arXiv subjects

Takashi Yanagisawa

Publications and source records attributed to Takashi Yanagisawa.

At least 37 records · Page 2Linked to original sources

arXiv2017

Chiral sine-Gordon model

We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for $G$-valued fields and describes a new class of phase transitions, where $G$ is a compact Lie group. We show that the model is renormalizable by means of a perturbation expansion and we derive beta functions of the renormalization group theory. The coefficients of beta functions are represented by the Casimir invariants. The model contains both asymptotically free and ultraviolet strong coupling regions. The beta functions have a zero which is a bifurcation point that divides the parameter space into two regions; they are the weak coupling region and the strong coupling region. A large-$N$ model is also considered. This model is reduced to the conventional sine-Gordon model that describes the Kosterlitz-Thouless transition near the fixed point. In the strong-coupling limit, the model is reduced to a $U(N)$ matrix model.

hep-th↗

arXiv2016

Isotope shift of the ferromagnetic transition temperature in itinerant ferromagnets

We present a theory of the isotope effect of the Curie temperature $T_{\rm c}$ in itinerant ferromagnets. The isotope effect in ferromagnets occurs via the electron-phonon vertex correction and the effective attractive interaction mediated by the electron-phonon interaction. The decrease of the Debye frequency increases the relative strength of the Coulomb interaction, which results in a positive isotope shift of $T_{\rm c}$ when the mass $M$ of an atom increases. Following this picture, we evaluate the isotope effect of $T_{\rm c}$ by using the Stoner theory and a spin-fluctuation theory. When $T_{\rm c}$ is large enough as large as or more than 100K, the isotope effect on $T_{\rm c}$ can be measurable. Recently, precise measurements on the oxygen isotope effect on $T_{\rm c}$ have been performed for itinerant ferromagnet SrRuO$_3$ with $T_{\rm c}\sim 160$K. A clear isotope effect has been observed with the positive shift of $T_{\rm c}\sim 1$K by isotope substitution ($^{16}O\rightarrow ^{18}O$). This experimental result is consistent with our theory.

cond-mat.mtrl-sci↗

arXiv2016

Crossover from weakly to strongly correlated regions in the two-dimensional Hubbard model -- Off-diagonal wave function Monte Carlo studies of Hubbard model II --

The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction $U$ increases. The antiferromagnetic correlation induced by $U$ is reduced for hole doping when $U$ is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which would result in high-temperature superconductivity.

cond-mat.str-el↗

arXiv2016

Nambu-Goldstone-Leggett modes in multi-condensate superconductors

Multi-gap superconductors exhibit interesting properties. In an $N$-gap superconductor, we have in general $U(1)^N$ phase invariance. This multiple-phase invariance is partially or totally spontaneously broken in a superconductor. The Nambu-Goldstone modes, as well as Higgs modes, are important and will play an important role in multi-condensate superconductors. The additional phase invariance leads to a new quantum phase, with help of frustrated Josephson effects, such as the time-reversal symmetry breaking, the emergence of massless modes and fractionally quantized-flux vortices. There is a possibility that half-flux vortices exist in two-component superconductors in a magnetic field. The half-quantum flux vortex can be interpreted as a monopole, and two half-flux vortices form a bound state connected by a domain wall. There is an interesting analogy between quarks and fractionally quantized-flux vortices in superconductors.

cond-mat.supr-con↗

arXiv2015

Kondo effect in Dirac systems

We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s-d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot σ$ for the wave number ${\bf k}$ where $σ_j$ are Pauli matrices. We derived the formula of the Kondo temperature $T_{\rm K}$ by means of the Green's function theory for small $J$. The $T_{\rm K}$ is determined from a singularity of Green's functions in the form $T_{\rm K}\simeq \bar{D}\exp(-{\rm const.}/ρ|J|)$ when the exchange coupling $|J|$ is small where $\bar{D}=D/\sqrt{1+D^2/(2μ)^2}$ for a cutoff $D$ and $ρ$ is the density of states at the Fermi surface. When $|μ|\ll D$, $T_{\rm K}$ is proportional to $|μ|$: $T_{\rm K}\simeq |μ|\exp(-{\rm const.}/ρ|J|)$. The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, $T_{\rm K}$ vanishes when the chemical potential $μ$ is just at the Dirac point. The resistivity and the specific heat exhibit a log-$T$ singularity in the range $T_{\rm K} < T\ll |μ|/k_{\rm B}$. Instead, for $T\sim O(|μ|)$ or $T>|μ|$, they never show log-$T$.

cond-mat.str-el↗

arXiv2015

Dirac fermions and Kondo effect

In this study, we investigate the Kondo effect induced by the s-d interaction where the conduction bands are occupied by Dirac fermions. The Dirac fermion has the linear dispersion and is described typically by the Hamiltonian such as $H_k= v{\bf k}\cdot σ+m σ_0$ for the wave number ${\bf k}$ where $σ_j$ are Pauli matrices and $σ_0$ is the unit matrix. We derived the formula of the Kondo temperature $T_K$ by means of the Green's function theory for Green's functions including Dirac fermions and the localized spin. The $T_K$ was determined from a singularity of Green's functions in the form $T_K\propto \exp(-{\rm const}/ρ|J|)$ when $ρ|J|$ is small. The Kondo effect will disappear when the Fermi surface is point like because $T_K$ vanishes as the chemical potential $μ$ approaches the Dirac point.

cond-mat.str-el↗

arXiv2015

Inhomogeneous Electronic Distribution in High-Tc Cuprates

We theoretically investigate the doping evolution of the electronic state of high-Tc cuprate on both sides of the half-filling on the basis of the three-dimensional three-band Hubbard model with a layered structure using the Hartree-Fock approximation. Once a small amount of holes or electrons are doped into the half-filled state, our model exhibits the charge-transfer insulator-to-metal transition along with a chemical potential jump. At the same time, the doped holes or electrons are inhomogeneously distributed, and they tend to form clusters in the vicinity of the half-filling. This suggests the possibility of microscopic phase separation with the separation between the metallic and the insulating regions.

cond-mat.str-el↗

arXiv2015

High Temperature Superconductivity from Strong Correlation

It is important to understand the mechanism of high-temperature superconductivity. It is obvious that the interaction with large energy scale is responsible for high critical temperature $T_c$. The Coulomb interaction is one of candidates that bring about high-temperature superconductivity because its characteristic energy is of the order of eV. There have been many works for the Hubbard model including three-band d-p model with the on-site Coulomb repulsion to investigate a possibility of high-temperature superconductivity. It is, of course, not trivial whether the on-site Coulomb interaction leads to a pairing interaction between two electrons. We argue that high-temperature superconductivity is possible in the strongly correlated region by using the variational Monte Carlo method for the two-dimensional t-U-J-V model. The exchange interaction J and the nearest-neighbour attractive interaction V cooperate with U and will act to enhance the critical temperature.

cond-mat.str-el↗

arXiv2014

Fluctuation-induced Nambu-Goldstone bosons in a Higgs-Josephson model

We present a new mechanism of fluctuation-induced Nambu-Goldstone bosons in a scalar field theory of Higgs-Josephson systems. We consider a simple scalar field model with $U(1)^n$ rotational symmetry. When there is an interaction which violates the rotational symmetry, the Nambu-Goldstone bosons become massive and massless bosons are concealed. We present a model where the massive boson becomes a massless boson as a result of the perturbative fluctuation. In our model the ${\bf Z}_2$-symmetry associated with the chirality is also broken. The transition occurs as a (weak) first-order transition at the critical point. The ground state at absolute zero will flow into the state with more massless bosons due to fluctuation effects at finite temperature.

cond-mat.supr-con↗

arXiv2014

Mott transition in cuprate high-temperature superconductors

In this study, we investigate the metal-insulator transition of charge transfer type in high-temperature cuprates. We first show that we must introduce a new band parameter in the three-band d-p model to reproduce the Fermi surface of high temperature cuprates such as BSCCO, YBCO and Hg1201. We present a new wave function of a Mott insulator based on the improved Gutzwiller function, and show that there is a transition from a metal to a charge-transfer insulator for such parameters by using the variational Monte Carlo method. This transition occurs when the level difference $Δ_{dp}\equiv ε_p-ε_d$ between d and p orbitals reaches a critical value $(Δ_{dp})_c$. The energy gain $ΔE$, measured from the limit of large $Δ_{dp}$, is proportional to $1/Δ_{dp}$ for $Δ_{dp}>(Δ_{dp})_c$: $ΔE\propto -t_{dp}^2/Δ_{dp}$. We obtain $(Δ_{dp})_c\simeq 2t_{dp}$ using the realistic band parameters.

cond-mat.str-el↗

arXiv2013

Massless modes and abelian gauge fields in multi-band superconductors

In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously broken. We propose a model for $N$-band superconductors where the phase differences between gaps are represented by abelian gauge fields. This model corresponds to an $SU(N)$ gauge theory with the abelian projection. We show that there are massless modes as well as massive modes when the number of gaps $N$ is greater than 3. There are $N-3$ massless modes and two massive modes near a minimum of the Josephson potential when $N$ bands are equivalent and Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$ is broken down by the Josephson term to $U(1)^{N-3}$. A non-trivial configuration of the gauge field, that is, a monopole singularity of the gauge field results in a fractional quantum-flux vortex. The fractional quantum-flux vortex corresponds to a monopole in superconductors.

cond-mat.supr-con↗

arXiv2013

Systematics of the strength of superconductivity of the d-p model in relation to cuprates

Cuprate high-Tc superconductors are known to have several relationships between Tc and features of electronic structure. In the firstly found one, Tc is correlated with the Madelung potential difference between planar Cu and O sites. Another one relates Tc to the relative ratio of hole densities at the Cu and O sites. In this work we analyze the dependences of the strength of superconductivity (SC) on the model parameters of the d-p model. We first transform the d-p model into a Hubbard model that proves to have k-dependent Coulomb interaction. To this model we apply a kind of mean-field theory, i. e., Kondo's theory of the d-wave SC gap in cuprates. The obtained so-called SC strength parameter increases with increase of |ep - ed| on both positive and negative sides of ep - ed due to increase of effective on-site Coulomb interaction U. ep and ed are hole energy levels of O2p and Cu3d orbitals referenced to the d9 configuration. The above-mentioned two relationships are shown to be understandable in terms of the d-wave SC, if ep - ed < 0.

cond-mat.supr-con↗

arXiv2013

Gauge invariance, massless modes and topology of gauge fields in multi-band superconductors

Multi-phase physics is a new physics of multi-gap superconductors. Multi-band superconductors exhibit many interesting and novel properties. We investigate the dynamics of the phase-difference mode and show that this mode yields a new excitation mode. The phase-difference mode is represented as an abelian vector field. There are massless modes when the number of gaps is greater than three and the Josephson term is frustrated. The fluctuation of phase-difference modes with non-trivial topology leads to the existence of a fractional-quantum flux vortex in a magnetic field. A superconductor with a fractional-quantum flux vortex is regarded as a topological superconductor with the integer Chern number.

cond-mat.supr-con↗

arXiv2013

Spin vortices, skyrmions and the Kosterlitz-Thouless transition in the two-dimensional antiferromagnet

We investigate spin-vortex excitations in the two-dimensional antiferromagnet on the basis of the nonlinear sigma model. The model of two-dimensional Heisenberg quantum antiferromagnet is mapped onto the (2+1)D nonlinear sigma model. The 2D nonlinear sigma model has an instanton (or skyrmion) solution which describes an excitation of spin-vortex type. Quantum fluctuations of instantons are reduced to the study of the Coulomb gas, and the gas of instantons of the 2D nonlinear sigma model is in the plasma phase. We generalize this picture of instanton gas to the (2+1)D nonlinear sigma model. We show, using some approximation, that there is a Kosterlitz-Thouless transition from the plasma phase to the molecular phase as the temperature is lowered.

cond-mat.str-el↗

arXiv2013

Correlated-Electron Systems and High Temperature Superconductivity

We present recent theoretical results on superconductivity in correlated-electron systems, especially in the two-dimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlo method. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa_2Cu_3O_7. We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. The relationship of the hole density x and incommensurability δ, δ\sim x, is satisfied in the lower doping region, as indicated by the variational Monte Carlo calculations. We have performed a variational Monte Carlo simulation on a two-dimensional t-t'-t"-U Hubbard model with a Bi-2212 type band structure and found that the 4\times 4 period checkerboard spin modulation, that is characterized by multi Q vectors, is stabilized. We also present a new algorithm of the diagonalization quantum Monte Carlo method that is a method for the evaluation of expectation values without the negative sign difficulty. We show that the pair correlation function is not enhanced at half-filling, and is indeed enhanced with hole doping.

cond-mat.str-el↗

arXiv2013

Enhanced pair-correlation functions in the two-dimensional Hubbard model

In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in quantum Monte Carlo method which is free from the negative sign problem. We show that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling. When the system size becomes large, the pair correlation function P_d is increased for U>0 compared to the non-interacting case, while P_d is suppressed for U>0 when the system size is small. The enhancement ratio P_d[U]/P_d[U=0] will give a criterion on the existence of superconductivity. The ratio P_d[U]/P_d[U=0] increases almost linearly \propto L as the system size L\times L is increased. This increase is a good indication of an existence of superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions at half-filling, which indicates the absence of superconductivity without hole doping.

cond-mat.supr-con↗

arXiv2013

Kondo Effect in the Presence of Spin-Orbit Coupling

Recently, a series of noncentrosymmetric superconductors has been a subject of considerable interest since the discovery of superconductivity in CePt_3Si. In noncentrosymmetric materials, the degeneracy of bands is lifted in the presence of spin-orbit coupling. This will bring about new effects in the Kondo effect since the band degeneracy plays an important role in the scattering of electrons by localized spins. We investigate the single-impurity Kondo problem in the presence of spin-orbit coupling. We examine the effect of spin-orbit coupling on the scattering of conduction electrons, by using the Green's function method, for the s-d Hamiltonian, with employing a decoupling procedure. As a result, we obtain a closed system of equations of Green's functions, from which we can calculate physical quantities. The Kondo temperature T_K is estimated from a singularity of Green's functions. We show that T_K is reduced as the spin-orbit coupling constant αis increased. When 2αk_F is comparable to or greater than k_BT_K(α=0), T_K shows an abrupt decrease as a result of the band splitting. This suggests a Kondo collapse accompanied with a sharp decrease of T_K. The log T-dependence of the resistivity will be concealed by the spin-orbit interaction.

cond-mat.str-el↗

arXiv2012

Vortices and chirality in multi-band superconductors

We investigate several important properties of multi-band superconductors. They are time-reversal symmetry breaking, chirality and fractional quantum flux vortices in three-band superconductors. The BCS (Bardeen-Cooper-Schrieffer) gap equation has a solution with time-reversal symmetry breaking in some cases. We derive the Ginzburg-Landau free energy from the BCS microscopic theory. The frustrating pairing interaction among Fermi surfaces leads to a state with broken time-reversal symmetry, that is, a chiral solution. The Ginzburg-Landau equation for three-component superconductors leads to a double sine-Gordon model. A kink solution exists to this equation as in the conventional sine-Gordon model. In the chiral region of the double sine-Gordon model, an inequality of Bogomol'nyi type holds, and fractional-$π$ kink solutions exist with the topological charge Q. This yields multi-vortex bound states in three-band superconductors.

cond-mat.supr-con↗