Gauge covariant formulation of Wigner representation through deformational quantization --Application to Keldysh formalism with electromagnetic field--

We developed a gauge-covariant formulation of the non-equilibrium Green function method for the dynamical and/or non-uniform electromagnetic field by means of the deformational quantization method. Such a formulation is realized by replacing the Moyal product in the so-called Wigner space by the star product, and facilitates the order-by-order calculation of a gauge-invariant observable in terms of the electromagnetic field. An application of this formalism to the linear response theory is discussed

Effective mass staircase and the Fermi liquid parameters for the fractional quantum Hall composite fermions

Effective mass of the composite fermion in the fractional quantum Hall system, which is of purely interaction originated, is shown, from a numerical study, to exhibit a curious nonmonotonic behavior with a staircase correlated with the number (=2,4,...) of attached flux quanta. This is surprising since the usual composite-fermion picture predicts a smooth behavior. On top of that, significant interactions are shown to exist between composite fermions, where the excitation spectrum is accurately reproduced in terms of Landau's Fermi liquid picture with negative (i.e., Hund's type) orbital and spin exchange interactions.Comment: 4 pages, 3 figures, REVTe

Universal Scaling Behavior of Anomalous Hall Effect and Anomalous Nernst Effect in Itinerant Ferromagnets

Anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in a variety of ferromagnetic metals including pure metals, oxides, and chalcogenides, are studied to obtain unified understandings of their origins. We show a universal scaling behavior of anomalous Hall conductivity $\sigma_{xy}$ as a function of longitudinal conductivity $\sigma_{xx}$ over five orders of magnitude, which is well explained by a recent theory of the AHE taking into account both the intrinsic and extrinsic contributions. ANE is closely related with AHE and provides us with further information about the low-temperature electronic state of itinerant ferromagnets. Temperature dependence of transverse Peltier coefficient $\alpha_{xy}$ shows an almost similar behavior among various ferromagnets, and this behavior is in good agreement quantitatively with that expected from the Mott rule.Comment: 4pages, 4figures, 1tabl

Magneto-optics induced by the spin chirality in itinerant ferromagnet Nd2_2Mo2_2O7_7

It is demonstrated both theoretically and experimentally that the spin chirality associated with a noncoplanar spin configuration produces a magneto-optical effect. Numerical study of the two-band Hubbard model on a triangle cluster shows that the optical Hall conductivity $\sigma_{xy}(\omega)$ is proportional to the spin chirality. The detailed comparative experiments on pyrochlore-type molybdates $R_2$Mo$_2$O$_7$ with $R=$Nd (Ising-like moments) and $R=$Gd (Heisenberg-like ones) clearly distinguishes the two mechanisms, i.e., spin chirality and spin-orbit interactions. It is concluded that for $R$=Nd, $\sigma_{xy}(\omega)$ is dominated by the spin chirality for the dc ($\omega=0$) and the $d \to d$ incoherent intraband optical transitions between Mo atoms.Comment: 4 pages, 5 figures. submitted to Phys. Rev.

Topological nature of polarization and charge pumping in ferroelectrics

Electric polarization or transferred charge due to an adiabatic change of external parameters $\vec{Q}$ is expressed in terms of a vector field defined in the $\vec{Q}$ space. This vector field is characterized by strings, i.e., trajectories of band-crossing points. In particular, the transverse component is given by the Biot-Savart law in a nonlocal way. For a cyclic change of $\vec{Q}$ along a loop C, the linking number between this string and C represents the amount of the pumped charge, which is quantized to be an integer as discussed by Thouless.Comment: 5 pages including 4 figure

Mott Transition vs Multicritical Phenomenon of Superconductivity and Antiferromagnetism -- Application to κ\kappa-(BEDT-TTF)2_2X --

Interplay between the Mott transition and the multicritical phenomenon of d-wave superconductivity (SC) and antiferromagnetism (AF) is studied theoretically. We describe the Mott transition, which is analogous to a liquid-gas phase transition, in terms of an Ising-type order parameter $\eta$. We reveal possible mean-field phase diagrams produced by this interplay. Renormalization group analysis up to one-loop order gives flows of coupling constants, which in most cases lead to fluctuation-induced first-order phase transitions even when the SO(5) symmetry exists betwen the SC and AF. Behaviors of various physical quantities around the Mott critical point are predicted. Experiments in $\kappa$-(BEDT-TTF)$_2$X are discussed from this viewpoint.Comment: 4 pages, 9 figures, to appear in J. Phys. Soc. Jp

Charge and spin Hall effect in graphene with magnetic impurities

We point out the existence of finite charge and spin Hall conductivities of graphene in the presence of a spin orbit interaction (SOI) and localized magnetic impurities. The SOI in graphene results in different transverse forces on the two spin channels yielding the spin Hall current. The magnetic scatterers act as spin-dependent barriers, and in combination with the SOI effect lead to a charge imbalance at the boundaries. As indicated here, the charge and spin Hall effects should be observable in graphene by changing the chemical potential close to the gap.Comment: 7 page

Excitation spectrum and effective mass of the even-fraction quantum Hall liquid

To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by means of exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell structure) between the spectrum and those for free (composite) fermions, (ii) a surprisingly straight scaling plot for the excitation energy that gives a zero gap (metal) in the thermodynamic limit, (iii) the effective mass evaluated from the scaling becoming heavier for filling factor = 1/2, 1/4, 1/6, but (iv) some deviations from the single-mode or the Hartree-Fock composite fermion approximation as well.Comment: 4 pages, REVTeX format, 4 eps-figure

Effective gauge field theory of the t-J model in the charge-spin separated state and its transport properties

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, $A_i$. The charge-spin separation occurs below certain temperature, $T_{\rm CSS}$, as a deconfinement phenomenon of the dynamics of $A_i$. Below certain temperature $T_{\rm SG} (< T_{\rm CSS})$, the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and $A_i$ acquires a mass $m_A$. The effective field theory near $T_{\rm SG}$ takes the form of Ginzburg-Landau theory of a complex scalar field $\lambda$ coupled with $A_i$, where $\lambda$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at $T_{\rm SG}$. By using this field theory, we calculate the dc resistivity $\rho$. At $T > T_{\rm SG}$, $\rho$ is proportional to $T$. At $T < T_{\rm SG}$, it deviates downward from the $T$-linear behavior as $\rho \propto T \{1 -c(T_{\rm SG}-T)^d \}$. When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\lambda$, the exponent $d$ deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data