Lightelement superconductors
 Unified understanding of superconductivity and Mott transition in alkalidoped fullerides from first principles

Y. Nomura, S. Sakai, M. Capone and R. Arita, Science Advances 1 e1500568 (2015)
Alkalidoped fullerides A_{3}C_{60} (A = K, Rb, Cs) are surprising materials where conventional phononmediated superconductivity and unconventional Mott physics meet, leading to a remarkable phase diagram as a function of volume per C_{60} molecule. We address these materials with a stateoftheart calculation, where we construct a realistic lowenergy model from first principles without using a priori information other than the crystal structure and solve it with an accurate manybody theory. Remarkably, our scheme comprehensively reproduces the experimental phase diagram including the lowspin Mottinsulating phase next to the superconducting phase. More remarkably, the critical temperatures T_{c}’s calculated from first principles quantitatively reproduce the experimental values. The driving force behind the surprising phase diagram of A_{3}C_{60} is a subtle competition between Hund’s coupling and JahnTeller phonons, which leads to an effectively inverted Hund’s coupling. Our results establish that the fullerides are the first members of a novel class of molecular superconductors in which the multiorbital electronic correlations and phonons cooperate to reach high T_{c} swave superconductivity.
 Firstprinciples study of the pressure and crystalstructure dependences of the superconducting transition temperature in compressed sulfur hydrides

R. Akashi, M. Kawamura, S. Tsuneyuki, Y. Nomura and R. Arita, Phys. Rev. B 91, 224513 (2015)
We calculate the superconducting transition temperatures (T_{c}) in sulfur hydrides H_{2}S and H_{3}S from first principles using the density functional theory for superconductors. At pressures higher than 150 GPa, the high values of T_{c} observed in a recent experiment (A. P. Drozdov et al., Nature 2015) are accurately reproduced by assuming that H_{2}S decomposes into R3m H_{3}S and S. For higher pressures, the calculated T_{c}'s for Im3m H_{3}S are systematically higher than those for R3m H_{3}S and the experimentally observed maximum value (190 K), which suggests the possibility of another higherT_{c} phase. We also quantify the isotope effect from first principles and demonstrate that the isotope effect coefficient can be larger than the conventional value (0.5) when multiple structural phases energetically compete.
 Development of DensityFunctional Theory for a PlasmonAssisted Superconducting State: Application to Lithium Under High Pressures

R. Akashi and R. Arita, Phys. Rev. Lett., 111 057006 (2013)
We extend the densityfunctional theory for superconductors (SCDFT) to take account of the dynamical structure of the screened Coulomb interaction. We construct an exchangecorrelation kernel in the SCDFT gap equation on the basis of the randomphase 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 (T_{c}) when the plasmon and phonon cooperatively mediate pairing and it improves the agreement between the calculated and experimentally observed T_{c}. The present formalism opens the door to nonempirical studies on unconventional electron mechanisms of superconductivity based on densityfunctional theory.
Ironbased superconductors
 Firstprinciples study of magnetic properties in Feladder compound BaFe_{2}S_{3}

M. Suzuki, R. Arita and H. Ikeda, Phys. Rev. B 92, 085116 (2015)
We study the magnetic, structural, and electronic properties of the recently discovered ironbased superconductor BaFe_{2}S_{3} based on density functional theory with the generalized gradient approximation. The calculations show that the magnetic alignment in which the spins are coupled ferromagnetically along the rung and antiferromagnetically along the leg is the most stable in the possible magnetic structure within an Fe ladder and is further stabilized with the periodicity characterized by the wave vector Q=(π,π,0), leading to the experimentally observed magnetic ground state. The magnetic exchange interaction between the Fe ladders creates a tiny energy gap, the size of which is in excellent agreement with the experiments. Applied pressure suppresses the energy gap and leads to an insulatormetal transition. Finally, we also discuss what type of orbitals can play crucial roles on the magnetic and insulatormetal transition.
 Ab initio downfolding study of the ironbased ladder superconductor BaFe_{2}S_{3}

R. Arita, H. Ikeda, Shiro Sakai, and MichiTo Suzuki, Phys. Rev. B 92, 054515 (2015)
Motivated by the recent discovery of superconductivity in the ironbased ladder compound BaFe_{2}S_{3} under high pressure, we derive lowenergy effective Hamiltonians from first principles. We show that the complex band structure around the Fermi level is represented only by the Fe 3d_{xz} (mixed with 3d_{xy}) and 3d_{x2−y2} orbitals. The characteristic band degeneracy allows us to construct a fourband model with the band unfolding approach. We also estimate the interaction parameters and show that the system is more correlated than the 1111 family of ironbased superconductors. Provided the superconductivity is mediated by spin fluctuations, the 3d_{xz}like band plays an essential role, and the gap function changes its sign between the Fermi surface around the Γ point and that around the Brillouinzone boundary.
Skyrmion systems
 Control of DzyaloshinskiiMoriya interaction in Mn_{1x}Fe_{x}Ge a firstprinciples study

T. Koretsune, N. Nagaosa and R. Arita, Scientific Reports 5, 13302 (2015)
Motivated by the recent experiment on the size and helicity control of skyrmions in Mn_{1−x}Fe_{x}Ge, we study how the DzyaloshinskiiMoriya (DM) interaction changes its size and sign in metallic helimagnets. By means of firstprinciples calculations, we successfully reproduce the nontrivial 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.
 DzyaloshinskiiMoriya Interaction as a Consequence of a Doppler Shift due to SpinOrbitInduced Intrinsic Spin Current

T. Kikuchi, T. Koretsune, R. Arita and G. Tatara, Phys. Rev. Lett., 116, 247201 (2016) Editors' suggestion
We present a physical picture for the emergence of the DzyaloshinskiiMoriya (DM) interaction based on the idea of the Doppler shift by an intrinsic spin current induced by spinorbit interaction under broken inversion symmetry. The picture is confirmed by a rigorous effective Hamiltonian theory, which reveals that the DM coefficient is given by the magnitude of the intrinsic spin current. Our approach is directly applicable to first principles calculations and clarifies the relation between the interaction and the electronic band structures. Quantitative agreement with experimental results is obtained for the skyrmion compounds Mn_{1−x}Fe_{x}Ge and Fe_{1−x}Co_{x}Ge.
Transition metal dichalcogenides
 TwoDimensional Valley Electrons and Excitons in Noncentrosymmetric 3RMoS_{2}

R. Akashi, M. Ochi, S.Bordacs, R. Suzuki, Y. Tokura, Y. Iwasa and R. Arita, Phys. Rev. Applied 4, 014002 (2015)
We find that the motion of the valley electrons―electronic states close to the K and K′ points of the Brillouin zone―is confined into two dimensions when the layers of MoS_{2} form the 3R stacking, while in the 2H polytype, the bands have dispersion in all three dimensions. According to our firstprinciples bandstructure calculations, the valley states have no interlayer hopping in 3R−MoS_{2}, which is proven to be the consequence of the rotational symmetry of the Bloch functions. By measuring the reflectivity spectra and analyzing an anisotropic hydrogenatom model, we confirm that the valley excitons in 3R−MoS_{2} have twodimensional hydrogenlike spectral series, and the spreads of the wave function are smaller than the interlayer distance. In contrast, the valley excitons in 2H−MoS2 are well described by the threedimensional model and, thus, not confined in a single layer. Our results indicate that the dimensionality of the valley degree of freedom can be controlled simply by the stacking geometry, which can be utilized in future valleytronics.
5d electron systems
 Ab initio Studies on the Interplay between SpinOrbit Interaction and Coulomb Correlation in Sr_{2}IrO_{4}
and Ba_{2}IrO_{4}

R. Arita, J. Kunes, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, Phys. Rev. Lett. 108, 086403 (2012)
Ab initio analyses of A_{2}IrO_{4} (A=Sr, Ba) are presented. Effective Hubbardtype models for
Ir 5d t_{2g} manifolds downfolded from the global band structure are solved based on the dynamical
meanfield theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions
to insulators below the Neel temperature T_{N}. These compounds are classified not into Mott insulators but into
Slater insulators. However, the insulating gap opens by a synergy of the Neel order and significant band renormalization,
which is also manifested by a 2D bad metallic behavior in the paramagnetic phase near the quantum criticality.
Heavy electron systems
 Emergent LoopNodal s_{+}Wave Superconductivity in CeCu_{2}Si_{2}: Similarities to the IronBased Superconductors

H. Ikeda, MT. Suzuki and R. Arita, Phys. Rev. Lett. 114, 147003 (2015)
Heavyfermion superconductors are prime candidates for novel electronpairing states due to the spinorbital coupled degrees of freedom and electron correlations. Superconductivity in CeCu_{2}Si_{2} discovered in 1979, which is a prototype of unconventional (nonBCS) superconductors in strongly correlated electron systems, still remains unsolved. Here we provide the first report of superconductivity based on the advanced firstprinciples theoretical approach. We find that the promising candidate is an s_{+}wave state with loopshaped nodes on the Fermi surface, different from the widely expected linenodal dwave state. The dominant pairing glue is magnetic but highrank octupole fluctuations. This system shares the importance of multiorbital degrees of freedom with the ironbased superconductors. Our findings reveal not only the longstanding puzzle in this material, but also urge us to reconsider the pairing states and mechanisms in all heavyfermion superconductors.
Ab initio downfolding
 Ab initio downfolding for electroncoupled systems: Constrained densityfunctional perturbation theory

Y. Nomura and R. Arita, Phys. Rev. B 92, 245108 (2015) Editors' suggestion
We formulate an ab initio downfolding scheme for electronphononcoupled systems. In this scheme, we calculate partially renormalized phonon frequencies and electronphonon coupling, which include the screening effects of highenergy electrons, to construct a realistic Hamiltonian consisting of lowenergy electron and phonon degrees of freedom. We show that our scheme can be implemented by slightly modifying the density functionalperturbation theory (DFPT), which is one of the standard methods for calculating phonon properties from first principles. Our scheme, which we call the constrained DFPT, can be applied to various phononrelated problems, such as superconductivity, electron and thermal transport, thermoelectricity, piezoelectricity, dielectricity, and multiferroicity. We believe that the constrained DFPT provides a firm basis for the understanding of the role of phonons in strongly correlated materials. Here, we apply the scheme to fullerene superconductors and discuss how the realistic lowenergy Hamiltonian is constructed.
Cluster Multipole Theory
 Cluster multipole theory for anomalous Hall effect in antiferromagnets

M.T. Suzuki, T. Koretsune, M. Ochi, and R. Arita,
Phys. Rev. B 95, 094406 (2017) Editors' suggestion
We introduce a cluster extension of multipole moments to discuss the anomalous Hall effect (AHE) in both ferromagnetic (FM) and antiferromagnetic (AFM) states in a unified framework. We first derive general symmetry requirements for the AHE in the presence or absence of the spinorbit coupling by considering the symmetry of the Berry curvature in k space.The cluster multipole (CMP) moments are then defined to quantify the macroscopic magnetization in noncollinear AFM states as a natural generalization of the magnetization in FM states. We identify the macroscopic CMP order which induces the AHE. The theoretical framework is applied to the noncollinear AFM states of Mn_{3}Ir, for which an AHE was predicted in a firstprinciples calculation, and Mn_{3}Z (Z=Sn, Ge), for which a large AHE was recently discovered experimentally. We further compare the AHE in Mn_{3}Z and bcc Fe in terms of the CMP. We show that the AHE in Mn_{3}Z is characterized by the magnetization of a cluster octupole moment in the same manner as that in bcc Fe characterized by the magnetization of the dipole moment.
Manybody wave function theory
 Correlated Band Structure of a Transition Metal Oxide ZnO Obtained from a ManyBody Wave Function Theory

M. Ochi, R. Arita and S. Tsuneyuki,
Phys. Rev. Lett. 118, 026402 (2017)
Obtaining accurate band structures of correlated solids has been one of the most important and challenging problems in firstprinciples electronic structure calculation. There have been promising recent active developments of wave function theory for condensed matter, but its application to bandstructure calculation remains computationally expensive. In this Letter, we report the first application of the biorthogonal transcorrelated (BITC) method: selfconsistent, free from adjustable parameters, and systematically improvable manybody wave function theory, to solidstate calculations with
d electrons: wurtzite ZnO. We find that the BITC band structure better reproduces the experimental values of the gaps between the bands with different characters than several other conventional methods. This study paves the way for reliable firstprinciples calculations of the properties of strongly correlated materials.
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