Electron-phonon Interaction Properties Research Articles

Investigation of superconductivity of A15 type cubic Nb3Os material by using density functional theory

In this study, the structural, elastic, electronic, phonon and electron-phonon interaction properties of A15 type cubic Nb3Os compound were investigated by density functional theory. The lattice constant of this compound was obtained in agreement with experiments, and the investigation of elastic properties revealed its ductile nature. From electronic calculations for Nb3Os, the density of states at Fermi level (N(EF)) was found to be 5.31 states/eV with the largest contribution of Nb 4d orbitals. According to the results obtained from phonon calculations, Nb3Os was found to be dynamically stable in the cubic A15 structure and phonon modes were largely formed by the vibrations of Nb atoms. Using the electronic and phonon properties, we determined the Eliashberg spectral function, which illustrates the electron-phonon interaction. The electron-phonon interaction parameter and average phonon frequency values for Nb3Os were found to be 0.41 and 222.97 K, respectively. The calculated superconducting transition temperature of 1.05 K is in excellent agreement with the experimental value of 1.02 K.

The Influence of Spin‐Orbit Interaction on the Electron‐Phonon Coupling in Tl‐Rich Cubic AuCu3‐Type Superconductors: Comparison with La3Tl

AbstractIn this work, the role of spin‐orbit coupling (SOC) in ATl3 (A = Ca, Y, La, and Th) and La3Tl is investigated by theoretical investigation of their structural, electronic, elastic, mechanical, phonon, and electron–phonon interaction properties. The effect of SOC on the electronic band structures of these compounds is that some of the degeneracies at the high symmetry points that would exist in a scalar relativistic calculation without SOC are removed by considering this coupling. The replacement of La and Tl atoms in LaTl3 increases the value of the density of states at the Fermi level N() by a factor of 2.1. Furthermore, this replacement makes almost all phonon modes in La3Tl softer than those in LaTl3. Both softer phonon modes and higher N() make the electron–phonon interaction in La3Tl much stronger than in LaTl3. The presence of SOC increases the values of LaTl3 by 34% (from 1.151 to 1.542 K) and of ThTl3 by 65% (from 0.479 to 0.793 K), resulting in good agreement with the corresponding experimental values of 1.63 and 0.87 K. The inclusion of SOC also improves the agreement with the experiment for values of CaTl3, YTl3, and La3Tl.

Role of spin–orbit coupling on the physical properties of APb[formula omitted] (A = Na, Ca, Y, and Th) superconductors

Structural, electronic, elastic, mechanical phonon and electron–phonon interaction properties of APb3 (A = Na, Ca, Y, and Th) superconductors have been investigated by using the density functional theory and the spin–orbit coupling (SOC) effects. It is found that the inclusion of SOC leads to significant changes in the electronic band structure of all the investigated compounds while the changes in the phonon properties essentially depend on the type of A atoms. While the phonon dispersion curves of YPb3 and ThPb3 are only weakly influenced, the inclusion of SOC produces significant amount of softening in the phonon dispersion curves for NaPb3 and CaPb3. Similarly, while the inclusion of SOC only weakly affects the electron–phonon interaction in YPb3 and ThPb3, it increases the electron–phonon coupling parameters in NaPb3 and CaPb3 by 27% and 33%, respectively. From the calculated elastic constants and related mechanical properties, all the superconductors studied are found to be ductile, which is favorable for their technological applications.

The effect of the spin–orbit coupling on the physical properties of ScGa[formula omitted] and LuGa[formula omitted] superconductors

In this work, we have aimed to reveal the impacts of spin–orbit coupling (SOC) on the elastic, mechanical, electronic, phonon, and electron–phonon interaction properties of ScGa3 and LuGa3 by executing both scalar and full-relativistic ab initio pseudopotential calculations based on the density functional theory with its local density approximation. The effect of this coupling on the physical properties of LuGa3 is slightly more pronounced than those of ScGa3. This finding has a physical explanation because spin–orbit interaction in an atom is due to the interaction of electronic spin moment with the magnetic field formed by the traveling electron in the electric field of the nucleus. Since the nuclear charge enhances with the rise in atomic number of the elements, heavier atoms are characterized by larger SOC strength and the mass of Lu atom is considerably heavier than that of Sc atom. In particular, the inclusion of SOC changes the value of the electron–phonon coupling parameter for LuGa3 from 0.593 to 0.583 by less 2%, while the corresponding parameter of ScGa3 remains almost unchanged (from 0.536 to 0.537). The superconducting transition temperature is estimated to be 2.09 K for ScGa3, and 2.15 K for LuGa3 are almost equal to their experimental values of 2.1 and 2.2 K, respectively. Finally, we have estimated three superconducting parameters: the Ginzburg–Landau parameter (κ(0)), the London penetration depth (λL(0)) and the coherence length (ξ(0)). Their calculated values confirm the existence of type-I superconductivity in both superconductors.

The effect of spin–orbit coupling on the physical and superconducting properties of the Ir-rich cubic Laves superconductors AIr[formula omitted] (A = Y, Lu, and Th)

We have examined the impact of spin–orbit coupling (SOC) in cubic Laves superconductors AIr2 (A = Y, Lu, and Th) by realizing ab initio pseudopotential calculations of their physical and electron–phonon interaction properties. The inclusion of SOC removes the degeneracy of the electronic states and moderately influences the elastic and mechanical properties of all the compounds investigated. A critical examination of the elastic and mechanical properties reveals that all the compounds studied are soft (ductile) because of significant metallic bonding. The SOC effect on the phonon and electron–phonon interaction properties depends on the type of A element. This coupling has little influence on the phonon properties of YIr2. However, differently from YIr2, three optical phonon branches of LuIr2 and ThIr2 originating from the triply degenerate zone-center T2u mode are significantly affected by the inclusion of SOC. Although the effect of SOC on the electron–phonon interaction properties changes with the type of A atom, the presence of this coupling improves the agreement with experiment for the superconducting transition temperatures of all the cubic Laves superconductors investigated.

Physical properties and superconductivity in the cubic A15-type Ta[formula omitted]Ge compound: A first principles study

In this theoretical study, we have targeted to present the characteristic features of the superconductivity in the cubic A15-type compound Ta3Ge by investigating its structural, electronic, elastic, mechanical, phonon, and electron–phonon interaction properties in detail. A critical examination of elastic moduli of Ta3Ge reveals that it is soft (ductile) due to significant metallic bonding. A critical surveying of electronic density of states reveals that Ge electronic states make negligible additive to the main valence band region of Ta3Ge while its transition metal d states dominate this region. An examination of our phonon results indicate that the low-frequency optical phonon branches and three acoustic phonon branches of Ta3Ge are mainly dominated by the vibrations of Ta atoms. Thereby, their d states and their vibrations become the main actors of the transition from the normal state to the superconducting state for Ta3Ge. From the integration of the Eliashberg spectral function of Ta3Ge, the values of average electron–phonon coupling parameter and logarithmically averaged phonon frequency are found to be 1.08 and 123.05 K, respectively, producing its superconducting temperature Tc = 8.3 K, being in good accordance with the experimental value of 8.0 K.

First-principles calculations of physical properties and superconductivity of orthorhombic Mo2BC and Nb2BN

Ab initio pseudopotential calculations have made for the structural, electronic, elastic, mechanical, and electron–phonon interaction properties of molybdenum borocarbide (Mo2BC) and niobium boronitride (Nb2BN) superconductors. Analysis of the structural and electronic properties reveals that the nature of bonding in both these compounds is a combination of covalent, ionic, and metallic. The near-Fermi electronic states in both compounds are occupied by the d states of transition metal atoms. The electronic density of states at the Fermi level in Mo2BC is significantly higher than that in Nb2BN. Lattice dynamical calculations verify their dynamical stability in the base-centered orthorhombic Mo2BC-type crystal structure. We find that the total electron–phonon coupling constant is equal to 0.745 for Mo2BC and 0.539 for Nb2BN. The calculated superconducting transition temperature of 7.41 K for Mo2BC and 3.50 K for Nb2BN is comparable with their experimental values of 7.2 and 4.4 K, respectively.

Elucidating the underlying mechanism of relatively high T c value of the orthorhombic MoRuP: a first-principles study

ABSTRACT In this paper, the structural, electronic, elastic, mechanical, phonon and electron-phonon interaction properties of orthorhombic MoRuP have been analysed by using the generalised gradient approximation of the density functional theory and the plane-wave pseudopotential method. An examination of elastic constants and elastic moduli indicates that the orthorhombic MoRuP is mechanical stable and ductile. A critical assessment of electronic structure and electronic density of states implies that the electronic states in the vicinity of the Fermi level are mostly composed of the 4d states of the molybdenum atoms in MoRuP. A comparison of Eliashberg spectral function with electronic and phonon density of states reveals that the mechanism behind the superconductivity for the orthorhombic MoRuP is the coupling of Mo 4d electrons with Mo-related lattice vibrations. The integration of Eliashberg spectral function gives the electron-phonon coupling parameter of MoRuP to be 0.98, implying that the orthorhombic MoRuP belongs to the conventional BCS-type superconductors with strong coupling. Finally, the value of superconducting transition temperature for MoRuP amounts to 16.5 K, harmonising with the experimental value of 15.5 K.

Probing the physical and superconducting properties of hexagonal ZrRuAs: A first-principles calculation

In the presented work, ab initio pseudopotential calculations have been realized on structural, electronic, elastic, mechanical, phonon and electron-phonon interaction properties for ZrRuAs with the hexagonal ZrNiAl-type layer crystal structure. In the vicinity of the Fermi level, Ru 4d and Zr 4d states dominate and mainly contribute to the conduction properties of ZrRuAs. A critical assessment of elastic and mechanical properties for ZrRuAs reveals that, this superconductor is soft (ductile) due to remarkable metallic bonding. Phonon anomalies have been observed in the phonon spectrum of ZrRuAs for the lowest transverse acoustic branch and low-frequency transverse optical branches along the Γ-K and Γ-M-K symmetry directions. Our electron-phonon interaction calculations indicated that ZrRuAs is a conventional phonon-mediated superconductor with strong electron-phonon coupling parameter of 1.32. The strong electron-phonon coupling parameter of ZrRuAs produces its superconducting transition temperature to be 11.12 K which accords nicely with its experimental values of 12 K.

A first-principles investigation of physical properties and superconductivity of NbPS

This study reports a theoretical examination of the structural, elastic, mechanical, electronic, phonon and electron–phonon interaction properties of the body-centered orthorhombic structure of NbPS by using the generalized gradient approximation of the density functional theory and the planewave ab initio pseudopotential method. An analysis of the elastic and mechanical properties reveals ductile nature of this compound. The electronic density of states at the Fermi energy is heavily contributed by d orbitals, revealing a more active role for transition metal Nb atoms in determining the lattice dynamical as well as the superconducting properties of NbPS. The phonon spectrum is characterized by anomalies in the lowest acoustic and lowest optical branches which are dominated by the vibrations of Nb atoms. The characteristic features in the electron and phonon spectra clearly suggest that the lowest branches of acoustic and optical nature are more involved in the process of scattering of electrons than the remaining ones due to their phonon anomalies and the significant existence of Nb d electrons at the Fermi level. From the integration of the Eliashberg spectral function, we obtain a value of average electron–phonon coupling constant λ = 1.07, confirming strong interaction between electrons and phonons. The computed value of superconducting critical temperature Tc = 13.7 K harmonizes very well with the experimentally reported value of 13.0 K.

Electron-phonon interaction and zero-field charge carrier transport in the nodal-line semimetal ZrSiS

We study electron-phonon interaction and related transport properties of nodal-line semimetal ZrSiS using first-principles calculations. We find that ZrSiS is characterized by a weak electron-phonon coupling on the order of 0.1, which is almost energy independent. The main contribution to the electron-phonon coupling originates from long-wavelength optical phonons, causing no significant renormalization of the electron spectral function. At the charge neutrality point, we find that electrons and holes provide a comparable contribution to the scattering rate. The phonon-limited resistivity calculated within the Boltzmann transport theory is found to be strongly direction-dependent with the ratio between out-of-plane and in-plane directions being $\rho_{zz}/\rho_{xx}\sim 7.5$, mainly determined by the anisotropy of carrier velocities. We estimate zero-field resistivity to be $\rho_{xx}\approx12$ $\mu\Omega$ cm at 300 K, which is in good agreement with experimental data. Relatively small resistivity in ZrSiS can be attributed to a combination of weak electron-phonon coupling and high carrier velocities.

Physical properties and superconductivity of Heusler compound LiGa[formula omitted]Rh: A first-principles calculation

We have conducted ab initio pseudopotential calculations with and without spin orbit coupling on the physical properties of LiGa2Rh in order to explain the formation of superconductivity. Although the inclusion of spin orbit coupling lifts the degeneracies of electronic bands, its influence remains small near the Fermi level. The elastic calculations reveal that this Heusler superconductor is ductile. Phonon and electron–phonon interaction properties of LiGa2Rh are weakly influenced by the inclusion of spin orbit coupling. An analysis of electron–phonon interaction properties reveals that acoustic phonon branches are more involved in the process of scattering of electrons than optical phonon branches. From the Allen–Dynes modified McMillan formula, the value of superconducting transition temperature is obtained to be 2.68 K which is compatible with the recently reported experimental value of 2.4 K.

Ab initio investigation of physical properties of LaT2B2C (T=ir, Rh) compounds: A density functional theory approach

The structural, electronic, lattice dynamical, and electron-phonon interaction properties of LaIr2B2C and LaRh2B2C crystallised in body-centred tetragonal structure are investigated by using the generalised gradient approximation of the density functional theory and the planewave pseudopotential method. The structural results are in good accordance with previous experimental studies. The electronic studies show that the density of states at the Fermi level of both borocarbide compounds are dominated by the d states of transition metal Ir(Rh). Also it is observed that the electron-phonon interaction in LaIr2B2C and LaRh2B2C are mainly carried out by the low-frequency phonon modes. By integrating Eliashberg spectral function, the superconducting transition temperature for LaIr2B2C and LaRh2B2C are obtained as 0.22 K and 0.20 K, respectively.

Investigating the normal state and superconducting state properties of orthorhombic and hexagonal ZrRuP: A first-principles study

We have executed ab initio pseudopotential calculations on the structural, electronic, elastic, mechanical, vibrational, and electron-phonon interaction properties of hexagonal ZrRuP (h-ZrRuP) and orthorhombic ZrRuP (o-ZrRuP). The electronic states of both phases near the Fermi energy are found to be dominated by the $d$ electrons of transition metal atoms, suggesting that they play a more active role in the generation of superconducting state for both phases of ZrRuP. A critical assessment of their elastic and mechanical properties reveals that the lattice of h-ZrRuP is softer than that of o-ZrRuP. A comparison of phonon dispersion curves for both phases indicates that the lower transverse acoustic branch of h-ZrRuP is much softer than that of o-ZrRuP. The soft character of this phonon branch gives rise to strong electron-phonon interaction in h-ZrRuP. Therefore the electron-phonon coupling parameter for h-ZrRuP equals to 1.25 which is considerably larger than the corresponding value of 0.57 for o-ZrRuP. As a consequence, phonon and electron-phonon interaction properties are crucial in making superconducting transition temperature much higher for h-ZrRuP than o-ZrRuP. At the end, the value of this temperature is found to be 12.49 K for h-ZrRuP and 3.89 K for o-ZrRuP which coincide with their experimental values of 12.93 and 3.82 K.

Physical properties of hexagonal BaPtAs with noncentrosymmetric SrPtSb-type and centrosymmetric YPtAs-type crystal structures: Effects of spin-orbit coupling

Recently, superconductivity in BaPtAs with the noncentrosymmetric SrPtSb and the centrosymmetric YPtAs-structure has been discovered. Its noncentrosymmetric and centrosymmetric structures make BaPtAs a charming compound for searching the effect of spin-orbit coupling (SOC) onto superconductors with broken and preserved spatial inversion symmetry. We have investigated the effect of SOC on the physical and electron-phonon interaction properties of these phases of BaPtAs by using the generalized gradient approximation of the density functional theory and the plane-wave pseudopotential method. The inclusion of SOC has moderate effect on the elastic and electronic properties, and on phonon frequencies for both phases of BaPtAs. However, SOC makes an opposite impact on their Eliashberg spectral function. For the noncentrosymmetric phase, this coupling decreases the strength of dominant peaks of Eliashberg spectral function, reducing the values of average electron-phonon coupling and superconducting transition temperature. The scenario is exactly opposite for the centrosymmetric phase. For both phases, the hybridized Pt-As vibrations play a strongly significant role in determining their electron-phonon interaction properties since their electronic states have the dominant contribution near the Fermi level. The superconducting temperature is estimated to be 2.87 K for the SrPtSb phase and 2.38 K for the YPtAs phase. These values compare well with the reported measured values of 2.8 K and 2.1--3.0 K, respectively.

Theoretical investigation of antisymmetric spin-orbit coupling effect on the physical properties of noncentrosymmetric BaPtSb superconductor

First principles pseudopotential calculations have been performed to explore the effect of spin-orbit coupling on the electronic, elastic, mechanical, vibrational and electron-phonon interaction properties of noncentrosymmetric BaPtSb crystallizing in the hexagonal SrPtSb-type. This coupling makes only moderate changes to the elastic and mechanical properties but significant changes to the phonon spectrum in the acoustic range. Analysis of the Eliashberg spectral function reveals that these low-frequency phonon modes originate from the vibrations of Pt and Sb atoms and couple strongly to their d and p electronic states at the Fermi level. The spin-orbit coupling has a significant effect on the electron-phonon interaction properties by decreasing the frequencies of some phonon modes and increasing the strength of the most dominant peak of the Eliashberg spectral function. The average electron-phonon coupling increases from 0.617 without spin-orbit coupling to 0.629 with spin-orbit coupling, resulting in the corresponding changes to the superconducting transition temperature from 1.46 to 1.54 K. The latter value of superconducting transition temperature compares very well with its experimental value of 1.64 K.

Theoretical investigation of electron-phonon interaction in the orthorhombic phase of Mo2C

We have studied the structural, electronic, elastic, mechanical, vibrational and electron-phonon interaction properties of Mo2C crystallizing in the simple orthorhombic ζ-Fe2N-type crystal structure by using the generalized gradient approximation of the density functional theory and the plane wave ab initio pseudopotential method. A critical assessment of the calculated electronic structure and density of states reveals that the bonding in this material is a combination of covalent, ionic and metallic in nature. The calculated values of the second order elastic constants signal its mechanical stability. An examination of the calculated Eliashberg spectral function reveals that Mo-related phonon modes couple strongly to electrons due to the significant presence of Mo d electrons at the Fermi energy. From the integration of this spectral function, the value of average electron-phonon coupling parameter is determined to be of the intermediate strength 0.709. Finally, the value of the superconducting critical temperature is calculated to be 7.37 K, in excellent accordance with its measured value of 7.30 K.

Ab initio investigation of spin orbit coupling effect on the physical properties of IrGe superconductor

We have aimed to explore the influence of spin orbit coupling (SOC) on the electronic, elastic, mechanical, lattice dynamical and electron-phonon interaction properties of the simple orthorhombic IrGe using first principles density functional calculations within the generalized gradient approximation. The effect of SOC on the above properties of IrGe is mainly associated with Ir atom which possesses a 5d orbital and much heavier mass than that of Ge atom. The calculated values of nine independent elastic constants satisfy all the stability criteria, indicating that IrGe is mechanically stable in its MnP-type crystal structure. Also, no imaginary phonon frequencies are found in the phonon dispersion curves, indicating the dynamical stability of IrGe in its orthorhombic structure. Inclusion of SOC leads to the hardening of some low-frequency phonon modes which influences the electron-phonon interaction. Furthermore, inclusion of SOC leads to a decrease in dominant peaks of the Eliashberg function, and thus decrease in the values of the electron-phonon scattering parameter λ as well as the superconducting transition temperature Tc. Using the calculated value of λ with SOC, the value of Tc is obtained to be 5.09 K which compares very well with the recent measured value of 5.17 K.

Theoretical investigation of superconductivity in the non-centrosymmetric SrPtGe3 and CaPtSi3 compounds

First-principles calculations are made to investigate structural, elastic, electronic, vibrational and electron–phonon interaction properties of non-centrosymmetric superconductors SrPtGe3 and CaPtSi3. Electronic structure calculation results show that the density of states at the Fermi level for both compounds mainly comes from the p electrons of Ge (or Si), which considerably hybridise with Pt d states. The calculated Eliashberg spectral function with and without spin–orbit interaction reveals that while all phonon branches are involved in the process of scattering of electrons near the Fermi level, the average electron–phonon coupling parameter values of 0.47 for SrPtGe3 and 0.49 for CaPtSi3 indicate that these compounds are phonon-mediated BCS-type superconductors with a weak strength. By using a reasonable value of = 0.11 for the effective Coulomb repulsion parameter, the superconducting transition temperatures for SrPtGe3 and CaPtSi3 are found to be 1.3 K and 2.4 K, respectively, which compare very well with the corresponding experimental values of 1.0 K and 2.3 K.

Role of spin-orbit coupling in the physical properties of LaX3 ( X=In , P, Bi) superconductors

We report a comprehensive and complementary study on structural, elastic, mechanical, electronic, phonon, and electron-phonon interaction properties of $\mathrm{La}{X}_{3}$ ($X$ = In, Pb, and Bi) using first-principles density functional calculations within the local density approximation with and without the spin-orbit coupling (SOC). The calculated lattice parameters for these intermetallic compounds with and without SOC are found to differ by less than $2%$ from their experimental values. The effect of SOC on the elastic, mechanical, electronic, phonon, and electron-phonon interaction properties is more profound for ${\mathrm{LaPb}}_{3}$ and ${\mathrm{LaBi}}_{3}$ containing heavier $X$ elements rather than ${\mathrm{LaIn}}_{3}$ containing lighter $X$ element. The inclusion of SOC considerably removes the degeneracies of some bands near the Fermi level and makes some phonon branches in ${\mathrm{LaPb}}_{3}$ and ${\mathrm{LaBi}}_{3}$ softer and increases the strength of dominant peaks in their Eliashberg spectral functions. Thus the SOC related enhancement of their electron-phonon coupling parameter values can be related to both a softening of their phonon dispersion curves and an increase in their electron-phonon coupling matrix elements. The superconducting transition temperature with SOC is computed to be 0.69 K for ${\mathrm{LaIn}}_{3}$, 4.23 K for ${\mathrm{LaPb}}_{3}$, and 6.87 K for ${\mathrm{LaBi}}_{3}$, which agree very well with the respective measured values of 0.70, 4.18, and 7.30 K.