Light-element superconductors
Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles
Y. Nomura, S. Sakai, M. Capone and R. Arita, Science Advances 1 e1500568 (2015)

C60
Alkali-doped fullerides A3C60 (A = K, Rb, Cs) are surprising materials where conventional phonon-mediated superconductivity and unconventional Mott physics meet, leading to a remarkable phase diagram as a function of volume per C60 molecule. We address these materials with a state-of-the-art calculation, where we construct a realistic low-energy model from first principles without using a priori information other than the crystal structure and solve it with an accurate many-body theory. Remarkably, our scheme comprehensively reproduces the experimental phase diagram including the low-spin Mott-insulating phase next to the superconducting phase. More remarkably, the critical temperatures Tc’s calculated from first principles quantitatively reproduce the experimental values. The driving force behind the surprising phase diagram of A3C60 is a subtle competition between Hund’s coupling and Jahn-Teller 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 Tc s-wave superconductivity.

First-principles study of the pressure and crystal-structure 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 (Tc) in sulfur hydrides H2S and H3S from first principles using the density functional theory for superconductors. At pressures higher than 150 GPa, the high values of Tc observed in a recent experiment (A. P. Drozdov et al., Nature 2015) are accurately reproduced by assuming that H2S decomposes into R3m H3S and S. For higher pressures, the calculated Tc's for Im3m H3S are systematically higher than those for R3m H3S and the experimentally observed maximum value (190 K), which suggests the possibility of another higher-Tc 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 Density-Functional Theory for a Plasmon-Assisted Superconducting State: Application to Lithium Under High Pressures
R. Akashi and R. Arita, Phys. Rev. Lett., 111 057006 (2013)

SCDFT
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 nonempirical studies on unconventional electron mechanisms of superconductivity based on density-functional theory.

Iron-based superconductors
First-principles study of magnetic properties in Fe-ladder compound BaFe2S3
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 iron-based superconductor BaFe2S3 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 insulator-metal transition. Finally, we also discuss what type of orbitals can play crucial roles on the magnetic and insulator-metal transition.

Ab initio downfolding study of the iron-based ladder superconductor BaFe2S3
R. Arita, H. Ikeda, Shiro Sakai, and Michi-To Suzuki, Phys. Rev. B 92, 054515 (2015)

BaFe2S3
Motivated by the recent discovery of superconductivity in the iron-based ladder compound BaFe2S3 under high pressure, we derive low-energy effective Hamiltonians from first principles. We show that the complex band structure around the Fermi level is represented only by the Fe 3dxz (mixed with 3dxy) and 3dx2−y2 orbitals. The characteristic band degeneracy allows us to construct a four-band 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 iron-based superconductors. Provided the superconductivity is mediated by spin fluctuations, the 3dxz-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 Brillouin-zone boundary.

Skyrmion systems
Control of Dzyaloshinskii-Moriya interaction in Mn1-xFexGe a first-principles study
T. Koretsune, N. Nagaosa and R. Arita, Scientific Reports 5, 13302 (2015)

MnGe
Motivated by the recent experiment on the size and helicity control of skyrmions in Mn1−xFexGe, 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.

Dzyaloshinskii-Moriya Interaction as a Consequence of a Doppler Shift due to Spin-Orbit-Induced Intrinsic Spin Current
T. Kikuchi, T. Koretsune, R. Arita and G. Tatara, Phys. Rev. Lett., 116, 247201 (2016) Editors' suggestion

MnGe2
We present a physical picture for the emergence of the Dzyaloshinskii-Moriya (DM) interaction based on the idea of the Doppler shift by an intrinsic spin current induced by spin-orbit 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 Mn1−xFexGe and Fe1−xCoxGe.

Transition metal dichalcogenides
Two-Dimensional Valley Electrons and Excitons in Noncentrosymmetric 3R-MoS2
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 MoS2 form the 3R stacking, while in the 2H polytype, the bands have dispersion in all three dimensions. According to our first-principles band-structure calculations, the valley states have no interlayer hopping in 3R−MoS2, which is proven to be the consequence of the rotational symmetry of the Bloch functions. By measuring the reflectivity spectra and analyzing an anisotropic hydrogen-atom model, we confirm that the valley excitons in 3R−MoS2 have two-dimensional 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 three-dimensional 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 Spin-Orbit Interaction and Coulomb Correlation in Sr2IrO4 and Ba2IrO4
R. Arita, J. Kunes, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, Phys. Rev. Lett. 108, 086403 (2012)

Ab initio analyses of A2IrO4 (A=Sr, Ba) are presented. Effective Hubbard-type models for Ir 5d t2g manifolds downfolded from the global band structure are solved based on the dynamical mean-field theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the Neel temperature TN. 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 Loop-Nodal s+--Wave Superconductivity in CeCu2Si2: Similarities to the Iron-Based Superconductors
H. Ikeda, M-T. Suzuki and R. Arita, Phys. Rev. Lett. 114, 147003 (2015)

Heavy-fermion superconductors are prime candidates for novel electron-pairing states due to the spin-orbital coupled degrees of freedom and electron correlations. Superconductivity in CeCu2Si2 discovered in 1979, which is a prototype of unconventional (non-BCS) superconductors in strongly correlated electron systems, still remains unsolved. Here we provide the first report of superconductivity based on the advanced first-principles theoretical approach. We find that the promising candidate is an s+--wave state with loop-shaped nodes on the Fermi surface, different from the widely expected line-nodal d-wave state. The dominant pairing glue is magnetic but high-rank octupole fluctuations. This system shares the importance of multiorbital degrees of freedom with the iron-based superconductors. Our findings reveal not only the long-standing puzzle in this material, but also urge us to reconsider the pairing states and mechanisms in all heavy-fermion superconductors.

Ab initio downfolding
Ab initio downfolding for electron-coupled systems: Constrained density-functional perturbation theory
Y. Nomura and R. Arita, Phys. Rev. B 92, 245108 (2015) Editors' suggestion

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 can be implemented by slightly modifying the density functional-perturbation 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 phonon-related 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 low-energy 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

Cluster Multipole
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 spin-orbit 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 Mn3Ir, for which an AHE was predicted in a first-principles calculation, and Mn3Z (Z=Sn, Ge), for which a large AHE was recently discovered experimentally. We further compare the AHE in Mn3Z and bcc Fe in terms of the CMP. We show that the AHE in Mn3Z 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.

Many-body wave function theory
Correlated Band Structure of a Transition Metal Oxide ZnO Obtained from a Many-Body 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 first-principles electronic structure calculation. There have been promising recent active developments of wave function theory for condensed matter, but its application to band-structure calculation remains computationally expensive. In this Letter, we report the first application of the biorthogonal transcorrelated (BITC) method: self-consistent, free from adjustable parameters, and systematically improvable many-body wave function theory, to solid-state 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 first-principles calculations of the properties of strongly correlated materials.