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M. Kohmoto

Publications and source records attributed to M. Kohmoto.

At least 19 recordsLinked to original sources
arXiv2012

Multifractals Competing with Solitons on Fibonacci Optical Lattice

We study the stationary states for the nonlinear Schrödinger equation on the Fibonacci lattice which is expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are called critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions, a forbidden region, the spectrum of critical states, and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact irrespective of the nonlinearity in the sea of a large number of stationary solitons.

cond-mat.quant-gas↗
arXiv2006

Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 πp/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.

cond-mat.mes-hall↗
arXiv2003

Superconductivity and Abelian Chiral Anomalies

Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the $x,y$ and $z$-directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called $q$-helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.

cond-mat.supr-con↗
arXiv2002

Polarization of Bloch electrons and Berry phase in the presence of electromagnetic fields

We consider Bloch electrons in the presence of the uniform electromagnetic field in two- and three-dimensions. It is renowned that the quantized Hall effect occurs in such systems. We suppose a weak and homogeneous electric field represented by the time-dependent vector potential which is changing adiabatically. The adiabatic process can be closed in the parameter space and a Berry phase is generated. In the system, one can define the macroscopic electric polarization whose time derivative is equivalent to the quantized Hall current and its conductivity is written by the Chern number. Then, the polarization is induced perpendicular to the electric field. We show that the induced polarization per a cycle in the parameter space is quantized and closely related to the Berry phase as well as the Chern number. The process is adiabatic and the system always remains the ground state, then, the polarization is quite different from the usual dielectric polarization and has some similarity to the spontaneous polarization in the crystalline dielectrics which is also written by the Berry phase. We also point out the relation between our results and the adiabatic pumping.

cond-mat.mes-hall↗
arXiv2002

On the nature of antiferromagnetism in the CO_2 planes of oxide superconductors

Recent results on electrons and holes doped CuO 2 planes confirm the marked covalency of CuO bonding, suggesting a band picture of long and short range antiferromagnetism. The maxima of superconductive T c versus doping can be related to the crossing by the Fermi level of the edges of the pseudogap due to antiferromagnetic short range order (bonding edge for holes doping, antibonding one for electrons doping). The symmetry of the superconductive gap can be related to the Bragg scattering of electronic Bloch states near the edges of the AF pseudogap. Assuming a standard phonon coupling, one then predicts for commensurate AF a pure d symmetry of the superconductive gap for underdoped samples and d symmetry plus an ip contribution increasing linearly with overdoping. This seems in agreement with recent measurements of gap symmetry for YBCO, but should be more fully tested, especially for electron doped samples. The simple band approximation used here could no doubt be made more realistic by a specific inclusion of electron correlations and by a better description of AF short range order. Uncommensurate AF, as in LSCO, is not considered here.

cond-mat.supr-con↗
arXiv2002

Berry phase and quantized Hall effect in three-dimension

We consider Bloch electrons in the electromagnetic field and argue the relation between the Berry phase and the quantized Hall conductivity in three-dimension. The Berry phase we consider here is induced by the adiabatic change of the time-dependent vector potential. The relation has been shown in two-dimensional systems, and we generalize the relation in three-dimensional systems.

cond-mat.mes-hall↗
arXiv1999

Anisotropy and magnetism of high temperature oxides superconductors

Phonon or electron mediated weak BCS attraction is enough to have high critical temperature if a van Hove anomaly is at work. This could apply to electron doped compounds and also to compounds with CuO$_2$ planes overdoped in holes, where $T_c$ decreases with increasing doping. If phonons dominate, it should lead to an anisotropic but mainly $s$ superconductive gap, as observed recently in overdoped LaSrCuO, and probably also in electron doped compounds. If electrons dominate, a $d$ gap should develop as observed in a number of cases. In the underdoped range, the observed decrease of $T_c$ with hole doping can be related in all cases to the development of antiferromagnetic fluctuations which produces a magnetic pseudogap, thus lowering the density of states at the Fermi level. The observed mainly $d$ superconductive gap then can be due to a prevalent superconductive coupling through antiferromagnetic fluctuations; it could also possibly be attributed to the same phonon coupling as in the overdoped range, now acting on Bloch functions scattered in the magnetic pseudogap. More systematic studies of superconductive gap anisotropy and of magnetic fluctuations would be in order.

cond-mat.supr-con↗
arXiv1998

Stability of the vortex lattice in D-wave superconductors

Use is made of Onsager's hydrodynamic equation to derive the vibration spectrum of the vortex lattice in d-wave superconductor. In particular the rhombic lattice (i.e. the $45^\circ$ tilted square lattice) is found to be stable for $B>H_{cr}(t)$. Here $H_{cr}(t)$ denotes the critical field at which the vortex lattice transition takes place.

cond-mat↗
arXiv1997

Charge and current oscillations in Fractional quantum Hall systems with edges

Stationary solutions of the Chern-Simons effective field theory for the fractional quantum Hall systems with edges are presented for Hall bar, disk and annulus. In the infinitely long Hall bar geometry (non compact case), the charge density is shown to be monotonic inside the sample. In sharp contrast, spatial oscillatory modes of charge density are found for the two circular geometries, which indicate that in systems with compact geometry, charge and current exist also far from the edges.

cond-mat.mes-hall↗
arXiv1997

Molecular conductors with two-chain orbitals

We investigate a theoretical model applicable to molecular conductors, such as TTP and $M(dmit)_2$ salts [M=Ni, Pd, Pt], whose charge carriers orig inate from two kinds of molecular orbitals. The model Hamiltonian consists of two independent Hubbard chains. The degree of charge transfer between the two chains is calculated. The results qualitatively agree with some experimental data.

cond-mat↗
arXiv1997

Low-lying excitations around a single vortex in a d-wave superconductor

A full quantum-mechanical treatment of the Bogoliubov-de Gennes equation for a single vortex in a d-wave superconductor is presented. First, we find low-energy states extended in four diagonal directions, which have no counterpart in a vortex of s-wave superconductors. The four-fold symmetry is due to 'quantum effect', which is enhanced when $p_{F}ξ$ is small. Second, for $p_{F}ξ\sim 1$, a peak with a large energy gap $E_{0}\sim Δ$ is found in the density of states, which is due to the formation of the lowest bound states.

cond-mat.supr-con↗
arXiv1997

Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids

Quasielectrons and quasiholes in the fractional quantum Hall liquids obey fractional (including nontrivial mutual) exclusion statistics. Their statistics matrix can be determined from several possible state-counting scheme, involving different assumptions on statistical correlations. Thermal activation of quasiparticle pairs and thermodynamic properties of the fractional quantum Hall liquids near fillings $1/m$ ($m$ odd) at low temperature are studied in the approximation of generalized ideal gas. The existence of hierarchical states in the fractional quantum Hall effect is shown to be a manifestation of the exclusonic nature of the relevant quasiparticles. For magnetic properties, a paramagnetism-diamagnetism transition appears to be possible at finite temperature.

cond-mat.mes-hall↗
arXiv1997

Simple Exactly Solvable Models of non-Fermi Liquids

We generalize the model of Hatsugai and Kohmoto [J. Phys. Soc. Jpn, 61, 2056 (1992)] and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it is straightforward to generalize to higher dimensions. The ground state is highly degenerate and there is no discontinuity in the momentum distribution; i.e., there is no Fermi surface. The Green's function generically has a branch cut.

cond-mat.str-el↗
arXiv1996

Thermal activation of exclusonic quasiparticles in the fractional quantum Hall effect

Quasiparticles of the fractional quantum Hall systems obey fractional (including mutual) exclusion statistics. In this note we study the effects of exclusion statistics on thermal activation of quasiparticle pairs in the approximation of generalized ideal gas. The distribution function for thermally activated quasiparticles is found explicitly for the statistics matrix given by the composite fermion picture and the thermodynamic consequences are discussed analytically. In particular, at low temperatures, there is a quasielectron-quasihole duality in the description of the system between two adjacent magic fillings $ν(m,p)\equiv m/(2pm+1)$ and $ν(m+1,p)$.

cond-mat.mes-hall↗
arXiv1996

Quasi-particle spectra around a single vortex in a d-wave superconductor

Using the Bogoliubov-de Gennes equation, we study quasi-particle spectra around a single vortex in a d-wave superconductor, where a magnetic field is parallel to the c-axis. In the temperature region where the Ginzburg-Landau theory is valid, we find that the local density of states preserves a circular symmetry when the symmetry of the superconducting order parameter is {\it pure} d-wave. It, however, exhibits a four-fold symmetry when the mixing of a s-wave component occurs. A peak with a {\it large energy gap} is found in the local density of states at the center of the vortex, which corresponds to the lowest bound state. Our results are consistent with a recent scanning tunneling microscopy experiment in an YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) monocrystal. The breakdown of the Eilenberger theory in YBCO in particular and in the high-T$_{c}$ superconductors in generalis discussed.

cond-mat↗
arXiv1996

Mutual Exclusion Statistics in Exactly Solvable Models in One and Higher Dimensions at Low Temperatures

We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chain, the Hubbard chain, and a model in higher dimensions which exhibits the Mott metal-insulator transition. It is shown that the ground state of these systems is all described by that of a generalized ideal gas of particles (called exclusons) which have mutual exclusion statistics, either between different rapidities or between different species. For the Bethe ansatz solvable models, the low temperature properties are well described by the excluson description if the degeneracies due to string solutions with complex rapidities are taken into account correctly. {For} the Hubbard chain with strong but finite coupling, charge-spin separation is shown for thermodynamics at low temperatures. Moreover, we present an exactly solvable model in arbitrary dimensions which, in addition to giving a perspective view of spin-charge separation, constitutes an explicit example of mutual exclusion statistics in more than two dimensions.

cond-mat↗
arXiv1995

Superconducting correlation in the one-dimensional $t$-$J$ model with anisotropic spin interaction and broken parity

A variant of the one-dimensional $t$-$J$ model with anisotropic spin interaction and broken parity is studied by the nested algebraic Bethe-ansatz method. The gapless charge excitations and the gapful spin excitations are obtained. It is shown that the singlet-superconducting correlation dominates in the low-density region by applying the finite-size scaling analysis in the conformal field theory.

cond-mat↗