太田 幸則

We study third-harmonic generation (THG) in an excitonic insulator (EI) described in a two-band correlated electron model. Employing the perturbative expansion with respect to the external electric field, we derive the THG susceptibility taking into account the collective dynamics of the excitonic order parameter. In the inversion-symmetric EI, the collective order parameter motion is activated at second order of the external field and its effects arise in THG. We find three peaks in the THG susceptibility at energies ℏω=Δg/3, Δg/2, and Δg, where Δg is the band gap. While the THG response at Δg/3 is caused by bare three-photon excitation of the independent particle across the band gap, the latter two peaks involve the motion of the order parameter activated at second order. The resulting resonant peaks are prominent in particular in the BCS regime but they become less significant in the BEC regime. We demonstrate that the resonant peak originated by the collective excitation is observable in the temperature profile of the THG intensity. Our study suggests that the THG measurement should be promising for detecting the excitonic collective nature of materials.

<title>Abstract</title>Electronic instabilities in transition metal compounds often spontaneously form orbital molecules, which consist of orbital-coupled metal ions at low temperature. Recent local structural studies utilizing the pair distribution function revealed that preformed orbital molecules appear disordered even in the high-temperature paramagnetic phase. However, it is unclear whether preformed orbital molecules are dynamic or static. Here, we provide clear experimental evidence of the slow dynamics of disordered orbital molecules realized in the high-temperature paramagnetic phase of LiVS₂, which exhibits vanadium trimerization upon cooling below 314 K. Unexpectedly, the preformed orbital molecules appear as a disordered zigzag chain that fluctuate in both time and space under electron irradiation. Our findings should advance studies on soft matter physics realized in an inorganic material due to disordered orbital molecules.

We study a kagomelike spin-12 Heisenberg ladder with competing ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions. Using the density-matrix renormalization group based calculations, we obtain the ground-state phase diagram as a function of the ratio between the FM and AFM exchange interactions. Five different phases exist. Three of them are spin-polarized phases: An FM phase and two kinds of ferrimagnetic (FR) phases (referred to as FR1 and FR2 phases). The spontaneous magnetization per site is m=12, 13, and 16 in the FM, FR1, and FR2 phases, respectively. This can be understood from the fact that an effective spin-1 Heisenberg chain formed by the upper and lower leg spins has a three-step fractional quantization of the magnetization per site as m=1, 12, and 0. In particular, an anomalous "intermediate"state m=12 of the effective spin-1 chain with the reduced Hilbert space of a spin from three to two dimensional is highly unexpected in the context of conventional spin-1 physics. Thus, surprisingly, the effective spin-1 chain behaves like a spin-12 chain with SU(2) symmetry. The remaining two phases are spin-singlet phases with translational symmetry breaking in the presence of valence bond formations. One of them is octamer-singlet phase with a spontaneous octamerization long-range order of the system, and the other is period-4 phase characterized by the magnetic superstructure with a period of four structural unit cells. In these spin-singlet phases, we find the coexistence of valence bond structure and gapless chain. Although this may be emerged through the order-by-disorder mechanism, there can be few examples of such a coexistence.

We analyze the measured optical conductivity spectra using the density-functional-theory-based electronic structure calculation and density-matrix renormalization group calculation of an effective model. We show that, in contrast to a conventional description, the Bose-Einstein condensation of preformed excitons occurs in Ta2NiSe5, despite the fact that a noninteracting band structure is a band-overlap semimetal rather than a small band-gap semiconductor. The system above the transition temperature is therefore not a semimetal but rather a state of preformed excitons with a finite band gap. A novel insulator state caused by the strong electron-hole attraction is thus established in a real material.

As an extension of our previous paper (Yamaguchi et al., 2017) [24], we study the carrier doping dependence of the excitonic condensation in Pr0.5Ca0.5CoO3 using the random-phase and mean-field approximations for the realistic five-orbital Hubbard model. We show that the spin-triplet excitonic phase with a magnetic multipole ordering is stable against the doping of carriers in a considerable range around Co3+ (or 3d6). We discuss experimental relevance of our results.

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer TiSe2 using a realistic multiorbital d-p model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti 3d and Se 4p orbitals in the monolayer TiSe2 on the basis of the first-principles band-structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the M point of the Brillouin zone. The stability of the triple-q CDW state is thus examined to show that the transverse phonon modes at the M1, M2, and M3 points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se 4p and conduction Ti 3d bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-q CDW state in TiSe2. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in TiSe2 is of a bond type and induces a vortexlike antiferroelectric polarization in the kagome network of Ti atoms.

Using the density-functional-theory-based electronic structure calculations, we study the electronic state of recently discovered mixed-valent manganese oxides AMg4Mn6O15(A=K,Rb,Cs), which are fully spin-polarized ferromagnetic insulators with a cubic crystal structure. We show that the system may be described as a three-dimensional arrangement of the one-dimensional chains of a 2p orbital of O and a 3d orbital of Mn running along the three axes of the cubic lattice. We thereby argue that in the ground state the chains are fully spin polarized due to the double-exchange mechanism and are distorted by the Peierls mechanism to make the system insulating.

Using the variational cluster approach based on the self-energy functional theory, we study the possible occurrence of excitonic order and superconductivity in the two-orbital Hubbard model with intra- and inter-orbital Coulomb interactions. It is known that an antiferromagnetic Mott insulator state appears in the regime of strong intra-orbital interaction, a band insulator state appears in the regime of strong inter-orbital interaction, and an excitonic insulator state appears between them. In addition to these states, we find that the s±-wave superconducting state appears in the small-correlation regime, and the dx2y2-wave superconducting state appears on the boundary of the antiferromagnetic Mott insulator state. We calculate the single-particle spectral function of the model and compare the band gap formation due to the superconducting and excitonic orders.

We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM.

In order to elucidate whether Ta2NiSe5 is in an excitonic condensation state or not, we study macroscopic quantum interferences in ultrasonic attenuation rate and nuclear magnetic resonance relaxation rate. Using the three-chain model describing the excitonic condensation of Ta2NiSe5, we demonstrate analytically that the ultrasonic attenuation rate shows a characteristic peak just below the transition temperature of the excitonic condensation, while the nuclear magnetic resonance relaxation rate shows a rapid drop. In particular, we find that the constructive interference originates from the hybridization between the conduction and valence bands induced by an external field.

We study the excitonic phase and low-energy excitation spectra of perovskite cobalt oxides. Constructing the fiveorbital Hubbard model defined on the three-dimensional cubic lattice for the 3d bands of Pr0.5Ca0.5CoO3, we calculate the excitonic susceptibility in the normal state in the random-phase approximation (RPA) to show the presence of the instability toward excitonic condensation. On the basis of the excitonic ground state with a magnetic multipole obtained in the mean-field approximation, we calculate the dynamical susceptibility of the excitonic phase in the RPA and find that there appear a gapless collective excitation in the spin-transverse mode (Goldstone mode) and a gapful collective excitation in the spin-longitudinal mode (Higgs mode). The experimental relevance of our results is discussed.

The variational cluster approximation is used to study the isotropic triangular-lattice Hubbard model at half filling, taking into account the nearest-neighbor (t(1)) and next-nearest-neighbor (t(2)) hopping parameters for magnetic frustrations. We determine the ground-state phase diagram of the model. In the strong-correlation-regime, the 120 degrees Neel-and stripe-ordered phases appear, and a nonmagnetic insulating phase emerges in between. In the intermediate correlation regime, the nonmagnetic insulating phase expands to a wider parameter region, which goes into a paramagnetic metallic phase in the weak-correlation regime. The critical phase boundary of the Mott metal-insulator transition is discussed in terms of the van Hove singularity evident in the calculated density of states and single-particle spectral function.

We study the bond-alternating Heisenberg model using the finite-size density-matrix renormalization-group (DMRG) technique and analytical arguments based on the matrix product state, where we pay particular attention to the boundary-condition dependence on the entanglement spectrum of the system. We show that, in the antiperiodic boundary condition (APBC), the parity quantum numbers are equivalent to the topological invariants characterizing the topological phases protected by the bond-centered inversion and pi rotation about the z axis. We also show that the odd parity in the APBC, which characterizes topologically nontrivial phases, can be extracted as a twofold degeneracy in the entanglement spectrum even with finite system size. We then determine the phase diagram of the model with the uniaxial single-ion anisotropy using the level spectroscopy method in the DMRG technique. These results not only suggest the detectability of the symmetry protected topological (SPT) phases via general twisted boundary conditions but also provide a useful and precise numerical tool for discussing the SPT phases in the exact diagonalization and DMRG techniques.

We study the charge and spin density distributions of excitonic insulator (EI) states in the tight-binding approximation. We first discuss the charge and spin densities of the EI states when the valence and conduction bands are composed of orthogonal orbitals in a single atom. We show that the anisotropic charge or spin density distribution occurs in a unit cell (or atom) and a higher rank electric or magnetic multipole moment becomes finite, indicating that the EI state corresponds to the multipole order. A full description of the multipole moments for the s, p, and d orbitals is then given in general. We find that, in contrast to the conventional density-wave states, the modulation of the total charge or net magnetization does not appear in this case. However, when the conduction and valence bands include the component of the same orbital, the modulation of the total charge or net magnetization appears, as in the conventional density-wave state. We also discuss the electron density distribution in the EI state when the valence and conduction bands are composed of orbitals located in different atoms. We show that the excitonic ordering in this case corresponds to the bond order formation. Based on the results thus obtained we discuss the EI states of real materials recently reported.

We study the orbital diamagnetic susceptibility in excitonic condensation phase using the mean-field approximation for a two-band model defined on a square lattice. We find that, in semiconductors, the excitonic condensation acquires a finite diamagnetic susceptibility due to spontaneous hybridization between the valence and the conduction bands, whereas in semimetals, the diamagnetic susceptibility in the normal phase is suppressed by the excitonic condensation. We also study the orbital diamagnetic and Pauli paramagnetic susceptibilities of Ta2NiSe5 using a two-dimensional three-band model and find that the calculated temperature dependence of the magnetic susceptibility is in qualitative agreement with experiment.

The variational cluster approximation is used to study the ground-state properties and single-particle spectra of the three-component fermionic Hubbard model defined on the two-dimensional square lattice at half filling. First, we show that either a paired Mott state or color-selective Mott state is realized in the paramagnetic system, depending on the anisotropy in the interaction strengths, except around the SU(3) symmetric point, where a paramagnetic metallic state is maintained. Then, by introducing Weiss fields to observe spontaneous symmetry breakings, we show that either a color-density-wave state or color-selective antiferromagnetic state is realized depending on the interaction anisotropy and that the first-order phase transition between these two states occurs at the SU(3) point. We moreover show that these staggered orders originate from the gain in potential energy (or Slater mechanism) near the SU(3) point but originate from the gain in kinetic energy (or Mott mechanism) when the interaction anisotropy is strong. The staggered orders near the SU(3) point disappear when the next-nearest-neighbor hopping parameters are introduced, indicating that these orders are fragile, protected only by the Fermi surface nesting.

The variational cluster approximation is used to study the frustrated Hubbard model at half filling defined on the two-dimensional square lattice with anisotropic next-nearest-neighbor hopping parameters. We calculate the ground-state phase diagrams of the model in a wide parameter space for a variety of lattice geometries, including square, crossed-square, and triangular lattices. We examine the Mott metal-insulator transition and show that, in the Mott insulating phase, magnetic phases with Neel, collinear, and spiral orders appear in relevant parameter regions, and in an intermediate region between these phases, a nonmagnetic insulating phase caused by the quantum fluctuations in the geometrically frustrated spin degrees of freedom emerges.

The microscopic quantum interference associated with excitonic condensation in Ta2NiSe5 is studied in a BCS-type mean-field approximation. We show that in ultrasonic attenuation the coherence peak appears just below the transition temperature Tc, whereas in NMR spin-lattice relaxation the rate rapidly decreases below Tc these observations can offer a crucial experimental test for the validity of the excitonic condensation scenario in Ta2NiSe5. We also show that excitonic condensation manifests itself in a jump of the heat capacity at Tc as well as in a softening of the elastic shear constant, in accordance with the second-order phase transition observed in Ta2NiSe5.

<p>我々は自己エネルギー汎関数理論に基づくVCAを拡張し、熱浴を介して粒子数ゆらぎの効果を取り込むCDIA (Cluster Dynamical Impurity Approximation) という計算手法を用いて励起子相の研究を行った。本研究はCDIAの多軌道系への有効な適用法に関して示唆を与え、また粒子数揺らぎの効果が励起子相に与える影響を議論することを可能とする。</p>

<p>遷移金属ダイカルコゲナイド1T-TiSe_2_は低温で電荷密度波(CDW)状態が実現することが古くから知れれているが、その起源として励起子凝縮の可能性が示唆されている。本研究では、密度汎関数理論をもとにしたバンド構造から、tight-binding近似のパラメーターを導出し、d-p模型を構築する。構築したd-p模型を用いて、1T-TiSe_2_のCDWと励起子凝縮の関係を強束縛・強相関の立場から議論する。</p>

<p>二軌道Hubbard模型における励起子相は、同サイトの軌道間相互作用が電子–ホールの引力となり励起子を形成し発現する。先行研究では軌道間ホッピングは無視しているが、現実物質は軌道間クロスポッピングが少なからず存在し、励起子形成に影響を与えると考えられる。本研究では、軌道間クロスホッピングを導入した二軌道Hubbard模型における励起子相を、平均場近似・変分クラスター近似を用いて詳細に調べ、クロスホッピングの効果を議論する。</p>

<p>固体中の電子と正孔が自発的に対形成をする相を励起子相と呼ぶ。Ta_2_NiSe_5_は励起子相にある有力な候補物質であり、精力的に研究が進められている。本講演では第一原理計算に基づいたTa_2_NiSe_5_の光学伝導度の計算を行い、その電子状態に関して議論する。また、Ta_2_NiSe_5_の電子状態を説明する有効二次元模型を構築し、励起子相における軌道磁化率およびスピン磁化率を議論する。</p>

<p>二軌道Hubbard模型において, 反強磁性相, バンド絶縁相の間には励起子絶縁相が存在することが知られている. 励起子絶縁相とは, 基底状態において電子と正孔が結び付き,二本の軌道の間に混成が生じた状態である. 我々は, Pr_0.5_Ca_0.5_CoO_3_等を背景として, この相の実験的な観測の可能性を検討する. そのため, 二軌道Hubbard模型に対して平均場+乱雑位相近似を用い, 低エネルギー励起スペクトル(スピン相関関数等)の解析を行った。</p>

<p>量子スピン系は強相関電子系における低エネルギー物性を理解する手がかりとして活発に研究がなされてきた。また点群対称性が保護するトポロジカル量子相との関連からHaldane相のもつ性質のさらなる理解が求められている。本研究では密度行列繰り込み群とレベルスペクトロスコピーを組み合わせた数値解析により、一般のスピンSをもつ量子スピン鎖に対して、対称性によって保護されたトポロジカル自明相の研究を行う。</p>