Density Functional Theory For Superconductors Research Articles

Prediction of quaternary hydrides based on densest ternary sphere packings

We exhaustively search quaternary metal hydrides based on the (13-2-1) and (13-3-1) structures that are two of the putative densest ternary sphere packings in cubic systems [R. Koshoji et al., Phys. Rev. E 104, 024101 (2021)]. The 73 304 candidate hydrides are generated by substituting the small spheres with hydrogen atoms, and the medium, large, and fourth spheres with metallic atoms. Specifically, the substitution of the small spheres with hydrogen atoms gives the unconventional hydrogen sublattices. We screen unstable hydrides in the candidates through geometrical optimizations, constant pressure molecular dynamics simulations, and phonon calculations under hydrostatic pressure of 10 GPa, and identify 23 hydrides with static and dynamic stability, including ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{La}$ and ${\mathrm{H}}_{12}\mathrm{Ti}{\mathrm{Ni}}_{3}\mathrm{Ba}$. The superconducting transition temperatures ${T}_{c}$, calculated by density functional theory for superconductors, are found to be 5.7 and 6.7 K for the selected two hydrides ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{Ca}$ and ${\mathrm{H}}_{12}{\mathrm{ScY}}_{2}\mathrm{Sr}$, respectively. We expect that the 23 candidates of hydrides screened by the exhaustive search for 73 304 hydrides provide a guideline to narrow down the search space for trials in the experimental synthesis of quaternary metal hydrides.

Superconductivity in black phosphorus and the role of dynamical screening

Simple cubic phosphorus exhibits superconductivity with a maximum $T_c$ of up to 12 K under pressure. The pressure dependence of $T_c$ cannot be consistently explained with a simple electron-phonon mechanism, which has stimulated investigations into the role of electronic correlations and plasmonic contributions. Here, we solve the gap equation of density functional theory for superconductors using different electron-electron and electron-phonon contributions to the kernel. We find that the phonon contribution alone yields an overestimation of $T_c$, while the addition of the static electronic contribution results in an underestimation. Taking into account the full frequency dependence of the screened interaction, the one-shot $GW$ approximation predicts $T_c$ values in good agreement with the experiments in the pressure range appropriate for the cubic phase. We also explore the use of quasi-particle bands in the calculation of the electronic and phononic kernels, and show that this modification significantly improves $T_c$ in the high-pressure region.

Eliashberg theory with ab-initio Coulomb interactions: a minimal numerical scheme applied to layered superconductors

We present a minimal approach to include static Coulomb interactions in Eliashberg theory of superconductivity from first principles. The method can be easily implemented in any existing Eliashberg code (isotropic or anisotropic) to avoid the standard use of the semiempirical parameter , which adds unnecessary uncertainty to T c predictions. We evaluate the prediction accuracy of the method by simulating the superconducting properties of a set of layered superconductors, which feature unconventional Coulomb effects: CaC6, MgB2, Li-doped β-ZrNCl and YNi2B2C. We find that the estimated critical temperatures are consistent with those from ab-initio density functional theory for superconductors, and in close agreement with the experimental values.

Chemical physics of superconductivity in layered yttrium carbide halides from first principles

We perform a thorough first-principles study on superconductivity in yttrium carbide halide ${\mathrm{Y}}_{2}{X}_{2}{\mathrm{C}}_{2}$ ($X=\mathrm{Cl}$, Br, I) whose maximum transition temperature (${T}_{\mathrm{c}}$) amounts to $\ensuremath{\sim}10$ K. A detailed analysis on the optimized crystal structures reveals that the ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}$ blocks are compressed uniaxially upon the halogen substitution from Cl, Br to I, contrary to the monotonic expansion of the lattice vectors. With a nonempirical method based on the density functional theory for superconductors within the conventional phonon mechanism, we successfully reproduce the halogen dependence of ${T}_{\mathrm{c}}$. An anomalously enhanced coupling of one ${\mathrm{C}}_{2}$ libration mode is observed in ${\mathrm{Y}}_{2}{\mathrm{I}}_{2}{\mathrm{C}}_{2}$, which implies a possible departure from the conventional pairing picture. Utilizing the Wannier representation of the electron-phonon coupling, we show that the halogen electronic orbitals and ionic vibrations scarcely contribute to the superconducting pairing. The halogen dependence of this system is hence an indirect effect of the halogen ions through the uniaxial compressive force on the superconducting ${\mathrm{Y}}_{2}{\mathrm{C}}_{2}$ blocks. We thus establish a quantitatively reliable picture of the superconducting physics of this system, extracting a unique effect of the atomic substitution which is potentially applicable to other superconductors.

Superconducting Chevrel phase PbMo6S8 from first principles

Chevrel ternary superconductors show an intriguing coexistence of molecular aspects, large electron-phonon and electron-electron correlations, which to some extent still impedes their quantitative understanding. We present a first principles study on the prototypical Chevrel compound PbMo$_{6}$S$_{8}$, including electronic, structural and vibrational properties at zero and high pressure. We confirm the presence of an extremely strong electron-phonon coupling, linked to the proximity to a R$\overline{3}$-P$\overline{1}$ structural phase transition, which weakens as the system, upon applied pressures, is driven away from the phase boundary. A detailed description of the superconducting state is obtained by means of fully \textit{ab initio} superconducting density functional theory (SCDFT). SCDFT accounts for the role of phase instability, electron-phonon coupling with different intra- and inter-molecular phonon modes, and without any empirical parameter, and accurately reproduces the experimental critical temperature and gap. This study provides the conclusive confirmation that Chevrel phases are phonon driven superconductors mitigated, however, by an uncommonly strong Coulomb repulsion. The latter is generated by the combined effect of repulsive Mo states at the Fermi energy and a band gap in close proximity to the Fermi level. This is crucial to rationalize why Chevrel phases, in spite of their extreme electron-phonon coupling, have critical temperatures below 15~K. In addition, we predict the evolution of the superconducting critical temperature as a function of the external pressure, showing an excellent agreement with available experimental data.

Anomalous High-Temperature Superconductivity in YH6.

Pressure-stabilized hydrides are a new rapidly growing class of high-temperature superconductors, which is believed to be described within the conventional phonon-mediated mechanism of coupling. Here, the synthesis of one of the best-known high-TC superconductors-yttrium hexahydride -YH6 is reported, which displays a superconducting transition at ≈224K at 166GPa. The extrapolated upper critical magnetic field Bc2 (0)of YH6 is surprisingly high: 116-158T, which is 2-2.5 times larger than the calculated value. A pronounced shift of TC in yttrium deuteride YD6 with the isotope coefficient 0.4 supports the phonon-assisted superconductivity. Current-voltage measurements show that the critical current IC and its density JC may exceed 1.75A and 3500A mm-2 at 4K, respectively, which is higher than that of the commercial superconductors, such as NbTi and YBCO. The results of superconducting density functional theory (SCDFT) and anharmonic calculations, together with anomalously high critical magnetic field, suggest notable departures of the superconducting properties from the conventional Migdal-Eliashberg and Bardeen-Cooper-Schrieffer theories, and presence of an additional mechanism of superconductivity.

Effect of spin fluctuations on superconductivity in V and Nb: A first-principles study

We study the superconductivity in typical $d$-band elemental superconductors V and Nb with the recently developed nonempirical computational scheme based on the density functional theory for superconductors. The effect of ferromagnetic fluctuation (paramagnon) on the superconducting transition temperature ${T}_{\mathrm{c}}$, which, in principle, suppresses the $s$-wave superconducting pairing, is quantified without any empirical parameter. We show that the strong paramagnon effect cancels the ${T}_{\mathrm{c}}$-enhancing effects of the phonon-mediated pairing and dynamical screened Coulomb interaction.

Combining Eliashberg Theory with Density Functional Theory for the Accurate Prediction of Superconducting Transition Temperatures and Gap Functions.

We propose a practical alternative to Eliashberg equations for the abinitio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.

Benchmark of density functional theory for superconductors in elemental materials

Systematic benchmark calculations for elemental bulks are presented to validate the accuracy of density functional theory for superconductors. We developed a method to treat the spin-orbit interaction (SOI) together with the spin fluctuation (SF) and examine their effect on the superconducting transition temperature. We found the following results from the benchmark calculations: (1) The calculations, including SOI and SF, reproduce the experimental superconducting transition temperature ($T_c$) quantitatively. (2) The effect by SOI is small excepting a few elements such as Pb, Tl, and Re. (3) SF reduces $T_c$s, especially for the transition metals, while this reduction is too weak to reproduce the $T_c$s of Zn and Cd. (4) We reproduced the absence of superconductivity for alkaline (earth) and noble metals. These calculations confirm that our method can be applied to a wide range of materials and implies a direction for the further improvement of the methodology.

Microscopic characterization of the superconducting gap function in Sn1−xInxTe

Superconductivity in the doped topological crystalline insulator ${\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{Te}$ is studied by first-principles calculation based on superconducting density functional theory (SCDFT) and tunneling spectroscopy. By considering the spin-orbit coupling and frequency dependence of the screened Coulomb interaction in SCDFT, we succeed in reproducing the critical temperature of ${\mathrm{Sn}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}\mathrm{Te}$ quantitatively, in which the spin-orbit coupling is found to play an essential role. The leading gap function is a conventional $s$ wave with moderate anisotropy in $\mathbit{k}$ space, and we find that the subdominant odd-parity instability is significantly weaker than the $s$-wave instability. We perform tunneling spectroscopy measurement and confirm that the spectrum is consistent with the calculated gap function.

Density functional theory of superconductivity in doped tungsten oxides

We apply density functional theory for superconductors (SCDFT) to doped tungsten oxide in three forms: electrostatically doped ${\mathrm{WO}}_{3}$, perovskite ${\mathrm{WO}}_{3\ensuremath{-}x}{\mathrm{F}}_{x}$, and hexagonal ${\mathrm{Cs}}_{x}{\mathrm{WO}}_{3}$. We achieve a consistent picture in which the experimental superconducting transition temperature ${T}_{c}$ is reproduced, and superconductivity is understood as a weak-coupling state sustained by soft vibrational modes of the ${\mathrm{WO}}_{6}$ octahedra. SCDFT simulations of ${\mathrm{Cs}}_{x}{\mathrm{WO}}_{3}$ allow us to explain the anomalous ${T}_{c}$ behavior observed in most tungsten bronzes, where ${T}_{c}$ decreases with increasing carrier density. Here, the opening of structural channels to host Cs atoms induces a softening of strongly coupled W-O modes. By increasing the Cs content, these modes are screened and ${T}_{c}$ is strongly reduced.

Reduced density matrix functional theory for superconductors

We present an \textit{ab initio} theory for superconductors, based on a unique mapping between the statistical density operator at equilibrium, on the one hand, and the corresponding one-body reduced density matrix $\gamma$ and the anomalous density $\chi$, on the other. This new formalism for superconductivity yields the existence of a universal functional $\mathfrak{F}_\beta[\gamma,\chi]$ for the superconductor ground state, whose unique properties we derive. We then prove the existence of a Kohn-Sham system at finite temperature and derive the corresponding Bogoliubov-de Gennes-like single particle equations. By adapting the decoupling approximation from density functional theory for superconductors we bring these equations into a computationally feasible form. Finally, we use the existence of the Kohn-Sham system to extend the Sham-Schl\"uter connection and derive a first exchange-correlation functional for our theory. This reduced density matrix functional theory for superconductors has the potential of overcoming some of the shortcomings and fundamental limitations of density functional theory of superconductivity.

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, , with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications.

Representability problem of density functional theory for superconductors

Aiming at a unified treatment of correlation and inhomogeneity effects in superconductors, Oliveira, Gross and Kohn proposed in 1988 a density functional theory for the superconducting state. This theory relies on the existence of a Kohn-Sham scheme, i.e., an auxiliary noninteracting system with the same electron and anomalous densities of the original superconducting system. However, the question of noninteracting $v$-representability has never been properly addressed and the existence of the Kohn-Sham system has always been assumed without proof. Here, we show that indeed such a noninteracting system does not exist in at zero temperature. In spite of this result, we also show that the theory is still able to yield good results, although in the limit of weakly correlated systems only.

Superconductivity in hydrogenated carbon nanostructures

We present an application of density functional theory for superconductors to superconductivity in hydrogenated carbon nanotubes and fullerane (hydrogenated fullerene). We show that these systems are chemically similar to graphane (hydrogenated graphene) and like graphane, upon hole doping, develop a strong electron phonon coupling. This could lead to superconducting states with critical temperatures approaching 100 K, however this possibility depends crucially on if and how metallization is achieved.

Refined phase diagram of the H-S system with high- Tc superconductivity

Recently, hydrogen sulfide has attracted enormous attention due to the record high-temperature superconductivity of ${\text{H}}_{3}\text{S}$ with ${T}_{c}=203$ K at a pressure of 155 GPa. In addition to ${\text{H}}_{3}\text{S}$, there are many theoretically and experimentally confirmed compositions and crystal structures forming under high pressure. Here, using the ab initio variable-composition evolutionary algorithm USPEX, we performed a comprehensive search for new phases in the $\text{H}\ensuremath{-}\text{S}$ system and built a refined composition-pressure phase diagram. For ${\text{H}}_{3}{\text{S}}_{2}$, a new stable semiconducting $P{2}_{1}$ phase was found. We predicted a new sulfur-rich stable ${\text{HS}}_{2}$ phase and metastable compound ${\text{H}}_{5}{\text{S}}_{8}$ and calculated their ${T}_{c}$ using superconducting density functional theory (11 K at 100 GPa and 9.2 K at 80 GPa, respectively). Our results show that among stable phases only ${\text{H}}_{3}\text{S}$ is a high-${T}_{c}$ superconductor, and highlight that compositional descriptors alone are insufficient for indicating superconductivity, and crystal structure plays an essential role.

Weak phonon-mediated pairing in BiS2 superconductor from first principles

Superconductivity in novel bismuth-sulphur superconductors has attracted large research efforts, both experimental and theoretical, but a consensus on the nature of superconductivity in these materials has yet to be reached. Using density functional theory for superconductors, we study the electron-phonon pairing mechanism in LaO$_{0.5}$F$_{0.5}$BiS$_2$. We first confirm the presence of a commensurate charge density wave instability, in accordance with previous studies. Using a recently developed integration scheme for the electron-phonon coupling, we found that its strength is much lower than previously calculated, due to improved density of state calculations. We finally conclude that conventional phonon-mediated pairing cannot explain the high superconducting transition temperatures observed in this material.

Origin of the critical temperature discontinuity in superconducting sulfur under high pressure

Elemental sulfur shows a superconducting phase at high pressure (above 100 GPa), with critical temperatures that rise up to 20 K [Phys. Rev. B 65, 064504 (2002); Nature (London) 525, 73 (2015)] and presenting a jump at about 160 GPa, close to a structural phase transition to the $\ensuremath{\beta}$-Po phase. In this work we present a theoretical and fully ab initio characterization of sulfur based on superconducting density functional theory (SCDFT), focusing in the pressure range from 100 to 200 GPa. Calculations result in very good agreement with available experiments and point out that the origin of the critical temperature discontinuity is not related to the structural phase transition but induced by an electronic Lifshitz transition. This brings a strongly (interband) coupled electron pocket available for the superconducting condensation.

Anisotropic superconducting gaps inYNi2B2C: A first-principles investigation

We calculate superconducting gaps and quasiparticle density of states of ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ in the framework of the density functional theory for superconductors to investigate the origin of highly anisotropic superconducting gaps in this material. Calculated phonon frequencies, the quasiparticle density of states, and the transition temperature show good agreement with experimental results. From our calculation of superconducting gaps and orbital character analysis, we establish that the orbital character variation of the Fermi surface is the key factor of the anisotropic gap. Since the electronic states that consist of mainly Ni $3d$ orbitals couple weakly with phonons, the superconducting gap function is suppressed for the corresponding states, which results in the anisotropy observed in the experiments. These results are hints to increase the transition temperature of materials in the borocarbide family.

Nonempirical Calculation of Superconducting Transition Temperatures in Light-Element Superconductors.

Recent progress in the fully nonempirical calculation of the superconducting transition temperature (Tc ) is reviewed. Especially, this study focuses on three representative light-element high-Tc superconductors, i.e., elemental Li, sulfur hydrides, and alkali-doped fullerides. Here, it is discussed how crucial it is to develop the beyond Migdal-Eliashberg (ME) methods. For Li, a scheme of superconducting density functional theory for the plasmon mechanism is formulated and it is found that Tc is dramatically enhanced by considering the frequency dependence of the screened Coulomb interaction. For sulfur hydrides, it is essential to go beyond not only the static approximation for the screened Coulomb interaction, but also the constant density-of-states approximation for electrons, the harmonic approximation for phonons, and the Migdal approximation for the electron-phonon vertex, all of which have been employed in the standard ME calculation. It is also shown that the feedback effect in the self-consistent calculation of the self-energy and the zero point motion considerably affect the calculation of Tc . For alkali-doped fullerides, the interplay between electron-phonon coupling and electron correlations becomes more nontrivial. It has been demonstrated that the combination of density functional theory and dynamical mean field theory with the ab initio downfolding scheme for electron-phonon coupled systems works successfully. This study not only reproduces the experimental phase diagram but also obtains a unified view of the high-Tc superconductivity and the Mott-Hubbard transition in the fullerides. The results for these high-Tc superconductors will provide a firm ground for future materials design of new superconductors.