Isotope Effect Exponent Research Articles

Quantifying Actinide HEA Superconducting Secrets: A Compositional Odyssey

The superconductivity in the actinide-based high entropy alloy superconductor (AHEASC) (TaNb)x(TiUHf)[Formula: see text] is studied in the framework of Bardeen–Cooper–Schrieffer (BCS) theory, and McMillan’s formalism has been studied for the investigation of superconducting state (SC) parameters, viz., Coulomb pseudopotential [Formula: see text], electron–phonon coupling strength [Formula: see text], SC transition temperature [Formula: see text], interaction strength [Formula: see text], band gap [Formula: see text], energy or mass renormalization parameter [Formula: see text], and isotope effect exponent [Formula: see text]. BCS theory in conjunction with McMillan’s formalism has been used for the investigation. The study indicates a strong correlation between the electron–phonon interaction, and the superconducting properties of the high entropy alloy (TaNb)x(TiUHf)[Formula: see text] are highly dependent on its composition. An abrupt change in the isotope effect exponent suggests the presence of additional mechanisms such as magnetic interactions, spin fluctuations, or strong electron correlations.

Effect of the plasmon mechanism on s-wave superconductors under high pressure in the weak-coupling limit

In this research, we investigated the critical temperature (TC), gap-to-TC ratio (2ΔTC) and isotope effect exponent (α) of s-wave superconductors under high-pressure envelopments, including the electron-phonon interaction and electron-Plasmon attractive interaction in the weak-coupling limit. The analytic formula of TC, 2ΔTC and α with non-pressure and under pressure cases were used. The numerical calculations showed that the under-pressure case had a greater critical temperature than the non-pressure case. The effect of pressure had a significant impact on the gap-to-TC ratio, and the isotope effect exponent exhibited a range between 0.30 and 0.75.

Theoretical study of superconducting parameters of Al and Li Co-doping substitution on MgB2

In the present study we investigated the theoretical calculation of Superconducting state parameters by Al as electron doping and Li as hole co-doping on MgB2 superconductor for four different concentrations (Mg0.962Al0.018Li0.02B2, Mg0.854Al0.096Li0.05B2, Mg0.812Al0.138Li0.05B2, Mg0.77Al0.14Li0.09B2). The well-known Empty Core (EMC) model of Ashcroft potential was used to study the theoretical investigation of the superconducting state parameters (SSP) viz. Electron–Phonon Coupling Strength (λ), Coulomb Pseudopotential (µ*), Transition Temperature (Tc), Isotope Effect Exponent (α) and Effective Interaction Strength (N0V) of Mg1-x-yAlxLiyB2 system. It is observed that addition of Al & Li doping to superconductor MgB2 causes the parameters λ, Tc, α and N0V decreases. This suggests decrease in superconducting behaviour of MgB2 is due to effect of Al and Li co-doping in MgB2 which also shows strong coupling to intermediate coupling behaviour. Whereas Coulomb Pseudopotential (µ*) remains approximately same. In this paper it is also observed that Transition Temperature (Tc) for Mg1-x-yAlxLiyB2 alloys for different concentration is almost same with the experimental values.

Analysis of the superconductivity in perovskite oxides using three-square-well BCS formalism

Superconductivity in perovskite, BaKBiO, is studied in the Bardeen–Cooper–Schrieffer (BCS) model, with three-square-well potentials. Components of the new coupling are: the attractive acoustic phonon–electron, optical phonon–electron and repulsive Coulomb interactions. With these in the BCS pairing Hamiltonian, expressions for the superconducting transition temperature and isotope effect exponent are obtained. Results of our analysis are consistent with experiments. Contributions of interactions to system properties are exhibited and analysed. Acoustic phonon–electron and optical phonon–electron interactions have near-identical elevation of transition temperature, holding out possible explanations for high- Tc. Contrastingly, optical phonon–electron and Coulomb couplings cause debilitation of isotope exponent, a possible explanation for low isotope exponent in the cuprates and other high- Tc systems. It is found that BCS electron–phonon coupling appears synonymous with acoustic phonon–electron coupling.

Boron isotope effect in single crystals of superconductor

The influence of local moment magnetism on the boron isotope effect of was studied on single crystals of . Values of the partial isotope effect exponent of and were obtained based on two different criteria applied to extract . No significant change in the partial isotope effect exponent compared to the ones obtained for was observed. Based on this result, we conclude that pair-breaking due to the Er local magnetic moment appears to have no detectable influence on boron isotope effect of .

Theoretical Analysis of Isotope Effect Exponent of Diboride and Iron-Based Superconductors: Three-Square-Well Model Approach

Analytical calculations of isotope effect exponent of both s-wave and π-phase-shifted s-wave two-band superconductors are presented within the framework of Bogoliubov–Valatin formalism using three-square-well model approach. The effective pairing interaction consists of contributions from the attractive acoustic electron–phonon, optical electron–phonon contributions in addition to repulsive electron–electron or antiferromagnetic fluctuation mediated pairing contributions for the diboride or pnictide superconductors, respectively. These are used to obtain analytical results that are applied in studying the isotope effect exponent in the diboride and pnictide superconductors, and the results are compared with experimental data.

Phonon-induced superconductivity and physical properties in intercalated fullerides Rb3C60

The nature of electron pairing mechanism and physical properties leading to superconducting state and normal state resistivity in alkali metal (Rb) intercalated fullerenes are explored. Keeping in mind that free electrons in lowest molecular orbital are coupled with inter-molecular phonons, the coupling with inter-molecular phonon leads to transition temperature (Tc) of about 4.17 K. The electrons also couple with the intra-molecular phonons. Within the framework of strong coupling theory, Tc is estimated at 34 K. The carbon isotope effect exponent, the energy gap ratio, influence of pressure and volume on Tc, and thermodynamical parameters describing the superconducting state confer that Rb3C60 as s-wave superconductor. Estimated contribution to resistivity using scattering with inter- and intra-molecular phonon, when subtracted from single crystal data, infers quadratic temperature dependence over most of the temperature range and is attributed to electron–electron inelastic scattering. Both low frequency intermolecular and high frequency intra-molecular phonons have significant bearing in Rb3C60 superconductor.

The superconducting state parameters of glassy superconductors

We present theoretical investigations of the superconducting state parameters (SSPs), i.e. the electron–phonon coupling strength, λ, Coulomb pseudopotential, μ*, transition temperature, Tc, isotope effect exponent, α, and effective interaction strength, N0V, of glassy superconductors by employing Ashcroft's well know empty core model potential for the first time using five screening functions proposed by Hartree (H), Taylor, Ichimaru–Utsumi (IU), Farid et al and Sarkar et al. The Tc obtained from the H and IU screening functions is found to be in excellent agreement with available experimental data. Also, the present results confirm the superconducting phase in bulk metallic glass superconductors. A strong dependency of the SSPs of the glassy superconductors on the ‘Z’ valence is found.

Influence of linear-energy-dependent density of states on two-band superconductors: Three-square-well model approach

We have derived the expressions for the transition temperature and the isotope effect exponent within the framework of Bogoliubov–Valatin two-band formalism using a linear-energy-dependent electronic density of states assuming a three-square-well potentials model. Our results show that the approach could be used to account for a wide range of values of the transition temperature and isotope effect exponent. The relevance of the present calculations to MgB2 is analyzed.

Intrinsic and structural isotope effects in iron-based superconductors

The currently available results of the isotope effect on the superconducting transition temperature T_c in Fe-based high-temperature superconductors (HTS) are highly controversial. The values of the Fe isotope effect (Fe-IE) exponent \alpha_Fe for various families of Fe-based HTS were found to be as well positive, as negative, or even be exceedingly larger than the BCS value \alpha_BCS=0.5. Here we demonstrate that the Fe isotope substitution causes small structural modifications which, in turn, affect T_c. Upon correcting the isotope effect exponent for these structural effects, an almost unique value of \alpha~0.35-0.4 is observed for at least three different families of Fe-based HTS.

The study of superconducting state parameters of In1 − x Tl x binary alloys by pseudopotential theory

The study of the superconducting state parameters (SSP) viz. electron-phonon coupling strength In1 − x Tl x , Coulomb pseudopotential μ*, transition temperature T C , isotope effect exponent and effective interaction strength of N 0 V of In1 − x Tl x (0 < x < 1) binary alloys have been made extensively in the present work using a model potential. A considerable influence of various exchange and correlation functions on λ and μ* is found from the present study. The present results of the SSP are found in qualitative agreement with the available experimental or theoretical data wherever exist.

Superconducting state parameters of Ag x Zn1 − x and Ag x Al1 − x binary alloys superconductors

A well-known pseudopotential is used to investigate the superconducting state parameters (SSP), viz., electronphonon coupling strength, Coulomb pseudopotential, transition temperature, isotope effect exponent and effective interaction strength for AgxZn1 − x and AgxAl1 − x binary alloys theoretically for the first time. We have incorporated here five different types of the local field correction functions to show the effect of exchange and correlation on the aforesaid properties. Very strong influence of various exchange and correlation functions is concluded from the present study. Comparison with others such experimental values is encouraging, which confirms applicability of the model potential in explaining the superconducting state parameters of binary mixture.

INTERMEDIATELY COUPLED PHONON AND CHARGE FLUCTUATION INDUCED SUPERCONDUCTIVITY IN MgB2 PROBED BY A THREE SQUARE WELL APPROACH

A three square well model is developed, which allows one to easily calculate the correlation between the coupling strength parameters and superconducting transition temperature (T c ), pressure and volume derivative of T c and isotope effect exponent for MgB 2. Upon considering the three interactions, namely, electron-phonon, electron-plasmon and Coulomb, the analytical solutions for the energy gap equation allow us to understand the relative interplay of these interactions. The values of the coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the intermediate coupling regime. The superconducting transition temperature of MgB 2 for the 2D band is estimated as 41 K for [Formula: see text] and μσ*≈0.28. We present correlation curves of T c with various coupling strengths as electron-phonon [Formula: see text], electron-plasmon [Formula: see text] and the Coulomb screening parameter (μσ*). The present approach also explains the reported boron isotope effect and the pressure derivative of T c in the test material. We suggest from these results that both the plasmons and phonons within the framework of a three square well scheme consistently explain the effective electron-electron interaction leading to superconductivity in MgB 2. The implications of the effective interactive potential with both σ and π carriers and its analysis are discussed.

Screening dependence of superconducting state parameters of Cu–Zr binary metallicglasses

Screening dependence investigations of the superconducting stateparameters (SSP), namely the electron–phonon coupling strengthλ, Coulomb pseudopotentialμ*, transition temperatureTC, isotope effectexponent α and effectiveinteraction strength NOV of ten binary CuCZr100−C (C = 0.25,0.30,0.33,0.35,0.40,0.45,0.50,0.55,0.57 and 0.60) metallic glasses have been reported using Ashcroft’s empty core (EMC)model potential. Five local field correction functions proposed by Hartree(H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al (F) and Sarkar et al (S)are used in the present investigation to study the screening influence on theaforesaid properties. It is observed that the electron–phonon coupling strengthλ and the transitiontemperature TC are quite sensitive to the selection of the local field correction functions, whereas the Coulomb pseudopotentialμ*, isotope effectexponent α and effectiveinteraction strength NOV show weak dependences on the local field correction functions. TheTC obtained from the H-local field correction function is found to be in qualitative agreement withavailable theoretical or experimental data and shows an almost linear nature with the concentrationC of the elementCu. A linear TC equation is proposed by fitting the present outcomes for the H-local field correctionfunction, which is in conformity with other results for the experimental data.Also, the present results are found to be in qualitative agreement with other suchdata earlier reported, which confirms the superconducting phase in the metallicglasses.

Isotope effect in cuprates: A competition between Coulomb and phonon-mediated pairing

There are asymmetric and symmetric solutions of the self-consistency equation which takes into account both screened Coulomb and phonon-mediated pairing interactions. The first of them leads to the order parameter with a nodal line and, in the case of pairing with large momentum, exists at any repulsive and attractive strengths. The second one arises if the attraction exceeds a level depending on the repulsion strength and dominates the pairing in the strong attraction limit. The competition of attraction and repulsion results in unusual isotope-effect exponent observed in the cuprates.

Effect of interband interaction on isotope effect exponent of MgB2 superconductors

The exact formula of Tc’s equation and the isotope effect exponent of two-band s-wave superconductors in the weak-coupling limit are derived by considering the influence of interband interaction. In each band, our model consists of two pairing interactions: the electron-phonon interaction and non-electron-phonon interaction. We find that the isotope effect exponent of MgB2, α = 0.3 with Tc ≈ 40 K can be found in the weak coupling regime and interband interaction of electron-phonon shows more effect on the isotope effect exponent than on the interband interaction of non-phonon.

Effect of density of state on isotope effect exponent of two-band superconductors

The exact formula of T c’s equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of two kinds of density of state: constant and van Hove singularity. The paring interaction in each band consisted of two parts: the electron–phonon interaction and non-electron–phonon interaction are included in our model. We find that the interband interaction of electron–phonon show more effect on isotope exponent than the intraband interaction and the isotope effect exponent with constant density of state can fit to experimental data, MgB 2 and high- T c superconductor, better than van Hove singularity density of state.

Effect of local field correction in screening dependence of superconducting state parameters for Be90Al10 and Be70Al30 metallic glasses

AbstractThe superconducting state parameters (SSP) viz. electron–phonon coupling strength (λ), Coulomb pseudopotential (μ*), transition temperature (Tc), isotope effect exponent (α) and interaction strength (N0V) for two metallic glasses, i.e. Be90Al10 and Be70Al30, have been investigated by extending the BCS–Eliasberg–McMillan formalism for the metallic glass superconductors incorporating the effect of local field correction in dielectric screening functions which in turn become prominent in determining superconducting state parameters of the metallic glasses under consideration. We have employed eleven forms of dielectric screening functions – viz. Hartree, RPA, Modified Hubbard, Overhauser, Geldart–Vosko, Animalu, King–Cutler, SCS, Vashistha–Singwi, Ichimaru–Utsumi, and Farid et al. – in conjunction with Ashcroft's potential to predict superconducting state parameters. It is observed that the values of SSP are quite sensitive to the form of dielectric screening functions. In conclusion the present computed values of SSP for the RPA form of dielectric screening are in good agreement with the experimental values and other theoretical results for both glassy materials, which confirms the validity of the proposed formalism. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Crossover from phonon-mediated to repulsion-induced superconducting pairing with large momentum

There are asymmetric and symmetric solutions of the self-consistency equation which takes into account both phonon-mediated and Coulomb pairing interactions. The first of them leads to the order parameter with a nodal line and, in the case of pairing with large momentum, exists at any repulsive and attractive strengths. The second one arises if the attraction exceeds a level depending on the repulsion strength and dominates the pairing in the strong attraction limit. The competition of attraction and repulsion results in unusual isotope-effect exponent observed in the cuprates.

Interpretation of the temperature-dependent resistivity ofK3C60 fulleride superconductors: an electron–phonon mechanism

The temperature-dependent normal state resistivity of single crystalK3C60 is theoretically analysed within the framework of the electron–phonon model ofresistivity, i.e., the Bloch–Gruneisen model. Keeping in mind that a largeamount of impurities develop due to the doping of alkali metal in pureC60, zerotemperature limited resistivity has first been estimated. Due to the inherent intermolecular phonon(ωer) andintramolecular (ωra) phonon, the contributions to the resistivity have been estimated as a next step. Theintramolecular phonon yields a relatively larger contribution to the resistivitycompared to the contribution of intermolecular phonons above 260 K. In addition,below this temperature, the intermolecular phonon is a major source of resistivity.The estimated contribution to resistivity when subtracted from single crystaldata infers a quadratic temperature dependence till 200 K and there exists adeparture until near room temperature. The power temperature dependence ofρdiff = [ρexp−{ρ0+ρe−ph (= ρer+ρra)}] may be attributed to the contribution of the three dimensional transport mechanismand has been related to electron–electron interaction. We then emphasizedthe role of intramolecular phonons to estimate the transition temperatureTc, carbon isotopeeffect exponent α and pressure as well as the volume derivative ofTc and the results are consistent with the reported data. It therefore appears that bothelectron–electron and electron–phonon interaction play an important role in retracing thenormal state resistivity behaviour and some of the superconducting state properties.