Comparative Experimental and Density Functional Theory (<Emphasis Type="Italic">DFT</Emphasis>) Study of the Physical Properties of MgB<Subscript>2</Subscript> and AlB<Subscript>2</Subscript>

In the present study, we report an intercomparison of various physical and electronic properties of MgB₂ and AlB₂. In particular, the results of phase formation, resistivity ρ(T), thermoelectric power S(T), magnetization M(T), heat capacity (C _P ), and electronic band structure are reported. The original stretched hexagonal lattice with a=3.083 Å, and c=3.524 Å of MgB₂ shrinks in c-direction for AlB₂ with a=3.006 Å, and c=3.254 Å. The resistivity ρ(T), thermoelectric power S(T) and magnetization M(T) measurements exhibited superconductivity at 39 K for MgB₂. Superconductivity is not observed for AlB₂. Interestingly, the sign of S(T) is +ve for MgB₂ the same is ?ve for AlB₂. This is consistent with our band structure plots. We fitted the experimental specific heat of MgB₂ to Debye–Einstein model and estimated the value of Debye temperature (Θ _D) and Sommerfeld constant (γ) for electronic specific heat. Further, from γ, the electronic density of states (DOS) at Fermi level N(E _F) is calculated. From the ratio of experimental N(E _F) and the one being calculated from DFT, we obtained value of λ to be 1.84, thus placing MgB₂ in the strong coupling BCS category. The electronic specific heat of MgB₂ is also fitted below T _c using α-model and found that it is a two gap superconductor. The calculated values of two gaps are in good agreement with earlier reports. Our results clearly demonstrate that the superconductivity of MgB₂ is due to very large phonon contribution from its stretched lattice. The same two effects are obviously missing in AlB₂, and hence it is not superconducting. DFT calculations demonstrated that for MgB₂, the majority of states come from σ and π 2p states of boron on the other hand σ band at Fermi level for AlB₂ is absent. This leads to a weak electron phonon coupling and also to hole deficiency as π bands are known to be of electron type, and hence obviously the AlB₂ is not superconducting. The DFT calculations are consistent with the measured physical properties of the studied borides, i.e., MgB₂ and AlB₂.     

The Effect of Inhomogeneous Phase on the Critical Temperature of Smart Meta-superconductor MgB<Subscript>2</Subscript>

The critical temperature (T_C) of MgB₂, one of the key factors limiting its application, is highly desired to be improved. On the basis of the meta-material structure, we prepared a smart meta-superconductor structure consisting of MgB₂ micro-particles and inhomogeneous phases by an ex situ process. The effect of inhomogeneous phase on the T_C of smart meta-superconductor MgB₂ was investigated. Results showed that the onset temperature (\(T_{\mathrm {C}}^{\text {on}}\)) of doping samples was lower than those of pure MgB₂. However, the offset temperature (\({T}_{\mathrm {C}}^{\text {off}}\)) of the sample doped with Y₂O₃:Eu³⁺ nanosheets with a thickness of 2 ～ 3 nm which is much less than the coherence length of MgB₂ is 1.2 K higher than that of pure MgB₂. The effect of the applied electric field on the T_C of the sample was also studied. Results indicated that with the increase of current, \({T}_{\mathrm {C}}^{\text {on}}\) is slightly increased in the samples doping with different inhomogeneous phases. With increasing current, the \({T}_{\mathrm {C}}^{\text {off}}\) of the samples doped with nonluminous inhomogeneous phases was decreased. However, the \({T}_{\mathrm {C}}^{\text {off}}\) of the luminescent inhomogeneous phase doping samples increased and then decreased with increasing current.     

Influence of coronene addition on some superconducting properties of bulk MgB<Subscript>2</Subscript>

This study reports the effect of coronene (C₂₄H₁₂) addition on some superconducting properties such as critical temperature (T_c), critical current density (J_c), flux pinning force density (F_p), irreversibility field (H_irr), upper critical magnetic field (H_c2), and activation energy (U₀), of bulk MgB₂ superconductor by means of magnetisation and magnetoresistivity measurements. Disk-shaped polycrystalline MgB₂ samples with varying C₂₄H₁₂ contents of 0, 2, 4, 6, 8, 10 wt%, were produced at 850 °C in Ar atmosphere. The obtained results show an increase in field-J_c values at 10 and 20 K resulting from the strengthened flux pinning, and a decrease in critical temperature (T_c) because of C substitution into MgB₂ lattice, with increasing amount of C₂₄H₁₂ powder. The H_c2(0) and H_irr(0) values are respectively found as 144, 181, 172 kOe, and 128, 161, 145 kOe for pure, 4 wt% and 10 wt% C₂₄H₁₂ added samples. The U₀ depending on the magnetic field curves were plotted using thermally activated flux flow model. The maximum U₀ values are respectively obtained as 0.20, 0.23 and 0.12 eV at 30 kOe for pure, 4 wt% and 10 wt% C₂₄H₁₂ added samples. As a result, the superconducting properties of bulk MgB₂ at high fields was improved using C₂₄H₁₂, active carbon source addition, because of the presence of uniformly dispersed C particles with nanometer order of magnitude, and acting as effective pinning centres in MgB₂ structure.     

Critical Temperature of Smart Meta-superconducting MgB<Subscript>2</Subscript>

Enhancing the critical temperature (T _C ) is important not only to widen the practical applications but also to expand the theories of superconductivity. Inspired by the meta-material structure, we designed a smart meta-superconductor consisting of MgB₂ microparticles and Y₂O₃/Eu³⁺ nanorods. In the local electric field, Y₂O₃/Eu³⁺ nanorods generate an electroluminescence (EL) that can excite MgB₂ particles, thereby improving the T _C by strengthening the electron–phonon interaction. An MgB₂-based superconductor doped with one of four dopants of different EL intensities was prepared by an ex situ process. Results showed that the T _C of MgB₂ doped with 2 wt% Y₂O₃, which is not an EL material, is 33.1 K. However, replacing Y₂O₃ with Y₂O₃/Eu³⁺II, which displays a strong EL intensity, can improve the T _C by 2.8 to 35.9 K, which is even higher than that of pure MgB₂. The significant increment in T _C results from the EL exciting effect. Apart from EL intensity, the micromorphology and degree of dispersion of the dopants also affected the T _C . This smart meta-superconductor provides a new method to increase T _C .     

Crystal Growth and Magneto-transport of Bi<Subscript>2</Subscript>Se<Subscript>3</Subscript> Single Crystals

In this letter, we report on the growth and characterization of bulk Bi ₂Se ₃ single crystals. The studied Bi ₂Se ₃ crystals are grown by the self-flux method through the solid-state reaction from high-temperature (950 °C) melt of constituent elements and slow cooling (2 ℃/h). The resultant crystals are shiny and grown in the [00l] direction, as evidenced from surface XRD. Detailed Reitveld analysis of powder X-ray diffraction (PXRD) of the crystals showed that these are crystallized in the rhombohedral crystal structure with a space group of R3m (D5), and the lattice parameters are a = 4.14 (2), b = 4.14 (2), and c = 28.7010 (7) Å. Temperature versus resistivity (ρ?T) plots revealed metallic conduction down to 2 K, with typical room temperature resistivity (ρ _{300 K}) of around 0.53 m Ω-cm and residual resistivity (ρ _{0 K}) of 0.12 m Ω-cm. Resistivity under magnetic field [ ρ(T)H] measurements exhibited large + ve magneto-resistance right from 2 to 200 K. Isothermal magneto-resistance [ ρH] measurements at 2, 100, and 200 K exhibited magneto-resistance (MR) of up to 240 %, 130 %, and 60 %, respectively, at 14 T. Further, the MR plots are nonsaturating and linear with the field at all temperatures. At 2 K, the MR plots showed clear quantum oscillations at above say 10 T applied field. Also, the Kohler plots, i.e., Δρ/ ρ _oversus B/ ρ, were seen consolidating on one plot. Interestingly, the studied Bi ₂Se ₃ single crystal exhibited the Shubnikov-de Haas (SdH) oscillations at 2 K under different applied magnetic fields ranging from 4 to 14 T.     

Effects of Iron Contents on the Vortex State in Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>0.5</Subscript>Te<Subscript>0.5</Subscript>

We investigate the effects of iron content on the upper critical field (H _c2) and the activation energy U(T) in thermally activated flux flow in Fe _x Se_0.5Te_0.5 near the superconducting transition temperature T _c . The variations in H _c2(T) with temperature are analyzed using Ginzburg-Landau (GL), Werthamer-Helfand-Hohenberg (WHH) models along with the empirical relation (ER). The obtained values of H _c2(0) depend strongly on the model and the criteria used to determine the transition temperature. However, the general trend is that that H _c2(0) increases with the increasing Fe content. The activation energy U(T) is maximum for x =? 1 and rapidly suppressed by excess or deficiency of iron. The low values of U(T) (～10 meV) reflect the low vortex-pinning nature (due to defects, vacancies, etc.) in the Fe _x Se_0.5Te_0.5 superconductor.     

Effect of Blocking and Superconducting Layer Doping on the Superconductivity and Magnetic Properties of Polycrystalline Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>6</Subscript>

The possible difference in the properties upon doping the Sr₂CaCu₂O₆ superconducting or blocking layers with Fe and Eu respectively was investigated in this work. The homogeneous Sr_2?yEu_yCaCu₂O_6+δ and Sr₂CaCu_2?xFe_xO_6+δ (y = 0, 0.1, 0.5, x = 0, 0.05) compounds were produced by a high-pressure synthesis route. Judging by the magnetic susceptibility measurements, all samples exhibit a superconductivity transition and the Eu/Fe concentration dependencies on the diamagnetic moment and average T_c have been constructed using the experimental data. As a result, an unusual behavior of the T_c value was observed for the samples with doped Eu: a fivefold reduction in the europium concentration in the sample does not give a noticeable effect on the transition temperature value while the diamagnetic signal becomes more stronger. Complex superconducting dome was found for Eu-doped material: 0.1 ≤ y ≤ 0.5 region T_c vs. concentration data were approximated by inverted parabola-like curve with a maximum at y = 0.3. Difference in properties of the Eu and Fe-doped samples was also found in the behavior of the hysteresis loops showed the opposite orientations.     

Role of Aniline Addition in Structural and Superconducting Properties of MgB<Subscript>2</Subscript> Bulk Superconductor

In this study, the structural and superconducting properties of aniline-added MgB₂ superconductors were investigated by X-ray diffraction (XRD), thermal analysis techniques, and ac susceptibility measurements. The amount of aniline was changed from 0 to 1 mol%. Phase analysis and lattice parameters were determined from XRD measurements. X-ray diffraction analysis indicates that the main phase is MgB₂ and that there is a small amount of Mg as the secondary phase in aniline-added samples. According to the determination of lattice parameters, it is seen that the addition of aniline does not give a proper distribution with the contribution amount of a and c lattice parameters. From DSC curves, two exothermic peaks and one endothermic peak were observed in all samples. Pure and aniline-added samples were found to be dependent on the magnetic field in the ac susceptibility measurements, and the superconducting transition temperature (T _c ) was found to decrease to lower temperatures due to an increase in the amount of aniline. It has been determined that changes in the in-phase (χ ^′) and out-of-phase (χ ^″) components of the ac susceptibility by increasing the aniline amount have weakened the MgB₂ phase structure and thus cause changes in the pinning mechanism. In addition, ac losses of all the samples were calculated under external fields ranging from 160 to 1280 A/m and at 25 K.     

The H-T and P-T Phase Diagram of the Superconducting Phase in Pd:Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript>

We study the magnetic field vs. temperature (H – T) and pressure vs. temperature (P – T) phase diagrams of the T _c ≈ 5.5 K superconducting phase in Pd _x Bi₂Te₃ (x ≈ 1) using electrical resistivity versus temperature measurements at various applied magnetic fields (H) and magnetic susceptibility versus temperature measurements at various applied magnetic fields (H) and pressure (P). The H – T phase diagram has an initial upward curvature as observed in some unconventional superconductors. The critical field extrapolated to T = 0 K is H _c (0) ≈ 6–10 kOe. The T _c is suppressed approximately linearly with pressure at a rate d T _c /d P ≈ ?0.28 K/GPa.     

Progress in Critical Current Density (<Emphasis Type="Italic">J</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript>) in Sintered MgB<Subscript>2</Subscript> Bulks

The present paper focuses on methods of further improving the flux pinning and critical current density of disk-shaped MgB₂ bulk superconductors by adding excess Mg metal in combination with an optimum silver content and optimized processing conditions. Bulk MgB₂ samples were produced by in situ solid-state reaction in Ar gas ambient using high purity commercial powders of Mg metal and 1.5 wt% carbon-coated amorphous B powders mixed in a fixed ratio of Mg/B = 1.1:2. Further, 4 wt% silver was added to improve flux pinning as well as mechanical performance of the bulk MgB₂ material. The magnetization measurements confirmed a sharp superconducting transition with T_c,onset at around 37 K, which is only by 1 K lower than in bulk MgB₂ material produced without carbon-coated amorphous boron. The critical current density (J_c) values significantly improved in the MgB₂ material with 4 wt% of silver and 1.5 wt% of carbon-coated amorphous boron, sintered at 775 ^°C for 3 h. At 20 K, this sample showed J_c at around 500 and 350 kA/cm² in the self-field and 1 T, respectively, which makes it suitable for several industrial applications.     

Time-Dependent Diffusion Coefficient of Fe in MgB<Subscript>2</Subscript> Superconductors

The iron (Fe) diffusion in superconducting MgB₂ bulk samples has been studied for sintering time durations of 15 min, 30 min, 1 h, 2 h, and 4 h at 900^°C. Fe coating bulk polycrstalline superconducting MgB₂ samples for Fe coating were prepared by pelletizing and used in the diffusion experiments with initial sintering at 800^°C for 1 h. A thin layer of Fe was coated on MgB₂ pellets by evaporation in vacuum. Effects of Fe diffusion on the structural, electrical, and superconducting properties of MgB₂ have been investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), infrared spectroscopy (IR), energy-dispersive X-ray spectroscopy (EDS), and resistivity measurements. Fe diffused samples have slightly increased critical transition temperatures and have larger lattice parameter c values, in comparison with bare samples. Fe diffusion coefficients were calculated from depth profiles of c parameter and room temperature resistivity values. Depth profiles were obtained by successive removal of thin layers from Fe diffused surfaces of the samples. Our results have shown that the Fe diffusion coefficient decreases with increasing sintering time and resistivity measurements can be utilized for determination of diffusion coefficient.     

Fluctuation induced conductivity of polycrystalline MgB<Subscript>2</Subscript> superconductor

We report fluctuation-induced conductivity (FIC) of the polycrystalline MgB₂ superconductor in the presence of magnetic field. The results are described in terms of the temperature derivative of the resistivity, dρ/dT. The dρ/dT peak temperature observed for H = 0 Tesla at 39 K remains very distinct under applied fields of 6 Tesla and 8 Tesla at 22 and 20 K respectively. Aslamazov and Larkin (AL) equations are used to explain the anisotropic nature of the polycrystalline MgB₂. The effective coherence length, ξ _p (0) determined experimentally is 55.17 Å, which roughly matches with previously reported experimental work.     

Effect of Ag Addition on the Surface Topography and the Vibrational Dynamics of MgB<Subscript>2</Subscript>

We fabricated MgB₂ samples with Ag additions using in situ solid-state reaction via a single-step sintering to study the effect of Ag on the structural, vibration, and superconducting properties of MgB₂ samples. Ag addition to MgB₂ resulted in a significant improvement in J _c although no appreciable effect was observed in the lattice parameters and the superconducting transition temperature T _c. Dramatic increase in the grain size was observed with Ag addition and topographic measurements with atomic force microscopy revealed the formation of Ag–Mg nanoparticles 5–20 nm in size at 2 and 4 wt% Ag additions. The fact that these samples showed high J _c values suggests that the nanoparticles formed as a result of Ag addition are responsible for enhanced flux pinning. Raman spectroscopy measurements showed that Ag additions also increased disorder in the system and thereby affected the line width of the Raman active E _2g mode.     

Studies on the Composite System of Bi-2212 Glass Ceramic and MgB<Subscript>2</Subscript> Superconductors

The composites of glass ceramic Bi-2212 and MgB₂ superconductors were prepared at ambient conditions. The transmission electron microscopy images of the composite samples illustrate the presence of glass ceramic inclusions in bulk MgB₂. Temperature-dependent magnetization of the composite samples shows two superconducting transitions: one at 80 K corresponding to the Bi-2212 phase and a second one at 39 K corresponding to the MgB₂ phase, suggesting that the two superconducting phases are separated with clear boundaries. The critical current density (J _c) and pinning force values are increased in composite systems by an order of magnitude compared to that of individual samples. The pinning mechanism in the composite sample is the same as in the matrix phase. Reduced field maxima (h _max) are observed at 0.15 for composite samples. A low value of h _max for composite samples indicates the random orientation of grain boundaries and repulsive pinning force in the composite samples.     

Improving the Critical Temperature of MgB<Subscript>2</Subscript> Superconducting Metamaterials Induced by Electroluminescence

The MgB₂ superconductor was doped with electroluminescent Y₂O₃:Eu, to synthesise a superconducting metamaterial. The temperature dependence of the resistivity of the superconductor indicates that the critical temperature (T _C) of samples decreases when increasing the amount of doped Y ₂ O ₃ nanorods, due to impurity (Y ₂ O ₃, MgO and YB ₄). However, the T _C of the samples increase with increasing amount of doped Y ₂ O ₃:Eu ³⁺ nanorods, which are opposite to doped Y ₂ O ₃ nanorods. Moreover, the transition temperature of the sample doped with 8 wt % Y ₂ O ₃:Eu ³⁺nanorods is higher than those of doped and pure MgB ₂. The T _C of the sample doped with 8 wt % Y ₂ O ₃:Eu ³⁺ nanorods is 1.15 K higher than that of the sample doped with 8 wt % Y ₂ O ₃. The T _C of sample doped with 8 wt% Y ₂ O ₃:Eu ³⁺ is 0.4 K higher than that of pure MgB ₂. Results indicate that doping electroluminescent materials into MgB ₂ increases the transition temperature; this novel strategy may also be applicable to other superconductors.     

High-temperature heat capacity and thermodynamic properties of Tb<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript>

Tb₂Sn₂O₇ has been prepared by solid-state reaction in air at 1473 K over a period of 200 h and its isobaric heat capacity has been studied experimentally in the range 350–1073 K. The C _p(T) data for this compound have no extrema and are well represented by the classic Maier–Kelley equation. The experimental C _p(T) data have been used to evaluate the thermodynamic properties of terbium stannate (pyrochlore structure): enthalpy increment H°(T)–H°(350 K), entropy change S°(T)–S°(350 K), and reduced Gibbs energy Ф°(Т).     

Inducement of Itinerant Electron Transport in Charge-Ordered Pr<Subscript>0.6</Subscript>Ca<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> by Ba Doping

The effects of Ba ²⁺ doping on the electrical and magnetic properties of charge-ordered Pr_0.6Ca_0.4MnO₃ were investigated through electrical resistivity and AC susceptibility measurements. X-ray diffraction data analysis showed an increase in unit cell volume with increasing Ba ²⁺ content indicating the possibility of substituting Ba ²⁺ for the Ca-site. Electrical resistivity measurements showed insulating behavior and a resistivity anomaly at around 220 K. This anomaly is attributed to the existence of charge ordering transition temperature, \(T^{\mathrm {R}}_{\text {CO}}\) for the x = 0 sample. The Ba-substituted samples exhibited metallic to insulator transition (MI) behavior, with transition temperature, T _MI, increasing from ～98 K (x = 0.1) to ～122 K (x = 0.3). AC susceptibility measurements showed ferromagnetic to paramagnetic (FM-PM) transition for Ba-substituted samples with FM-PM transition temperature, T _c, increasing from ～121 K (x = 0.1) to ～170 K (x = 0.3), while for x = 0, an antiferromagnetic to paramagnetic transition behavior with transition temperature, T _N, ～170 K was observed. In addition, inverse susceptibility versus T plot showed a deviation from the Curie–Weiss behavior above T _c, indicating the existence of the Griffiths phase with deviation temperature, T _G, increasing from 160 K (x = 0.1) to 206 K (x = 0.3). Magnetoresistance, MR, behavior indicates intrinsic MR mechanism for x = 0.1 which changed to extrinsic MR for x > 0.2 as a result of Ba substitution. The weakening of charge ordering and inducement of ferromagnetic metallic (FMM) state as well as increase in both T _c and T _MI are suggested to be related to the increase of tolerance factor, τ, and increase of e _g ?electron bandwidth as average ionic radius at A-site, <r _A> increased with Ba substitution. The substitution may have reduced MnO₆ octahedral distortion and changed the Mn–O–Mn angle which, in turn, promotes itinerancy of charge carrier and enhanced double exchange mechanism. On the other hand, increase in A-site disorder, which is indicated by the increase in σ ² is suggested to be responsible for the widening of the difference between T _c and T _MI.     

Anomalous Impact of Hydrostatic Pressure on Superconductivity of Polycrystalline LaO<Subscript>0.5</Subscript>F<Subscript>0.5</Subscript>BiSe<Subscript>2</Subscript>

We report bulk superconductivity at 2.5 K in LaO_0.5F_0.5BiSe₂ compound through the DC magnetic susceptibility and electrical resistivity measurements. The synthesized LaO_0.5F_0.5BiSe₂ compound is crystallized in tetragonal structure with space group P4/nmm and Reitveld refined lattice parameters are a = 4.15(1) Å and c = 14.02(2) Å. The lower critical field of H _c1 = 40 Oe, at temperature 2 K is estimated through the low field magnetization measurements. The LaO_0.5F_0.5BiSe₂ compound showed metallic normal state electrical resistivity with residual resistivity value of 1.35 m Ω cm. The compound is a type-II superconductor, and the estimated H _c2(0) value obtained by WHH formula is above 20 kOe for 90 % ρ _n criteria. The superconducting transition temperature decreases with applied pressure till around 1.68 GPa and with further higher pressures a high- T _c phase emerges with possible onset T _c of above 5 K for 2.5 GPa.     

Synthesis and high-temperature heat capacity of Gd<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript>

Gd₂Sn₂O₇ gadolinium stannate with the pyrochlore structure has been prepared by solid-state reaction and its high-temperature heat capacity has been determined by differential scanning calorimetry in the temperature range 350–1020 K. The C_p(T) data are shown to be well represented by the classic Maier–Kelley equation. The experimental C_p(T) data have been used to evaluate the thermodynamic functions of gadolinium stannate: enthalpy increment H°(T)–H°(339 K), entropy change S°(T)–S°(339 K), and reduced Gibbs energy Ф°(Т).     

Seebeck Coefficient Measurement and Its Narrow Band Model Interpretation in FeTe<Subscript>0.5</Subscript>Se<Subscript>0.5</Subscript> Superconductor

We have measured Seebeck coefficient (S) of FeTe_0.5Se_0.5 superconducting sample from 10 to 300 K. The variation of Seebeck coefficient with temperature of this system was found to be very anomalous, and the overall experimental observation of the S(T) was studied in the outline of a narrow-band model. In high-temperature region, the Seebeck coefficient is almost independent of temperature. Further, from the study of high-temperature magnitude of S, sample undergoes a change in sign in the Seebeck coefficient, wherein, appearance of a negative peak around 22 K and subsequently, its Seebeck coefficient goes to zero in the superconducting transition temperature regime around 11 to 13 K. It is revealed that the bandwidth and a small asymmetry involved in narrow bands give a realistic explanation to the anomalous temperature dependence of Seebeck coefficient of FeTe_0.5Se_0.5 system.