Orbital Magnetism of Bloch Electrons III. Application to Graphene

The orbital susceptibility for graphene is calculated exactly up to the first order with respect to the overlap integrals between neighboring atomic orbitals. The general and rigorous theory of orbital susceptibility developed in the preceding paper is applied to a model for graphene as a typical two-band model. It is found that there are contributions from interband, Fermi surface, and occupied states in addition to the Landau--Peierls orbital susceptibility. The relative phase between the atomic orbitals on the two sublattices related to the chirality of Dirac cones plays an important role. It is shown that there are some additional contributions to the orbital susceptibility that are not included in the previous calculations using the Peierls phase in the tight-binding model for graphene. The physical origin of this difference is clarified in terms of the corrections to the Peierls phase.Comment: 13 pages, 4 figure

Mean-Field Analysis of Electric Field Effect on Charge Orders in Organic Conductors

In order to investigate charge ordering phenomena under electric field, static nonequilibrium Hartree approximation (SNHA) method is formulated on the basis of the nonequilibrium Green's functions introduced by Keldysh. By applying the SNHA to the 3/4-filling extended Hubbard model on anisotropic triangular lattice, we study the stabilities and amplitudes of 3-fold and horizontal charge orders in ${\theta}$ and ${\theta}_d$-(BEDT-TTF)$_2X$ salts under the electric field. The obtained results show that the electric field stabilizes the 3-fold state in comparison to the horizontal state. The amplitude of the 3-fold state tends to decrease by the field, whereas that of the horizontal state does not change.Comment: 4pages, 6figures, and 1tabl

Meissner Effect of Dirac Electrons in Superconducting State due to Inter-band Effect

Dirac electrons in solids show characteristic physical properties due to their linear dispersion relation and two-band nature. Although the transport phenomena of Dirac electrons in a normal state have intensively been studied, the transport phenomena in a superconducting state have not been fully understood. In particular, it is not clear whether Dirac electrons in a superconducting state show Meissner effect (ME), since a diamagnetic term of a current operator is absent as a result of the linear dispersion. We investigate the ME of three dimensional massive Dirac electrons in a superconducting state on the basis of Kubo formula, and clarify that Meissner kernel becomes finite by use of the inter-band contribution. This mechanism of the ME for Dirac electrons is completely different from that for the electrons in usual metals. Our result shows that the Meissner kernel remains finite even when the superconducting gap vanishes. This is an unavoidable problem in the Dirac electron system as reported in the previous works. Thus, we use a prescription in which we subtract the normal state contribution. In order to justify this prescription, we develop a specific model where the Meissner kernel is obtained by the prescription. We also derive the result for the electron gas by taking the non-relativistic limit of Dirac Hamiltonian, and clarify that the diamagnetic term of the Meissner kernel can be regarded as the inter-band contribution between electrons and positrons in terms of the Dirac model.Comment: 7 pages, 5 figures. To be published in J. Phys. Soc. Jp

One-Dimensional t-J Model from a Variational Viewpoint

The one-dimensional (1D) $t$-$J$ model is investigated by using a Gutzwiller-Jastrow-type variation method and the exact diagonalization of small systems. Variational expectation values are estimated by the variational Monte Carlo method with sufficient accuracy. First, we represent the diagonalization results. Physical quantities like momentum distribution and some correlation functions show some behaviors which are not expected in repulsive models, as the value of $J/t$ increases. These properties as well as energy are well understood by introducing intersite correlation factors into wave functions. The phase transition to a separated phase in large-$J/t$ region can be described by an attractive Jastrow wave function in quantitative agreement with the exact results. On the other hand, for the supersymmetric case ($J/t=2$) the original Gutzwiller wave function becomes an extremely good trial function for all the range of electron density. Here a kind of \lq\lq free electron" state is realized, particularly in the low electron density. Next, the above wave functions are compared with the Tomonaga-Luttinger-liquid-type wave function proposed by Hellberg and Mele. It is found that the correlation factors in short distances control bulk quantities like energy and the magnitude of correlation functions, while the long-range part of correlataion factors determines the critical behavior of correlation functions. Lastly, using these functions, charge and spin susceptibilities and magnetization curve are estimated, which agree with the exact results. It is shown that the Mott transition in 1D $t$-$J$ model is quite different from the Brinkman-Rice transition.Comment: plain TeX, 37 pages. Hard copies of 25 figures are available on request. Submitted to Phys. Rev.

Doublon-Holon Binding Effects on Mott Transitions in Two-Dimensional Bose Hubbard Model

A mechanism of Mott transitions in a Bose Hubbard model on a square lattice is studied, using a variational Monte Carlo method. Besides an onsite correlation factor, we introduce a four-body doublon-holon factor into the trial state, which considerably improves the variational energy and can appropriately describe a superfluid-insulator transition. Its essense consists in binding (and unbinding) of a doublon to a holon in a finite short range, identical with the cases of fermions. The features of this transition are qualitatively different from those of Brinkman-Rice-type transitions.Comment: 5 pages, 6 figures, proceedings of SNS200

Competition between spin fluctuations in Ca2−x_{2-x}Srx_{x}RuO4_{4} around x=0.5x=0.5

We study the static susceptibilities for charge and spin sectors in paramagnetic states for Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ in $0.5\leq x \leq 2$ within random phase approximation on the basis of an effective Ru $t_{2g}$ orbital Hubbard model. We find that several modes of spin fluctuation around \boldq=(0,0) and \boldq\sim(0.797\pi,0) are strongly enhanced for the model of $x=0.5$. This enhancement arises from the increase of the corresponding susceptibilities for the $d_{xy}$ orbital due to the rotation-induced modifications of the electronic structure for this orbital (i.e., the flattening of the bandwidth and the increase of the density of state near the Fermi level). We also find that the ferromagnetic spin fluctuation becomes stronger for a special model than for the model of $x=0.5$, while the competition between the modes of spin fluctuation at \boldq=(0,0) and around \boldq\sim (\pi,0) is weaker for the special model; in this special model, the van Hove singularity (vHs) for the $d_{xy}$ orbital is located on the Fermi level. These results indicate that the location of the vHs for the $d_{xy}$ orbital, which is controlled by substitution of Ca for Sr, is a parameter to control this competition. We propose that the spin fluctuations for the $d_{xy}$ orbital around \boldq=(0,0) and \boldq\sim (\pi,0) play an important role in the electronic states around $x=0.5$ other than the criticality approaching the usual Mott transition where all electrons are localized.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Solitons in the Crossover between Band Insulator and Mott Insulator: Application to TTF-Chloranil under Pressure

Based on the Phase Hamiltonian, two types of solitons are found to exist in the crossover region between band insulator and Mott insulator in one-dimension. Both of these solitons have fractional charges but with different spins, zero and 1/2, respectively. The results are in accord with the experimental results by Kanoda et al. for TTF-Chloranil under pressure.Comment: Submitted to J. Phys. Soc. Japan, 8 pages, 4 figure

Unconventional Spin Hall Effect and Axial Current Generation in a Dirac Semimetal

We investigate electrical transport in a three-dimensional massless Dirac fermion model that describes a Dirac semimetal state realized in topological materials. We derive a set of interdependent diffusion equations with eight local degrees of freedom, including the electric charge density and the spin density, that respond to an external electric field. By solving the diffusion equations for a system with a boundary, we demonstrate that a spin Hall effect with spin accumulation occurs even though the conventional spin current operator is zero. The Noether current associated with chiral symmetry, known as the axial current, is also discussed. We demonstrate that the axial current flows near the boundary and that it is perpendicular to the electric current.Comment: 5 pages, 2 figure

Crossover from dilute-Kondo system to heavy-fermion system

Ground state properties of a Kondo lattice model with random configuration of $f$ electrons are investigated with a variational Monte Carlo method. We show that the crossover from a dilute-Kondo system to a heavy-fermion system occurs when the density of $c$ and $f$ electrons ($n_c$, $n_f$) become comparable, $n_f\lesssim n_c$. In the heavy-fermion region, the correlation between $f$ electrons is strong and the $f$ electrons themselves greatly contribute to the screening of other $f$-electron moments. We propose that the character of Kondo screening changes from "individual" to "collective" across the crossover.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Orbital Magnetism of Bloch Electrons I. General Formula

We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time.Comment: 18 pages, 2 figure