Dynamical scaling analysis of the optical Hall conductivity in the quantum Hall regime

Dynamical scaling analysis is theoretically performed for the ac (optical) Hall conductivity $\sigma_{xy}(\varepsilon_F,\omega)$ as a function of Fermi energy $\varepsilon_F$ and frequency $\omega$ for the two-dimensional electron gas and for graphene. In both systems, results based on exact diagonalization show that $\sigma_{xy}(\varepsilon_F,\omega)$ displays a well-defined dynamical scaling, for which the dynamical critical exponent as well as the localization exponent are fitted and plugged in. A crossover from the dc-like bahavior to the ac regime is identified. The dynamical scaling analysis has enabled us to quantify the plateau in the ac Hall conductivity previously obtained, and to predict that the plateaux structure in ac is robust enough to be observed in the THz regime.Comment: 5 pages, 3 figure

Light Quenched Hadron Spectrum and Decay Constants on different Lattices

We present a study of ${\cal O}(2000)$ (quenched) lattice configurations from the APE collaboration, for $6.0\le\beta\le 6.4$ using both the Wilson and the SW-Clover fermion action. We determine the light hadronic spectrum and meson decay constants. We extract the inverse lattice spacing using data at the simulated values of the quark mass. We find an agreement with the experimental data of $\sim 5$ for mesonic masses and $\sim 10$ for baryonic masses and pseudoscalar decay constants. A larger deviation is present for the vector decay constants.Comment: 3 pages, Talk presented at LATTICE96(spectrum

Multifractality: generic property of eigenstates of 2D disordered metals.

The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix theory, its decay at larger amplitudes is non-universal and much slower. This leads to the multifractal behavior of inverse participation numbers at any disorder. From the formal point of view, the multifractality originates from non-trivial saddle-point solutions of supersymmetric $\sigma$-model used in calculations.Comment: 4 two-column pages, no figures, submitted to PRL

High-Field Superconductivity at an Electronic Topological Transition in URhGe

The emergence of superconductivity at high magnetic fields in URhGe is regarded as a paradigm for new state formation approaching a quantum critical point. Until now, a divergence of the quasiparticle mass at the metamagnetic transition was considered essential for superconductivity to survive at magnetic fields above 30 tesla. Here we report the observation of quantum oscillations in URhGe revealing a tiny pocket of heavy quasiparticles that shrinks continuously with increasing magnetic field, and finally disappears at a topological Fermi surface transition close to or at the metamagnetic field. The quasiparticle mass decreases and remains finite, implying that the Fermi velocity vanishes due to the collapse of the Fermi wavevector. This offers a novel explanation for the re-emergence of superconductivity at extreme magnetic fields and makes URhGe the first proven example of a material where magnetic field-tuning of the Fermi surface, rather than quantum criticality alone, governs quantum phase formation.Comment: A revised version has been accepted for publication in Nature Physic

Pressure-temperature phase diagram of ferromagnetic superconductors

The symmetry approach to the description of the (P,T) phase diagram of ferromagnet superconductors with triplet pairing is developed. Taking into account the recent experimental observations made on UCoGe it is considered the case of a crystal with orthorhombic structure and strong spin-orbital coupling. It is shown that formation of ferromagnet superconducting state from a superconducting state is inevitably accompanied by the first order type transition.Comment: 4 pages, 1 figur

First Observation of Quantum Oscillations in the Ferromagnetic Superconductor UCoGe

We succeeded in growing high quality single crystals of the ferromagnetic superconductor UCoGe and measured the magnetoresistance at fields up to 34T. The Shubnikov-de Haas signal was observed for the first time in a U-111 system (UTGe, UTSi, T: transition metal). A small pocket Fermi surface (F~1kT) with large cyclotron effective mass 25m0 was detected at high fields above 22T, implying that UCoGe is a low carrier system accompanyed with heavy quasi-particles. The observed frequency decreases with increasing fields, indicating that the volume of detected Fermi surface changes nonlinearly with field. The cyclotron mass also decreases, which is consistent with the decrease of the A coefficient of resistivity.Comment: 5 pages, 5 figures, accepted for publication in J. Phys. Soc. Jp

Ferromagnetism and Superconductivity in Uranium Compounds

Recent advances on ferromagnetic superconductors, UGe2, URhGe and UCoGe are presented. The superconductivity (SC) peacefully coexists with the ferromagnetism (FM), forming the spin-triplet state of Cooper pairs. The striking new phenomena, such as SC reinforced by the magnetic field, are associated with Ising-type ferromagnetic fluctuations. A variety of ferromagnetic ordered moments between UGe2, URhGe and UCoGe affords to understand the relation between FM, tricriticality and SC.Comment: 11 pages, 16 figures, accepted for publication in J. Phys. Soc. Jpn. as a review article of Special Topics of "Recent developments in superconductivity

Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature

We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, which ensures the exact "chiral" symmetry at finite lattice spacings. Studying multi-point correlation functions in various channels and taking their thermodynamical limit (and then taking the chiral limit), we obtain stronger constraints than those found in the previous studies: both the eigenvalue density at the origin and its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons, suggesting that the 2nd order chiral phase transition with the O(4) scaling is not realized in 2 flavor QCD. Possible lattice artifacts when non-chiral lattice Dirac operator is employed are briefly discussed.Comment: 39 pages, 1 figure(2 eps files), a version published in PR

Chiral properties of domain-wall fermions from eigenvalues of 4 dimensional Wilson-Dirac operator

We investigate chiral properties of the domain-wall fermion (DWF) system by using the four-dimensional hermitian Wilson-Dirac operator. We first derive a formula which connects a chiral symmetry breaking term in the five dimensional DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator, and simplify the formula in terms of only the eigenvalues of the operator, using an ansatz for the form of the eigenvectors. For a given distribution of the eigenvalues, we then discuss the behavior of the chiral symmetry breaking term as a function of the fifth dimensional length. We finally argue the chiral property of the DWF formulation in the limit of the infinite fifth dimensional length, in connection with spectra of the hermitian Wilson-Dirac operator in the infinite volume limit as well as in the finite volume.Comment: Added a reference and modified the acknowledgmen