Development of Density-Functional Theory for Plasmon-Assisted Superconducting State: Application to Lithium Under High Pressures

We extend the density-functional theory for superconductors (SCDFT) to take account of the dynamical structure of the screened Coulomb interaction. We construct an exchange-correlation kernel in the SCDFT gap equation on the basis of the random-phase approximation, where electronic collective excitations such as plasmons are properly treated. Through an application to fcc lithium under high pressures, we demonstrate that our new kernel gives higher transition temperatures (Tc) when the plasmon and phonon cooperatively mediate pairing and it improves the agreement between the calculated and experimentally observed Tc. The present formalism opens the door to non-empirical studies on unconventional electron mechanisms of superconductivity based on density functional theory.Comment: 5 pages, 4 figures, title has been changed from that of the previously uploaded version for publication in Phys. Rev. Let

Exotic pairing state in quasicrystalline superconductors under magnetic field

We theoretically study the effect of a magnetic field on quasicrystalline superconductors, by modelling them as the attractive Hubbard model on the Penrose-tiling structure. We find that at low temperatures and under a high magnetic field there appears an exotic superconducting state with the order parameter changing its sign in real space. We discuss the state in comparison with the Fulde-Ferrell-Larkin-Ovchinnikov state proposed many years ago for periodic systems, clarifying commonalities and differences. It is remarkable that, even in the absence of periodicity, the electronic system finds a way to keep a coherent superconducting state with a spatially sign-changing order parameter compatible with the underlying quasiperiodic structure.Comment: 7 pages, 8 figure

Ab initio downfolding for electron-phonon coupled systems: constrained density-functional perturbation theory (cDFPT)

We formulate an ab initio downfolding scheme for electron-phonon coupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electron-phonon coupling, which include the screening effects of high-energy electrons, to construct a realistic Hamiltonian consisting of low-energy electron and phonon degrees of freedom. We show that our scheme, which we call constrained density-functional perturbation theory (cDFPT), can be implemented by slightly modifying the conventional DFPT, which is one of the standard methods to calculate phonon properties from first principles. Our scheme can be applied to various phonon-related problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity and multiferroicity. We believe that the cDFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to the fullerene superconductors and discuss how the realistic low-energy Hamiltonian is constructed.Comment: 18 pages, 5 figures, 4 table

Density Functional Theory for Plasmon-Assisted Superconductivity

We review the recent progress in the density functional theory for superconductors (SCDFT). Motivated by the long-studied plasmon mechanism of superconductivity, we have constructed an exchange-correlation kernel entering the SCDFT gap equation which includes the plasmon effect. For the case of lithium under high pressures, we show that the plasmon effect substantially enhances the transition temperature (Tc) by cooperating with the conventional phonon mechanism and results in a better agreement between the theoretical and experimentally observed Tc. Our present formalism will be a first step to density functional theory for unconventional superconductors.Comment: 9 pages, 7 figures; accepted for publication in J. Phys. Soc. Jpn. Special Topics; conference proceedings of The International Conference on Strongly Correlated Electron Systems (SCES) 201

Development of a two-particle self-consistent method for multi-orbital systems and its application to unconventional superconductors

We extend the two-particle self-consistent method proposed by Vilk and Tremblay (J. Phys. I France 7, 1309-1368 (1997)) to study superconductivity in multi-orbital systems. Starting with the sum rules for the spin and charge susceptibilities, we derive self-consistent equations to determine the renormalized effective interactions. We apply this method to the two-orbital $d_{x^2-y^2}$-$d_{3z^2-r^2}$ model for La$_2$CuO$_4$ and the five-orbital $d$-model for LaFeAsO. Comparing the results with those of the random phase approximation or the fluctuation exchange approximation in which vertex corrections are ignored, we discuss how the vertex corrections affect the pairing instability of La$_2$CuO$_4$ and the dominant pairing symmetry of LaFeAsO.Comment: 11 pages, 14 figures, published by Phys. Rev.

Ab initio Derivation of Correlated Superatom Model for Potassium Loaded Zeolite A

We derive an effective low-energy Hamiltonian for potassium loaded zeolite A, a unique ferromagnet from non-magnetic elements. We perform ab initio density functional calculations and construct maximally localized Wannier functions for low-energy states made from potassium s electrons. The resulting Wannier orbitals, spreading widely in the alminosilicate cage, are found to be the superatomic s and p orbitals in the confining potential formed by the host cage. We then make a tight-binding model for these superatomic orbitals and introduce interaction parameters such as the Hubbard U. After mean-field calculations for the effective model, we find that ab initio spin density functional results are well reproduced by choosing appropriate sets of the interaction parameters. The interaction parameters turn out to be as large as the band width, $\sim$ 0.5 eV, indicating the importance of electron correlation, and that the present system is an interesting analog of correlated multi-orbital transition metal oxides.Comment: 9 pages, 6 figures, and the top margin was adjuste

Ab initio Derivation of Low-Energy Model for Alkali-Cluster-Loaded Sodalites

An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. {\em Ab initio} screened Coulomb and exchange interactions are calculated by constrained random phase approximation. We find that the system resides in the strong coupling regime and thus the Heisenberg model is derived as a low-energy model of the extended Hubbard model. We obtain antiferromagnetic couplings $\sim$ $O$(10 K), being consistent with the experimental temperature dependence of the spin susceptibility. Importance of considering the screening effect in the derivation of the extended Hubbard model is discussed.Comment: 9 pages, 5 figures, 2 table

Physical properties of weak-coupling quasiperiodic superconductors

We numerically study the physical properties of quasiperiodic superconductors with the aim of understanding superconductivity in quasicrystals. Considering the attractive Hubbard model on the Penrose tiling as a simple theoretical model, we calculate various basic superconducting properties and find deviations from the universal values of the Bardeen-Cooper-Schrieffer theory. In particular, we find that the jump of the specific heat at the superconducting transition is about 10-20% smaller than that universal value, in consistency with the experimental results obtained for the superconducting Al-Mg-Zn quasicrystalline alloy. Furthermore, we calculate current-voltage characteristics and find that the current gradually increases with the voltage on the Penrose tiling in contrast to a rapid increase in the periodic system. These distinctions originate from the nontrivial Cooper pairing characteristic to the quasiperiodic system.Comment: 8 pages, 7 figure

Control of Dzyaloshinskii-Moriya interaction in Mn1−x_{1-x}Fex_xGe: a first-principles study

Motivated by the recent experiment on the size and helicity control of skyrmions in Mn$_{1-x}$Fe$_x$Ge [K. Shibata et al., Nature Nanotechnology 8, 732 (2013)], we study how the Dzyaloshinskii-Moriya (DM) interaction changes its size and sign in metallic helimagnets. By means of first-principles calculations, we successfully reproduce the non-trivial sign change of the DM interaction observed in the experiment. While the DM interaction sensitively depends on the carrier density or the detail of the electronic structure such as the size of the exchange splitting, its behavior can be systematically understood in terms of the distribution of anticrossing points in the band structure. By following this guiding principle, we can even induce gigantic anisotropy in the DM interaction by applying a strain to the system. These results pave the new way for skyrmion crystal engineering in metallic helimagnets.Comment: 7 pages, 8 figures, 1 tabl

First-Principles Evaluation of the Dzyaloshinskii--Moriya Interaction

We review recent developments of formulations to calculate the Dzyaloshinskii--Moriya (DM) interaction from first principles. In particular, we focus on three approaches. The first one evaluates the energy change due to the spin twisting by directly calculating the helical spin structure. The second one employs the spin gauge field technique to perform the derivative expansion with respect to the magnetic moment. This gives a clear picture that the DM interaction can be represented as the spin current in the equilibrium within the first order of the spin-orbit couplings. The third one is the perturbation expansion with respect to the exchange couplings and can be understood as the extension of the Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction to the noncentrosymmetric spin-orbit systems. By calculating the DM interaction for the typical chiral ferromagnets Mn$_{1-x}$Fe$_x$Ge and Fe$_{1-x}$Co$_x$Ge, we discuss how these approaches work in actual systems.Comment: invited review pape