wave gap function. Our spectroscopic data are confirmed by electronic heat capacity measurements, which also provide evidence for a twin-gap scenario.

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.

Enhancement of pairing interaction and magnetic fluctuations toward a band insulator in an electron-doped Li(x)ZrNCl Superconductor

The doping dependence of specific heat and magnetic susceptibility has been investigated for Li(x)ZrNCl superconductors derived from a band insulator. As the carrier concentration is decreased, the anisotropy of superconducting gap changes from highly anisotropic to almost isotropic. It was also found that, upon reducing carrier density, the superconducting coupling strength and the magnetic susceptibility are concomitantly enhanced in parallel with T(c), while the density of states at the Fermi level is kept almost constant. Theoretical calculations taking into account the on-site Coulomb interaction reproduced the experimental results, suggesting a possible pairing mediated by magnetic fluctuations, even in the doped band insulators.

Calorimetric evidence for a Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in the layered organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2

The specific heat of the layered organic superconductor kappa-(BEDT-TTF)(2)Cu(NCS)(2), where BEDT-TTF is bisethylenedithio-tetrathiafulvalene, has been studied in magnetic fields up to 28 T applied perpendicular and parallel to the superconducting layers. In parallel fields above 21 T, the superconducting transition becomes first order, which signals that the Pauli-limiting field is reached. Instead of saturating at this field value, the upper-critical-field increases sharply and a second first-order transition line appears within the superconducting phase. Our results give strong evidence that the phase, which separates the homogeneous superconducting state from the normal state is a realization of a Fulde-Ferrell-Larkin-Ovchinnikov state.

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.

Field dependence of the vortex core size in a multiband superconductor

The magnetic field dependence of the vortex core size in the multiband superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.

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.

Specific heat measurement of the layered nitride superconductor Li(x)ZrNCl

Specific heat has been investigated in a layered nitride superconductor, Li(0.12)ZrNCl, with T(c)=12.7 K. The obtained data have shown a marked dichotomy: The specific heat jump at T(c) (DeltaC/gamma(n)T(c)=1.8) and the superconducting gap ratio (2Delta/k(B)T(c)=4.6-5.2) have indicated an intermediate to a strong coupling of electrons, while the upper limit of the electron-phonon coupling constant lambda has directly been estimated to be 0.22, which belongs to a weak coupling regime. Furthermore, the rapid increase of gamma as a function of magnetic field suggests that the present material has an anisotropic s wave gap.

Anisotropies of the lower and upper critical fields in MgB2 single crystals

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.

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.

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.

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.

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.