Superconducting energy gap distribution in c-axis oriented MgB2 thin film from point contact study

We have analyzed about a hundred voltage-dependent differential resistance dV/dI(V) curves of metallic point contacts between c-axis-oriented MgB₂ thin film and Ag, which exhibit clear Andreev reflection features connected with the superconducting gap. About one half of the curves show the presence of a second larger gap. The histogram of the double gap distribution reveals distinct maxima at 2.4 and 7 meV, while curves with single-gap features result in a more broad maximum at 3.5 meV. The double-gap distribution is in qualitative agreement with the distribution of gap values over the Fermi surface calculated by H. J. Choi et al. (cond-mat/0111183). The data unequivocally show the presence of two gaps: Δ_S=2.45±0.15 meV and Δ_L=7.0±0.45 meV in MgB₂ with the gap ratio Δ_L/Δ_S=2.85±0.15. Our observations further prove a widely discussed multigap scenario for MgB₂, where two distinct gaps are seen in the clean limit, while a single averaged gap is present in the dirty one.     

Luminescence kinetics of dipolar excitons in circular traps

A detailed investigation of multiband superconductivity and Leggett’s mode in the Mg_1?x Al_xB₂ (0 ≤ x ≤ 0.45) system was carried out using tunneling and Andreev spectroscopy. Temperature dependences of superconducting gaps Δ_σ and Δ_π and their variation upon the degree of disorder and the Al concentration were studied. The dependence of the Leggett’s mode energy ε₀ upon the values of the gaps Δ_σ and Δ_π has been derived.     

Excess current in point contacts on two-band superconductor MgB2 in magnetic field

A series of I(V) characteristics and bias-dependent differential resistance dV/dI(V) curves of point contacts made between a single crystal of two-band superconductor MgB₂ and Cu were measured in magnetic fields up to 9 T. The magnetic field dependences of the excess current in the I(V) curves were obtained and analyzed using Koshelev and Golubov's [Phys. Rev. Lett. 90, 177002 (2003)] theoretical results for the mixed state of a dirty two-band superconductor. Introducing a simple model for the excess current in the point contact in the mixed state, our data can be qualitatively described using the theoretical magnetic field dependence of the superconducting order parameter of the σ and π-bands and the averaged electronic density of states in MgB₂.     

Evidence for a two-band behavior of MgB2 from point-contact and tunneling spectroscopy

The break-junction tunneling has been systematically investigated in MgB₂. Two types of the break-junction contacts have been exploited on the same samples, which demonstrated tunnel contact like (SIS) and point contact like (SnS) behavior. Both of them have shown the existence of the two distinct energy gaps. We have also observed peculiarities on the I(V)- characteristics related to Leggett's collective mode assisted tunneling.     

Determination of the electron-phonon coupling constants from the experimental temperature dependences of superconducting gaps in MgB2

Experimental temperature dependences Δ_{σ, π}(T) of the energy of superconducting gaps for MgB₂ samples with the critical temperatures 22 K < T _c < 41 K have been fitted by selecting the renormalized electron-phonon coupling constants λ _ij with the use of the Moskalenko-Shul system of equations, the expression for the frequency of collective plasma oscillations obtained by Leggett for two-gap superconductors, and two fitting parameters. We previously obtained the dependences Δ_{σ, π}(T) by the multiple Andreev reflection spectroscopy of superconductor-constriction-superconductor junctions based on MgB₂ with various degree of disorder of the crystal structure. It has been shown that the intraband pairing constants are decisive for the superconductivity mechanism in MgB₂; in this case, √V _σσ V _ππ/V _σπ = 8–22 and the ratio of the interband constants α can range from 3 to 11. The set of the Eliashberg coupling constants λ _ij ⁰ has been qualitatively determined for relatively pure MgB₂ with maximum values T _c ≈ 40 K. The leading constant is 0.7 < λ _σσ ⁰ ≈ λ _eff ⁰ < 0.9 and depends on the choice of the upper integration limit in the Bardeen-Cooper-Schrieffer (BCS) model and the effective Coulomb repulsion μ _iff ^* . The characteristic ratio for the gap in the σ band is 2Δ_σ/k _B T _c = 5.0–6.5.     

Generalized Gor’kov relation for two-band superconductor MgB<Subscript>2</Subscript>

A generalized Gor’kov relation between the upper critical magnetic field H _c2, the residual resistivity, and the parameters of the two-band electronic structure from the pure limit to the dirty limit was derived for two-gap superconductor MgB₂. The ratio of the relaxation times τ _π /τ _σ of π-and σ-band electrons for MgB₂ samples with various defect levels was determined from experimental data.     

Two-band nature of upper critical fields in MgB2 thin films investigated by 37 T pulsed magnet

We present experimental and calculated phase diagrams of the upper critical field H_c2 and the anisotropy parameter γ of various MgB₂ thin films prepared by the molecular beam epitaxy (MBE) and the multiple-targets sputtering system. Experimental data of the H_c2(T) and γ are analyzed by fitting the Gurevich theory. We obtained the result that for these MgB₂ films the H_c2(T) is explained as the case of D_π/D_σ>1, which means the films are classified to the cleaner π band than the σ band. We discuss temperature dependence of the transition width obtained from the magnetoresistance measurements.     

Calculation of Tc and the ratio 2Δ(0)/kBTc of MgB2 within a two-band model of superconductivity

Superconductivity in the MgB₂ superconductor is described within the framework of a two-band Eliashberg formalism. Different gaps are assumed to open on the different parts of the Fermi surface of this compound. Separation of the order parameter (OP) into two components is achieved by taking the Fourier transform of the OP using the momentum states of the σ- and π-bands of MgB₂. Expressions for the T_c and the ratio 2Δ_σ(0)/k_BT_c for this superconductor are obtained. Numerical values for these two properties are obtained for a range of values of the cut-off frequency of the phonons responsible for the superconductivity and for a range of values of the ratio between the two energy gaps. This was done for various values of the normalized partial densities of states on the σ-sheet of the Fermi surface.     

Phonon density-of-states in the new superconductor MgB 2

We provide here experimental data on the phonon density-of-states of MgB₂ obtained by the inelastic neutron scattering technique. The measurements were performed for the natural boron-based magnesium diboride with use of a time-of-flight neutron spectrometer. Several phonon bands were observed in the phonon spectrum at energies of about 33, 55, 82 and 99 meV. We show that the cut-off energy of the density-of-states occurs at around 105 meV which is much higher than expected so far from heat-capacity data and partially explains the high T _c value observed for MgB₂. The characteristic phonon energies are indicative of an intermediate coupling regime in this compound. We conclude that a much needed neutron experiment aimed at the study of the isotopic effect in the phonon density-of-states of MgB₂ is conceivable. Received 19 March 2001     

MgB2 thin film fabrication with excess Mg by sequential e-beam evaporation and transport properties under magnetic fields

Superconducting MgB₂ thin films with different thicknesses were fabricated by excess Mg using sequential electron beam evaporation technique. The flux rate of Mg and B were chosen as 3 nm/sn and 0.5 nm/sn respectively. The thickness of Mg/B layer was determined as 3/1 which causes an excess Mg for MgB₂ formation. After two-step preparation process, the superconducting transition temperatures were found in the range of 32–37 K with a sharp transition to zero resistance state. The irreversibility fields, upper critical fields and activation energies were derived from magneto resistivity curves. The transport critical current densities of films were determined from I–V characteristics under different applied fields and the data was extrapolated for determination of value of the 0 K.     

Superconductivity in two-band systems with a variable carrier density: The case of MgB<Subscript>2</Subscript>

A theory of the thermodynamic properties of a two-band superconductor with a low carrier density is developed; it is based on a phonon superconductivity mechanism with a strong electron-phonon coupling. This theory can describe the variation of the critical temperature T _c, the energy gaps Δ₁ and Δ₂, and the relative electronic specific heat jump (C _S ? C _N)/C _N at T = T _c with the carrier density in the compound MgB₂ when substitutional impurities of various valences are introduced into this system. The values of T _c, Δ₁, and Δ₂ are shown to decrease as this compound is doped by electrons and to remain constant (or almost constant) as it is doped by holes. This behavior follows from the mechanism of filling the σ and π energy bands, which overlap at the Fermi surface. The theory agrees qualitatively with experimental data. This agreement is found to be better when intra-and interband electron scattering by an impurity potential is taken into account.     

Multiple andreev reflections spectroscopy of superconducting LiFeAs single crystals: Anisotropy and temperature behavior of the order parameters

The superconducting state of LiFeAs single crystals with the maximum critical temperature T _c ≈ 17 K in the 111 family has been studied in detail by multiple Andreev reflections (MAR) spectroscopy implemented by the break-junction technique. The three superconducting gaps, Δ_Γ = 5.1–6.5 meV, Δ_L = 3.8–4.8 meV, and Δ_S = 0.9–1.9 meV (at T ? T _c), as well as their temperature dependences, have been directly determined in a tunneling experiment with these samples. The anisotropy degrees of the order parameters in the k space have been estimated as <8, ～12, and ～20%, respectively. Andreev spectra have been fitted within the extended Kümmel-Gunsenheimer-Nikolsky model with allowance for anisotropy. The relative electron-boson coupling constants in LiFeAs have been determined by approximating the Δ(T) dependences by the system of the two-band Moskalenko and Suhl equations. It has been shown that the densities of states in bands forming Δ_Γ and Δ_L are approximately the same, intraband pairing dominates in this case, and the interband coupling constants are related as λ_ΓL ≈ λ_LΓ ? λ_SΓ, λ_SL.     

Photoelectron spectra of substituted benzenes: II. Seven valence electron substituents

The He I photoelectron spectra of the isoelectronic series of substituted benzenes toluene, aniline, phenol, and fluorobenzene have been measured and the ionization bands in the low binding energy region of the spectra have been identified and assigned. The spectrum of pentafluoroaniline has also been obtained in order to use the “perfluoro effect” to identify the lowest energy σ ionization band. The photoelectron bands were assigned by using a “composite molecule” approach in which the known levels of benzene and the various substituents are correlated with those of the molecule, by using information supplied by vibrational analysis of the bands, and by reference to CNDO/2 and INDO MO calculations. The spectra of these composite molecules are consistent with the … 1a_2u(π), 3e_2g(σ), 1e_1g(π) MO configuration of benzene. The e_1g(π) orbital is split into two components in all of these substituted benzenes. Vibrational progressions in the ring CC stretching and the X-sensitive modes have been identified in these π ionization bands. Excitation of these two modes is evidence for delocalization of the π electrons over the composite molecule. The n (nonbonding) orbital of the substituents is shown to occur in the penultimate region along with the 1a_2u(π) and 3e_2g(σ) orbitals. The shifts in the n and π orbitals between the composite molecules and their constituent molecules are discussed in terms of resonance and inductive effects.     

Effects of competition between the anisotropy and the spin quantum number on the magnon energy gap in a four-layer ferromagnetic superlattice

The magnon energy bands are studied for a four-layer ferromagnetic superlattice, with regard to the effects of the competition between the anisotropy and the spin quantum number. A special attention is also paid on the effects of the symmetry of the system. It is found that three modulated energy gaps exist in the magnon energy band along K_x direction perpendicular to the superlattice plane. The magnetic anisotropy affects significantly the magnon energy gaps. The zero energy gap Δω₂₃ correlates with the conditions between anisotropy constants, D₁+D₃=D₂+D₄ and D₁=D₃ (or D₂=D₄), while the disappearance of the magnon energy gaps Δω₁₂ and Δω₃₄ corresponds to a translational symmetry of x-direction in a unit cell. When the parameters of the system deviate from these conditions, the energy gaps Δω₁₂, Δω₂₃ and Δω₃₄ become larger. There is a competition effect of the anisotropy and the spin quantum number on the magnon energy gaps Δω₁₂ and Δω₂₃. When the symmetry of the system is higher, the competition can achieve a balance to cause the zero energy gap.     

Memory switching of germanium tellurium amorphous semiconductor

The dc conductivity and switching properties of amorphous GeTe thin film of thickness 262 nm are investigated in the temperature range 303-373 K. The activation energy ΔE_σ, the room temperature electrical conductivity σ_RT and the pre-exponential factor σ₀ were measured and validated for the tested sample. The conduction activation energy ΔE_σ is calculated. The I-V characteristic curves of the thin film samples showing a memory switching at the turnover point (TOP) from high resistance state (OFF state) to the negative differential resistance state (NDRS) (ON state). It is found that the mean values of the threshold electrical field E_th decreased exponentially with increasing temperatures in the investigated range. The switching activation energy ΔE_th is calculated. Measurements of the dissipated threshold power P_th and the threshold resistance R_th were carried out at TOP point at different temperatures of the samples. The activation energies ΔE_R and ΔE_P caused by resistance and power respectively are deduced. The results obtained support thermal model for initiating switching process in this system.     

A tunneling spectroscopy study of the temperature dependence of the forbidden band in Bi2Te3 and Sb2Te3

Tunneling measurements of dI/dV, d ² I/dV ², and d ³ I/dV ³ were formed along the C ₃ axis (normally to layers) for Bi₂Te₃ and Sb₂Te₃ layered semiconductors in the temperature range 4.2<T>29 5 K. Temperature dependences of the forbidden band energy E _g were obtained. The forbidden band energy in Bi₂Te₃ was 0.20 eV at room temperature and increased to 0.24 eV at T=4.2 K. The E _g value for Sb₂Te₃ was 0.25 eV at 295 K and 0.26 eV at 4.2 K. The distance between the top of the higher valence band of light holes and the top of the valence band of heavy holes situated lower was found to be ΔE _V≈19 meV in Bi₂Te₃; this distance was independent of temperature. The conduction bands of Bi₂Te₃ and Sb₂Te₃ each contain two extrema with distances between them of ΔE _c≈25 and 30 meV, respectively.     

Characteristics electron energy loss studies of molecular halogens adsorbed on Fe(100)

The electron energy loss spectra for several molecular Br₂ monolayers adsorbed on a chemisorbed bromine overlayer on Fe(1 0 0) show a sharp loss at about 3.0 to 3.8 eV. For one or more molecular layers of I₂ adsorbed on a chemisorbed iodine overlayer on Fe (1 0 0), a sharp electron loss feature is observed at 4.4 ± 0.2 eV. It is suggested that the electron energy losses for condensed Br₂ at 3.0 eV and for condensed I₂ at 4.4 eV are a result of a 1π_g to 2σ_u electron excitation.     

Observation of multi-gap superconductivity in GdO(F)FeAs by Andreev spectroscopy

We have studied current-voltage characteristics of Andreev contacts in polycrystalline GdO_0.88F_0.12FeAs samples with bulk critical temperature T _c = (52.5 ± 1) K using break-junction technique. The data obtained can- not be described within the single-gap approach and suggests the existence of a multi-gap superconductivity in this compound. The large and small superconducting gap values estimated at T = 4.2 K are Δ _L = 10.5 ± 2 meV and Δ _s = 2.3 ± 0.4 meV, respectively.     

Interrelation of the critical magnetic field H c2 and the residual resistivity for the two-band superconductor MgB2

An expression that describes the upper critical magnetic field H _c2 and generalizes the Gor’kov relation has been derived for the two-band two-gap superconductor MgB₂. The expression relates the upper critical magnetic field H _c2 to the residual resistivity and the parameters of the band structure and holds in the range from the clean limit to the dirty limit. The ratios of the relaxation times τ_π/τ_σ and the mean free paths of π- and σ-band electrons for MgB₂ samples with a low defect level and Mg(B_{1 ? x} C _x )₂ samples with a partial substitution of carbon for boron are determined from experimental data.