Rigid Muffin-tin Approximation Research Articles

The effect of Ni doping on the electronic structure and superconductivity in the noncentrosymmetric ThCoC[formula omitted

ThCoC2 is a non-BCS, noncentrosymmetric superconductor with Tc≃2.5 K, in which pairing mechanism was suggested to be either spin fluctuations or the electron–phonon coupling. Earlier experimental work revealed that Tc can be greatly enhanced upon Ni doping in ThCo1−xNixC2, up to 12 K for x=0.4. In this work, using the Korringa–Kohn–Rostoker method with the coherent potential approximation (KKR-CPA), the evolution of the electronic structure upon Ni doping was studied and the increase of the density of states at the Fermi level was found. The electron–phonon coupling constant λ was calculated using the rigid muffin tin approximation (RMTA) and the increase in λ(x) was found. This indirectly confirms the electron–phonon coupling scenario as the trend in λ(x) is in qualitative agreement with the experiment when the electron–phonon pairing is assumed.

Pressure effects on the electronic structure and superconductivity of(TaNb)0.67(HfZrTi)0.33high entropy alloy

Effects of pressure on the electronic structure, electron-phonon interaction, and superconductivity of the high entropy alloy (TaNb)$_{0.67}$(HfZrTi)$_{0.33}$ are studied in the pressure range 0 - 100 GPa. The electronic structure is calculated using the Korringa-Kohn-Rostoker method with the coherent potential approximation. Effects of pressure on the lattice dynamics are simulated using the Debye-Gr\"{u}neisen model and the Gr\"{u}neisen parameter at ambient conditions. In addition, the Debye temperature and Sommerfeld electronic heat capacity coefficient were experimentally determined. The electron-phonon coupling parameter $\lambda$ is calculated using the McMillan-Hopfield parameters and computed within the rigid muffin tin approximation. We find, that the system undergoes the Lifshitz transition, as one of the bands crosses the Fermi level at elevated pressures. The electron-phonon coupling parameter $\lambda$ decreases above 10 GPa. The calculated superconducting $T_c$ increases up to 40 - 50 GPa and, later, is stabilized at the larger value than for the ambient conditions, in agreement with the experimental findings. Our results show that the experimentally observed evolution of $T_c$ with pressure in (TaNb)$_{0.67}$(HfZrTi)$_{0.33}$ can be well explained by the classical electron-phonon mechanism.

First-principles study of mechanical, thermodynamic, transport and superconducting properties of Sr3SnO

We have performed a comprehensive set of first-principles calculations to study mechanical, thermal, transport and superconducting properties of Sr3SnO, an antiperovskite Dirac-metal oxide. Sr3SnO cubic crystal is found to be elastically stable, anisotropic and brittle in nature. The Debye temperature and bulk modulus are found to decrease with increasing temperature but increase with increasing pressure. However, the specific heats are found to increase due to the increase of temperature. The Gaspari and Gyorffy formalism within the rigid muffin tin approximation is used to calculate the electron phonon coupling constant and hence transition temperature (Tc). The density of states is dominated by Sr-4d and Sn-5p electrons near the Fermi level and the mixing of Sr-4d and Sn-5p causes the topological superconductivity in Sr3SnO. The calculated Tc (8.38 K) is reasonably close to the experimental value (∼5 K).

Superconductivity of Ta34Nb33Hf8Zr14Ti11 high entropy alloy from first principles calculations

The Korringa–Kohn–Rostoker method with the coherent potental approximation (KKR‐CPA) is applied to study the first superconducting high entropy alloy (HEA) Ta34Nb33Hf8Zr14Ti11 (discovered in 2014 with Tc = 7.3 K), focusing on estimations of the electron–phonon coupling constant λ. The electronic part of λ has been calculated using the rigid muffin‐tin approximation (RMTA), while the phonon part has been approximated using average atomic mass and experimental Debye temperature. The estimated λ = 1.16 is close to the value determined from specific heat measurements, λ = 0.98, and suggests rather strong electron–phonon coupling in this material. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

Effect of the tetragonal distortion on the electronic structure, phonons and superconductivity in the Mo3Sb7 superconductor

Effect of tetragonal distortion on the electronic structure, dynamical properties and superconductivity in Mo3Sb7 is analyzed using first principles electronic structure and phonon calculations. Rigid muffin tin approximation (RMTA) and McMillan formulas are used to calculate the electron–phonon coupling constant λ and superconducting critical temperature. Our results show, that tetragonal distortion has small, but beneficial effect on superconductivity, slightly increasing λ, and the conclusion that the electron–phonon mechanism is responsible for the superconductivity in Mo3Sb7 is supported. The spin-polarized calculations for the ordered (ferromagnetic or antiferromagnetic), as well as disordered (disordered local moment) magnetic states yielded non-magnetic ground state. We point out that due to its experimentally observed magnetic properties the tetragonal Mo3Sb7 might be treated as noncentrosymmetric superconductor, which could have influence for the pairing symmetry. In this context the relativistic band structure is calculated and spin–orbit interaction effects are discussed.

Superconductivity in ordered LiBe alloy under high pressure: A first-principles study

The electronic, vibrational, and superconducting properties of LiBe alloy in the P2 1/m structure under pressure have been investigated using first-principles calculations. The calculated electron–phonon coupling (EPC) of LiBe with both linear response theory and the rigid muffin-tin approximation suggested that pairing electrons are mainly mediated by the Li low-lying phonon vibrations, and the increase of the Li EPC matrix element 〈 I i 2 〉 with pressure is responsible for the increased EPC parameter λ . The application of the Allen–Dynes modified McMillan equation reveals high superconducting critical temperatures of 15.2 K at 80 GPa and 18.4 K at 100 GPa for P2 1/m LiBe.

Interface two-dimensional metallicity but lack of superconductivity in heterobonded semiconductors: ZnS/Si and GaP/Si

As a follow up to our finding that CuCl/Si superlattices exhibit metallicity at the interfaces and possibly superconductivity, we explore other semiconductor superlattices for the same properties and present here our results for ZnS/Si and GaP/Si superlattices. As found for the CuCl/Si superlattices, both the ZnS/Si and GaP/Si superlattices exhibit two-dimensional metallicity at their interfaces, as shown by their band structures, Fermi surfaces, and charge-density distributions. Furthermore, to gauge any possible superconductivity, the McMillan-Hopfield electron-phonon coupling constant, , is calculated using the rigid muffin-tin approximation. Electron-phonon coupling is observed mostly at the interfaces but it is not strong enough to cause superconductivity at a finite temperature as estimated using the McMillan formula for Tc. This contrasts greatly with the CuCl/Si superlattices, in which electron-phonon coupling is strong enough to indicate superconductivity.

Electron–phonon coupling and spin fluctuations in 3d and 4d transition metals:implications for superconductivity and its pressure dependence

We have calculated the electron–phonon coupling for the complete 4d series and thenonmagnetic 3d transition metals using the linear response method and the linearmuffin-tin orbitals’ basis. A comparison of the linear response results and those obtainedvia the rigid muffin-tin approximation is provided. Based on the calculated values of theelectron–phonon coupling constants, band density of states and the measured values of theelectronic specific heat constants, we estimate the spin-fluctuation effects, i.e. theelectron–spin-fluctuation (electron–paramagnon) coupling constants in these systems. Forthe sake of comparison, several other metals, Cu, Zn, Ag, Cd, Al and Pb, are also studied.Alternative estimates of the electron–paramagnon coupling constants are obtainedfrom the values of the Stoner parameters and the band densities of states atthe Fermi level. Implications of these results on the superconductivity and itspressure dependence as well as the alloying effects of superconductivity in thesesystems are discussed. It is pointed out that spin fluctuations play an importantrole in the validity of the Matthias rule that in metallic systems the optimumconditions for (electron–phonon) superconductivity occur for 5 and 7 valenceelectrons/atom.

Interface electronic structure, two-dimensional metallicity, and possible interface superconductivity inCuCl∕Sisuperlattices

Results of highly precise all-electron full-potential linearized augmented plane wave density functional calculations demonstrate (i) two-dimensional metallicity, and (ii) possible superconductivity in $\mathrm{Cu}\mathrm{Cl}∕\mathrm{Si}$ superlattices for [111] and [001] directions. The feature of two-dimensional (2D) metallicity arises from the charge transfer at the interfaces between CuCl and Si, where there is the valence charge imbalance. The 2D features are well evidenced by band structure, Fermi surfaces, and charge densities. Furthermore, to investigate possible superconductivity, we use McMillan [Phys. Rev. 167, 331 (1968)] formula to estimate ${T}_{C}$, and evaluate the electron-phonon coupling constant, $\ensuremath{\lambda}$, using the rigid muffin-tin approximation. From our calculations, it is the interfaces that contribute to all intriguing physics: 2D metallicity, charge transfer, nonvanishing Hopfield [Phys. Rev. 186, 443 (1969)] parameter, and electron-phonon coupling. Moreover, our ${T}_{C}$ estimations $(0.03--4.40\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ reveal that the electron-phonon coupling is too weak to account for the high ${T}_{C}$ $(60--150\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ suggested in early experiments.

Pressure-induced enhancement of electron-phonon coupling in superconductingCaC6from first principles

The pressure effects on the electron-phonon coupling (EPC) in superconducting $\mathrm{Ca}{\mathrm{C}}_{6}$ have been extensively studied using first-principles calculations within the rigid muffin-tin approximation. It is found that pairing electrons are mainly attributed to the Ca $3d$ electrons mediated by Ca low-lying, in-plane phonon vibrations. An increase in mean square of the EPC matrix element $⟨{I}^{2}⟩$ and a decrease in Ca low-lying phonon frequency with increasing pressure are mainly responsible for the experimental observation of enhanced superconducting transition temperature. Furthermore, Mulliken population analysis suggests that the pressure-induced charge transfers from Ca to the graphite layers might mainly contribute to the softening behavior of Ca in-plane phonons.

Electronic structure and superconductivity of CaAlSi and SrAlSi

We report full-potential linear augmented plane-wave calculations for CaAlSi and SrAlSi in ordered structures and in the virtual-crystal approximation, at normal and elevated pressures. We also estimate the electron-phonon coupling using frozen-phonon calculations at the zone center, and the rigid muffin-tin approximation. We conclude that there is no simple way to explain the recently reported qualitative disparity in the superconducting properties of the two compounds. An assumption of an ultrasoft phonon mode, on the other hand, allows to reconcile the experimental findings with the theory in a reasonable way.

Pressure dependence of electron-phonon coupling and superconductivity in hcp Fe: A linear response study

A recent experiment by Shimizu et al. has provided evidence of a superconducting phase in hcp Fe under pressure. To study the pressure-dependence of this superconducting phase we have calculated the phonon frequencies and the electron-phonon coupling in hcp Fe as a function of the lattice parameter, using the linear response (LR) scheme and the full potential linear muffin-tin orbital (FP-LMTO) method. Calculated phonon spectra and the Eliashberg functions $\alpha^2 F$ indicate that conventional s-wave electron-phonon coupling can definitely account for the appearance of the superconducting phase in hcp Fe. However, the observed change in the transition temperature with increasing pressure is far too rapid compared with the calculated results. For comparison with the linear response results, we have computed the electron-phonon coupling also by using the rigid muffin-tin (RMT) approximation. From both the LR and the RMT results it appears that electron-phonon interaction alone cannot explain the small range of volume over which superconductivity is observed. It is shown that ferromagnetic/antiferromagnetic spin fluctuations as well as scattering from magnetic impurities (spin-ordered clusters) can account for the observed values of the transition temperatures but cannot substantially improve the agreeemnt between the calculated and observed presure/volume range of the superconducting phase. A simplified treatment of p-wave pairing leads to extremely small ($\leq 10^{-2}$ K) transition temperatures. Thus our calculations seem to rule out both $s$- and $p$- wave superconductivity in hcp Fe.

Soft modes and superconductivity in the layered hexagonal carbidesV2CAs,Nb2CAs,andNb2CS

The electronic structure, selected phonon frequencies, and electron phonon coupling of the hexagonal layered compounds Nb 2 CS, Nb 2 CAs, and V 2 CAs are elucidated using density functional calculations. All materials are good three-dimensional metals with moderate values of the density of states, N(E F ). The electronic structure of Nb 2 CS, the only superconductor within this family of materials, consists of well-hybridized Nb d-S p-C p derived bands characteristic around the Fermi energy. The S is more ionic in this compound than the As in the related arsenides Nb 2 CAs or V 2 CAs. This results in a relative softness for phonon modes involving S. Rigid muffin tin approximation calculations show moderate electron phonon couplings consistent with low-temperature superconductivity. The key difference from the carbo-arsenides is the presence of soft moderately coupled S modes.

Calculation of the electron-ion interaction-potential components linear and quadratic in the ion displacements for YBa2Cu3O7

A simple method is proposed to calculate the component of electron interaction potential with the ionic subsystem of a crystal quadratic in ionic displacement. The electron-ion interaction potential is calculated for the high-frequency Ag modes in YBa2Cu3O7. The important role of the Madelung potential, which results in violation of the selection rules valid in the rigid muffin-tin approximation, is pointed out. The quadratic component of the potential can greatly affect the calculated matrix elements which correspond to electronic transitions involving absorption or emission of zero wave-vector phonons.

Electronic structure of the BaA 1- xB xO 3 (A, B = Pb, Bi, Sn, Sb) alloy systems : Implications for superconductivity

Coherent potential approximation studies of the electronic structure of the BaA 1- x B x O 3 (where A and B are different combinations of the elements Pb, Bi, Sn and Sb) alloy systems have been performed with accurate tight-binding hamiltonians. The calculations show how semiconducting BaSnO 3 evolves into a metal upon alloying with Sb or Bi. Common characteristics of the densities of states are pointed out. Using the rigid muffin-tin approximation an analysis of the superconducting properties is given.

Nonspherical rigid-muffin-tin calculations of electron-phonon coupling in high-Tcperovskites

The Hopfield factor (electronic part of the electron-phonon coupling constant) is calculated in the rigid-muffin-tin approximation (RMTA) for several perovskite high-${\mathit{T}}_{\mathit{c}}$ superconductors. Calculations were performed in the conventional ``spherical'' approximation and take into account the proper local symmetry. It is shown that the layered perovskite crystal symmetry generally favors strong electron-phonon interaction on the copper sites. We also estimate some non-RMTA effects.

Possiblity of LiPdHx as a new ionic superconductor.

We report local-density-approximation-based electronic-structure calculations for the compound LiPdH. As in the case of the recently discovered family of CuO{sub 2}-based superconductors, LiPdH{sub {ital x}} is predicted to be a metal with substantial ionic character. We have used the band-structure results to calculate the McMillan-Hopfield parameters within the rigid muffin-tin approximation. These parameters have values close to those of PdH and lead to the prediction that LiPdH{sub {ital x}} may be a good superconductor.

Influence of local symmetry on the electron-phonon coupling in perovskites

The Hopfield factor (electronic part of the electron-phonon coupling constant) is calculated in the Rigid-Muffin-Tin approximation (RMTA) for several perovskite high-Tc superconductors. Calculations were performed in the conventional “spherical” approximation, as well as taking into account proper local symmetry. It is shown that the layered perovskite crystal symmetry generally favors strong electron-phonon interaction on copper site. We also estimate some for non-RMTA effects.

Electronic structure, photoemission, inverse photoemission, and x-ray emission spectra of superconducting Ba1-xKxBiO3.

The electronic structure of ${\mathrm{BaBiO}}_{3}$ is calculated by using the full-potential linearized augmented-plane-wave method in the local-density approximation, and the alloying effect of K additions is considered using the simple rigid-band model. The electron-phonon mechanism for the superconductivity is discussed within the rigid muffin-tin approximation. In this context, the difference of the electronic structure from the cuprate high-${T}_{c}$ materials is elucidated in detail. Photoemission, inverse photoemission, and x-ray emission spectra are compared with experiment to check the validity of the single-particle picture for these excitations.

Evaluation of the electron-phonon interaction and transition temperature in the oxide superconductors

The Allen-Dynes equation applicable to the oxide superconductors is studied, which shows that for moderate values of the electron-phonon coupling constant the superconducting transition temperature is found in the range of 100 K. This result is based on an approximate evaluation of large values of the McMillan-Hopfield parameter and evidence from frozen-phonon calculations that strong ionic character in the copper oxide superconductors invalidates the rigid muffintin approximation.