Phase transitions in a MgB<Subscript>2</Subscript> granular BCS superconductor in weak magnetic fields

The character of temperature dependences of the electric conductivity of MgB₂ granular BCS superconductors at temperatures of ~35–45 K in external magnetic fields H _ext of up to ~2 kOe is studied. An increase in the superconducting transition width ΔT _c with an increase in Hext is found. The presence of a system of weak links in MgB₂-based granular superconductors is established. On the basis of experimental data, MgB₂ granular superconductor is assigned to two-level superconducting systems and the H–T phase diagram is constructed.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Anomalous low-temperature behavior of the thermal characteristics of MgB<Subscript>2</Subscript>

We have studied the behavior of the thermal expansion coefficient α(T) (in a zero magnetic field and at H≈4 T), the heat capacity C(T), and the thermal conductivity κ(T) of magnesium boride (MgB₂) in the vicinity of T_c and at lower temperatures. It was established that MgB₂, like oxide-based high-temperature superconductors, exhibits a negative thermal expansion coefficient at low temperatures. The anomaly of α(T) in MgB₂ is significantly affected by the magnetic field. It was established that, in addition to the well-known superconducting transition at T_c≈40 K, MgB₂ exhibits an anomalous behavior of both heat capacity and thermal conductivity in the region of T≈10–12 K. The anomalies of C(T) and κ(T) take place in the same temperature interval where the thermal expansion coefficient of MgB₂ becomes negative. The low-temperature anomalies are related to the presence of a second group of charge carriers in MgB₂ and to an increase in the density of the Bose condensate corresponding to these carriers at T_c2≈10–12 K.     

Josephson effect in S<Subscript>F</Subscript>XS<Subscript>F</Subscript> junctions

We investigate the Josephson effect in S_FXS_F junctions, where S_F is a superconducting material with a ferromagnetic exchange field, and X is a weak link. The critical current I_c increases with the (antiparallel) exchange fields, if the distribution of transmission eigenvalues of the X layer has its maximum weight at small values. This exchange-field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S_FIS_F junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference in the exchange fields h₁-h₂ in an S_FIS_F junction corresponds to the potential difference V₁-V₂ in an SIS junction; i.e., the singularity in I_c [in an S_FIS_F junction] at |h₁-h₂|=Δ₁+Δ₂ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S_FIS_F junctions.     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω _J becomes equal to the natural frequency ω_rc of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

Anomalous transport properties of a paramagnetic NiTiO<Subscript>3</Subscript> + HTSC two-phase system representing a random Josephson junction network

Composites representing a network of random Josephson junctions and characterized by the compositions 92.5 at. % Y_3/4Lu_1/4Ba₂Cu₃O₇+7.5 at. % NiTiO₃ and 92.5 at. % Y_3/4Lu_1/4Ba₂Cu₃O₇+7.5 at.% MgTiO₃ are synthesized, and their magnetoresistance properties are studied. The temperature dependence of the resistance R(T) measured for the composite that contains the paramagnetic NiTiO₃ compound exhibits a characteristic feature below the superconducting transition temperature T_c of the high-T_c superconductor, namely, a region where R is independent of the current j and weakly depends on the magnetic field H. Below a certain temperature T_m, a strong dependence of R on j and H is observed, which is peculiar to a network of Josephson junctions. The dependences R(T, j, H) obtained for the “reference” samples with the nonmagnetic MgTiO3 compound exhibit no such features. The anomalous behavior of the HTSC + NiTiO3 composite is explained by the effect produced by the magnetic moments of Ni atoms in the insulating barriers on the transport current.     

Magnetic susceptibility of fine crystalline high-temperature YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> superconductors. The role of nanoscale structural disordering

Static magnetic susceptibility χ(T) in the normal state (T_c ≤ T ≤ 400 K) and specific heat C(T) near temperature T_c of the transition to the superconducting state are experimentally studied for a series of fine crystalline samples of high-temperature YBa₂Cu₃O_y superconductor, having y and T_c close to optimal but differing in the degree of nanoscale structural disordering. It is shown that under the influence of structural disordering, there is enhancement of anomalous pseudogap behavior of the studied characteristics and a significant increase in the width of the pseudogap.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.     

Low-temperature anomalies in MgB<Subscript>2</Subscript> thermal expansion

The thermal expansion coefficient α(T) of MgB₂ was measured at low temperatures both in a zero magnetic field and at H=36 kOe. As in the oxide HTSCs, a region of anomalous (negative) thermal expansion and a strong effect of magnetic field on α(T) were revealed. The results obtained indicate the anomalous properties of MgB₂ and the oxide HTSCs to follow a common pattern.     

Realization of a Double-Slit SQUID Geometry by Fermi Arc Surface States in a WTe<Subscript>2</Subscript> Weyl Semimetal

We experimentally study electron transport between two superconducting indium leads, coupled to the WTe₂ crystal surface. WTe₂ is characterized by presence of Fermi arc surface states, as a predicted type-II Weyl semimetal candidate. We demonstrate Josephson current in unprecedentedly long 5 µm In–WTe₂–In junctions, which is confirmed by I–V curves evolution with temperature and magnetic field. The Josephson current is mostly carried by the topological surface states, which we demonstrate in a double-slit superconducting quantum interference device geometry, realized by coupling the opposite WTe₂ crystal surfaces.     

Exponential Increase in the Resistivity upon Cooling and Superconductivity in Indium-Doped Pb<Subscript>0.45</Subscript>Sn<Subscript>0.55</Subscript>Te

We have analyzed the temperature and magnetic-field dependences of resistivity ρ(T, H) of semiconducting compound Pb_0.45Sn_0.55Te doped with 5 at % In under a hydrostatic compression at P < 12 kbar. It is found that the temperature dependence ρ(T) at all pressures at T < 100 K is exponential with the activation energy decreasing upon an increase in pressure; this is accompanied with a superconducting transition on the ρ(T) and ρ(H) dependences at P > 4.8 kbar at T > 1 K (T _c = 1.72 K at a level of 0.5ρ _N at P = 6.8 kbar). We consider the model describing the low-temperature “dielectrization” of the semiconducting solid solution and the formation of the superconducting state upon an increase in the hydrostatic compression P > 4 kbar.     

Band structure and properties of superconducting MgB<Subscript>2</Subscript> and related compounds (A review)

This paper presents an overview of the current state of the art in research into the electronic structure and properties of a new superconductor, namely, MgB₂, and a large number of related compounds by computational methods of the band theory. Consideration is given to the specific features of the surface states of magnesium diboride, the electron and hole doping effects in this compound, and the concentration dependences of the band structure and the properties of Mg_1?xMe_xB₂ and MgB_2?yX_y solid solutions and a number of superstructures. The electronic properties of AlB₂-like phases, boron, higher borides, a series of ternary layered boron-containing phases, and compounds with structures of the antiperovskite type (MgCNi₃ and others) are discussed in terms of their superconducting characteristics. The results obtained in modeling nanotubes and fullerene-like nanoparticles based on MgB₂ and related borides are analyzed.     

Microstructure and superconducting properties of the DyBaCuO ceramic doped with Na<Subscript>2</Subscript>CO<Subscript>3</Subscript>, NaCl,and KClO<Subscript>3</Subscript>

This paper reports on a study of the effect of doping with Na₂CO₃, NaCl, and KClO₃ salts on the microstructure and superconducting characteristics of ceramics with nominal compositions Dy_{1 ? x} M _x Ba₂Cu_{3 ? y} O_{7 ? δ} and DyBa₂Cu_{3 ? y} O_{7 ? δ} : M _x for M = Na, K; x = 0.2, 0.3, and y = 0, 0.2. The microstructure was characterized by transmission electron microscopy with local energy-dispersive x-ray in situ analysis (probe size ～1 nm). An analysis shows that none of the doping elements (Na, K, or Cl) enters into 123 grains in sizable amounts and that, as a result, the critical temperature of the superconducting transition remains practically constant in the range 90.0–93.5 K. Potassium and chlorine segregate at grain boundaries. It is shown that grain-boundary segregation of chlorine leads to a substantial increase in the superconducting critical current (by a factor 3–5 at 70 K) as compared to the undoped sample. The possible mechanisms accounting for the effect of Cl on intergrain critical current are discussed.     

On electron transport in ZrB<Subscript>12</Subscript>, ZrB<Subscript>2</Subscript>, and MgB<Subscript>2</Subscript> in normal state

We report on measurements of the temperature dependence of resistivity, ρ(T), for single-crystal samples of ZrB₁₂, ZrB₂, and polycrystalline samples of MgB₂. It is shown that the cluster compound ZrB₁₂ behaves as a simple metal in the normal state, with a typical Bloch-Grüneisen ρ(T) dependence. However, the resistive Debye temperature, T_R=300 K, is three times smaller than T_D obtained from specific heat data. We observe the T² term in ρ(T) of all these borides, which could be interpreted as an indication of strong electron-electron interaction.     

Visualization of the magnetic flux structure in phosphorus-doped EuFe<Subscript>2</Subscript>As<Subscript>2</Subscript> single crystals

Magnetic flux structure on the surface of EuFe₂(As_1-x P _x )₂ single crystals with nearly optimal phosphorus doping levels x = 0.20 and x = 0.21 is studied by low-temperature magnetic force microscopy and decoration with ferromagnetic nanoparticles. The studies are performed in a broad temperature range. It is shown that the single crystal with x = 0.21 in the temperature range between the critical temperatures T _SC= 22 K and T _C = (18 ± 0.3) K of the superconducting and ferromagnetic phase transitions, respectively, has the vortex structure of a frozen magnetic flux, typical for type-II superconductors. The magnetic domain structure is observed in the superconducting state below T _C. The nature of this structure is discussed.     

Manifestation of pseudogap features in structurally inhomogeneous optimally doped HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.92</Subscript>

Magnetization M(H,T) in magnetic fields H up to 90 kOe and at temperatures 2 K ≤ T < T _c (where Tc is the superconducting transition temperature), along with magnetic susceptibility χ(T) in the normal state T _c < T < 400 K for optimally oxygen-doped samples of YBa₂Cu₃O_6.92 with varying degrees of defects in the crystal structure, are studied to determine the influence of structural inhomogeneity on the electron systems characteristics of cuprate superconductors. It is shown that the existence of structural inhomogeneity of samples leads to the manifestation of peculiarities appropriate to pseudogap regime in their properties.     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Maximal supercurrent of a Josephson junction in a field of magnetic particles

The maximal supercurrent I_m of a short Josephson junction formed by an edge contact of two superconducting films is calculated for the case where the junction is placed in a periodic field produced by a chain of magnetic nanoparticles. The commensurability effects occurring when the magnetic flux of a homogeneous external field H₀ through an elementary cell is equal to an integral number of magnetic flux quanta Φ₀ are considered. The effects give rise to additional maxima in the I_m(H₀) dependence.