We elucidate the model parameters for a series of organic crystals called κ- and β'-type salts by constructing the maximally localized Wannier orbitals which reproduce the bulk energy band of the first-principles methods based on the density functional theory (DFT). These materials host a dimer Mott insulator, localizing one hole per dimerized ET molecules due to strong on-dimer interaction, Ud. For all these materials, we evaluate the parameters of the two representative effective lattice models in units of molecule and on dimer, and clarify two issues. First, the conventional relationships between the two models called "dimer approximation" does not hold. Second, contrary to the previous semiempirical estimates, the degree of dimerization (which approximates Ud) does not depend much on materials, and that the overall ground state properties are controlled by the degree of anisotropy of the triangular lattice, denoted as |tc/ta| in units of dimers. We update the DFT estimates |tc/ta| of κ-ET2Cu2(CN)3, showing that it falls on a class of regular triangle with the strongest degree of frustration.

We present experimental results on the band-gap energies of homoepitaxial diamond films with isotopic compositions ranging from nearly pure carbon-12 (12C) to nearly pure carbon-13 (13C). Diamond crystals were grown by microwave plasma-assisted chemical vapor deposition, which controls the isotope composition and minimizes the density of impurities and defects. We find that the isotope substitution of 12C by 13C increases the band-gap energy in diamond by up to 15.4 meV at 79 K. The increase at room temperature is estimated from the temperature dependence of the band-gap renormalization due to electron-phonon interaction and is found to be even larger than that at low temperatures. These results unambiguously demonstrate the possibility of band-gap engineering of diamond via control of the isotopic composition.

A peculiar manifestation of orbital angular momentum is proposed for a zeolite-templated carbon system, C36H9. The structure, being a network of nanoflakes in the shape of a "pinwheel", lacks inversion symmetry. While the unit cell is large, the electronic structure obtained with a first-principles density functional theory and captured as an effective tight-binding model in terms of maximally-localized Wannier functions, exhibits an unusual feature that the valence band top comes from two chiral states having orbital magnetic momenta of 1. The noncentrosymmetric lattice structure then makes the band dispersion asymmetric, as reminiscent of, but totally different from, spin-orbit systems. The unusual feature is predicted to imply a current-induced orbital magnetism when holes are doped.

We perform a systematic first-principles study of energetics and electronic properties of chiral carbon nanotubes (CNTs) in the density-functional theory. It is found that chiral CNTs possess slightly twisted ground-state geometries. Moderate-diameter CNTs show twisting-dependent electronic properties well classified by their chiral indices, while the electronic structures of small-diameter CNTs possess sizable but individually different twisting dependences, leading to metal-semiconductor transitions in some CNTs. The CNT having the widest fundamental gap is predicted to be the twisted (4,3) CNT.

We study the energetics, electronic structures, and electron-phonon couplings of a one-dimensional potassium-doped C60 chain encapsulated in a boron nitride nanotube using the framework of the density-functional theory. We demonstrate that the reaction of potassium doping is exothermic and the resulting material is one-dimensional metal where conducting electrons are only in the C60 chain. Interestingly, the Fermi-level density of states has a peculiar pressure dependence and can be larger than those in the three-dimensional alkali-doped fullerene compounds, indicating the possibility of various phase transitions. We also discuss the electron-phonon couplings and the possibility of superconductivity.

We study superlattices with alternate stacking of graphene and boron nitride monolayers. We propose several candidate stacking sequences of the superlattices, and optimize their geometries based on the energetics in the framework of the density functional theory. From the total energies of the superlattices with the candidate stacking sequences, we identify the most stable stacking sequence. The atomic configuration of the superlattice with the most stable stacking sequence is found to have the shortest B-C distance among all the optimized superlattice geometries, indicating a strong interaction between the carbon and boron atoms. We also study the electronic structure of the superlattices in detail. It is revealed that the most stable structure exhibits metallic electronic properties.

An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by ab initio downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. 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 ~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.

To discuss the gapless spin-liquid-like behavior of the second-layer solid-phase 3He adsorbed on graphite, we study a spin-1/2 Heisenberg model on a triangular lattice with two kinds of superexchange couplings due to the corrugation effects from the first-layer by using finite temperature Lanczos method and high-temperature expansions. In some parameter region, it is found that this model can be expressed by an effective Hamiltonian with two different energy scales consisting of kagome Heisenberg model and triangular Heisenberg model. We find that this effective Hamiltonian well reproduces the experimental behaviors such as the double-peak structure and the low-temperature linear-T behavior of the specific heat as well as the excess enhancement of the spin susceptibility at low temperatures.

We have performed first-principles calculations for body-centered tetragonal (bct) Si and Ge consisting solely of four-fold coordinated elements. The structural optimization has been carried out based on the local density approximation (LDA) in the density functional theory (DFT). For total-energy minimized structures, quasi-particle spectra have been calculated using GW approximation. We find that the bct Si and Ge are new stable crystalline phases reachable under tensile stress with moderate magnitude. We also find that the bct Ge is a semimetal with the carrier density of 2×1019 cm−3, whereas the bct Si is a semiconductor with the indirect band gap of 0.5 eV. The calculated density of states of the bct Si and Ge show characteristic features which are discriminated from those of the diamond structures. Effective masses of conduction-band electrons and valence-band holes are found to be relatively light compared with those of the diamond Si and Ge. The origins of reduction or closure of band gaps are discussed.

We study boron-doped single-walled carbon nanotubes by using first-principles methods based on the density functional theory. The total energy, band structure, and density of states are calculated. From the formation energy of boron-doped nanotubes with different diameters, it is found that a narrower tube needs a smaller energy cost to substitute a carbon atom with a boron atom. By using the result of different doping rates in the (10,0) tube, we extrapolate the result to low boron density limit and find that the ionization energy of the acceptor impurity level should be approximately 0.2 eV. Furthermore, we discuss the doping rate dependence of the density of states at the Fermi level, which is important to realize superconductivity.

We study Mott transition in the two-dimensional Hubbard model on an anisotropic triangular lattice. We use the Lanczos exact diagonalization of finite-size clusters up to eighteen sites, and calculate Drude weight, charge gap, double occupancy and spin structure factor. We average these physical quantities over twisted boundary conditions in order to reduce finite-size effects. We find a signature of the Mott transition in the dependence of the Drude weight and/or charge gap on the system size. We also examine the possibility of antiferromagnetic order from the spin structure factor. Combining these information, we propose a ground-state phase diagram which has a nonmagnetic insulating phase between a metallic phase and an insulating phase with antiferromagnetic order. Finally, we compare our results with those reported in the previous theoretical studies, and discuss the possibility of an unconventional insulating state.

Equal-time pairing correlation functions of the two-dimensional t-J model on the triangular lattice are studied using high-temperature expansions method. We calculate the pairing correlation lengths and the effective pairing interactions down to T ∼ 0.2t, and find the growth of pairing correlations. When t > 0 with hole doping, a rapid growth of effective d-wave pairing interaction is found which indicates the resonating-valence-bond superconductivity. In contrast, when t < 0 where the ferromagnetic correlation and antiferromagnetic correlation compete, correlation lengths of triplet pairings as well as d-wave pairing grow at low temperatures, although they do not diverge for T => 0 in the competing region, i.e. near half-filling. On the other hand, around n=0.4, f-wave pairing correlation tends to diverge, although its effective interaction is small. Relation of the present study to the recently discovered superconductor, NaxCoO2 yH2O, is discussed.

The equal-time pairing correlation function of the two-dimensional t-J model on a square lattice is studied using a high-temperature expansion method. The sum of the pairing correlation, its spatial dependence, and the correlation length are obtained as functions of temperature down to T∼0.2t. By comparison of single-particle contributions in the correlation functions, we find an effective attractive interaction between quasi-particles in dx2-y2-wave pairings. It is shown that d-wave correlation grows rapidly at low temperatures for 0.5 < n < 0.9, with n being the electron density. The temperature for this growth is roughly scaled by J/2. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there is no numerical evidence of superconductivity.

The two-dimensional t-J model of the triangular and kagome lattice is studied by high temperature expansions. The analyses of uniform susceptibility as well as the ground-state energy show strong evidence that ferromagnetic ground state exists in a wide region in the phase diagram with resprect to electron density, n, and superexchange coupling, J, which is a different feature from the case of the square lattice. This result means that the low-density region, where the ferromagnetism is understood by Kanamori's mechanism, continues to Nagaoka's ferromagnetism in frustrated lattices. We also find the possibility of partial ferromagnetism in the low-density region of the triangular lattice.

The two-dimensional t-J model on a triangular lattice is studied using high-temperature expansions. By studying the entropy and spin susceptibility, we find that the sign of the hopping integral t is very crucial. In the case of t>0, the peak of the spin susceptibility moves to the high-temperature region with hole doping, which indicates the appearance of the resonating-valence-bond state. In contrast, for t<0, the peak of the spin susceptibility disappears with hole doping and the entropy at low temperatures behaves as S=γT with large coefficient γ, representing a large effective mass. This behavior is understood from the competition between Nagaoka's ferromagnetism and singlet formation.

We study boron-doped carbon nanotubes by first-principles methods based on the density functional theory. To discuss the possibility of superconductivity, we calculate the electronic band structure and the density of states (DOS) of boron-doped (10,0) nanotubes by changing the boron density. It is found that the Fermi level density of states D(F) increases upon lowering the boron density. This can be understood in terms of the rigid band picture where the one-dimensional van Hove singularity lies at the edge of the valence band in the DOS of the pristine nanotube. The effect of three-dimensionality is also considered by performing the calculations for bundled (10,0) nanotubes and boron-doped double-walled carbon nanotubes (10,0)@(19,0). From the calculation of the bundled nanotubes, it is found that interwall dispersion is sufficiently large to broaden the peaks of the van Hove singularity in the DOS. Thus, to achieve the high D(F) using the bundle of nanotubes with single chirality, we should take into account the distance from each nanotube. In the case of double-walled carbon nanotubes, we find that the holes introduced to the inner tube by boron doping spread also on the outer tube, while the band structure of each tube remains almost unchanged.

To clarify the property of Mott transition in the strong correlation limit, we investigate the infinite-U Hubbard model using high-temperature expansion method. The free energies in various lattices are obtained as a function of inverse temperature and electron density. If we assume the low temperature behavior as S∝T, we can extrapolate the series down to T=0 with remarkable accuracy and find that the specific heat coefficient γ diverges with n = 1. Furthermore, it is revealed that the divergence is scaled as γ ∝ (1-n)^-x with x ∼ 1.7-1.8, which is almost irrespective of lattice structure.

We have studied the entropy of two-dimensional t-J model by high temperature expansions through 14th order in inverse temperature. We extrapolated the series of entropy as a function of internal energy down to T=0 and found that the entropy has wavy form in low doped case. We conclude that this indicate the spin-charge separation.