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Kazumasa Miyake

Publications and source records attributed to Kazumasa Miyake.

At least 37 records · Page 2Linked to original sources
arXiv2018

Effects of Crystalline Electronic Field and Onsite Interorbital Interaction in Yb-based Quasicrystal and Approximant Crystal

To get an insight into a new type of quantum critical phenomena recently discovered in the quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ and approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$ under pressure, we discuss the property of the crystalline electronic field (CEF) at Yb in the AC and show that uneven CEF levels at each Yb site can appear because of the Al/Au mixed sites. Then we construct the minimal model for the electronic state on the AC by introducing the onsite Coulomb repulsion between the 4f and 5d orbitals at Yb. Numerical calculation for the ground state shows that the lattice constant dependence of the Yb valence well explains the recent measurement done by systematic substitution of elements of Al and Au in the quasicrystal and AC, where the quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ is just located at the point from where the Yb-valence starts to change drastically. Our calculation convincingly demonstrates that this is indeed the evidence that this material is just located at the quantum critical point of the Yb-valence transition.

cond-mat.str-el↗
arXiv2017

Theory for Intrinsic Magnetic Field in Chiral Superconductor Measured by \muSR: Case of Sr_2RuO_4

The local magnetic field induced by $μ^{+}$ trapped at an interstitial site in a chiral superconductor with $p$-wave symmetry, such as Sr$_2$RuO$_4$, is discussed by solving the Bogoliubov-de Gennes equation on the two-dimensional square lattice. In the model Hamiltonian, the effect of the trapped $μ^{+}$ extracting the electrons at surrounding Ru sites is phenomenologically taken into account as a non-magnetic impurity potential which locally destroys the chiral superconducting order with $p$-wave symmetry giving rise to local circulating current around $μ^{+}$ site. It is shown that the size of the induced local magnetic field in the case with periodic boundary condition is far smaller compared to the case with open boundary condition without $μ^{+}$, in which the surface current induced by destruction of superconducting order at the surface boundary gives contribution corresponding to the intrinsic angular momentum of the order of $\hbar N_{\rm s}/2$, with $N_{\rm s}$ being the number of superconducting electrons. This result qualitatively explains why the magnetic field $\simeq0.5$G measured by $μ$SR in Sr$_2$RuO$_4$ is far smaller than the expected intrinsic magnetic field $\simeq 50$G which is nearly the same as the lower critical field $H_{{\rm c}1}\simeq 50$G.

cond-mat.supr-con↗
arXiv2017

New Quantum Criticality Revealed under Pressure

Unconventional quantum critical phenomena observed in Yb-based periodic crystals such as YbRh$_2$Si$_2$ and $β$-YbAlB$_4$ have been one of the central issues in strongly correlated electron systems. The common criticality has been discovered in quasicrystal Yb$_{15}$Au$_{51}$Al$_{34}$, which surprisingly persists under pressure at least up to $P=1.5$ GPa. The $T/H$ scaling where the magnetic susceptibility can be expressed as a single scaling function of the ratio of temperature $T$ and magnetic field $H$ has been discovered in the quasicrystal, which is essentially the same as that observed in $β$-YbAlB$_4$. Recently, the $T/H$ scaling as well as the common criticality has been also observed even in the approximant crystal Yb$_{14}$Au$_{51}$Al$_{35}$ under pressure. The theory of critical Yb-valence fluctuation gives a natural explanation for these striking phenomena in a unified way.

cond-mat.str-el↗
arXiv2016

Origin of Quantum Criticality in Yb-Al-Au Approximant Crystal and Quasicrystal

To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$, the approximant crystal Yb$_{14}$Al$_{35}$Au$_{51}$ is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits $χ\sim T^{-0.5}$ for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field $T/B$ over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to the strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size.

cond-mat.str-el↗
arXiv2016

Anomalous Local Fermi Liquid in $f^{2}$-Singlet Configuration: Impurity Model for Heavy-Electron System UPt_3

It is shown by the Wilson numerical renormalization group method that a strongly correlated impurity with a crystalline-electric-field singlet ground state in the f^2-configuration exhibits an anomalous local Fermi liquid state in which the static magnetic susceptibility remains an uncorrelated value while the NMR relaxation rate is enhanced in proportion to the square of the mass enhancement factor. Namely, the Korringa-Shiba relation is apparently broken. This feature closely matches the anomalous behaviors observed in UPt_3, i.e., the coexistence of an unenhanced value of the Knight shift due to quasiparticles contribution (the decrease across the superconducting transition) and the enhanced relaxation rate of NMR. Such an anomalous Fermi liquid behavior suggests that the Fermi liquid corrections for the susceptibility are highly anisotropic.

cond-mat.str-el↗
arXiv2016

Basic Properties of Conductivity and Normal Hall Effect in the Periodic Anderson Model

Exact formulas of diagonal conductivity $σ_{xx}$ and Hall conductivity $σ_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors in $σ_{xx}$ and $σ_{xy}$ causes remarkable increase in the valence-fluctuation regime as the f level increases while the cancellation of the renormalization factors causes slight increase in $σ_{xx}$ and $σ_{xy}$ in the Kondo regime. The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near quarter filling, which reflects the curvature of the Fermi surface. These results hold as far as the damping rate for f electrons is less than about $10~\%$ of the renormalized hybridization gap. From these results we discuss pressure dependence of residual resistivity and normal Hall effect in Ce- and Yb-based heavy electron systems.

cond-mat.str-el↗
arXiv2015

Non-Fermi Liquid and Fermi Liquid in Two-Channel Anderson Lattice Model: Theory for Pr$A_2$Al$_{20}$ ($A$=V, Ti) and PrIr$_2$Zn$_{20}$

We theoretically investigate electronic states and physical properties in a two-channel Anderson lattice model to understand the non-Fermi liquid behaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$ whose ground state of the crystalline electric field for local $f$-electron is the $Γ_3$ non-Kramers doublet of $f^2$-configuration and excited state is the $Γ_7$ Kramers doublet of $f^1$-configuration. We use the expansion from the limit of large degeneracy $N$ of the ground state ($1/N$-expansion), with $N$ being the spin-orbital degeneracy. Inclusion of the self-energy of the conduction electrons up to the order of $O(1/N)$ leads to heavy electron with channel and spin-orbit degeneracies. We find that the electrical resistivity is proportional to temperature $T$ in the limit of $T\to0$ and follows $\sqrt{T}$-law in the wide region of temperature, i.e., $T_x<T<T_0$, where typical values of $T_x$ and $T_0$ are $T_x\sim10^{-3}T_{\rm K}$ and $T_0\sim10^{-2}T_{\rm K}$, respectively, $T_{\rm K}$ being the Kondo temperature of the model. We also find non-Fermi liquid behaviors at $T\ll T_{\rm K}$ in a series of physical quantities; the chemical potential, the specific heat, and the magnetic susceptibility, explaining the non-Fermi liquid behaviors observed in PrV$_2$Al$_{20}$ and PrIr$_2$Zn$_{20}$. At the same time, we find that the Fermi liquid behavior becomes prominent for the system with smaller hybridization between $f$- and conduction electrons, explaining the Fermi liquid behaviors observed in PrTi$_2$Al$_{20}$.

cond-mat.str-el↗
arXiv2015

Intrinsic Angular Momentum and Intrinsic Magnetic Moment of Chiral Superconductor on Two-Dimensional Square Lattice

The intrinsic magnetic moment (IMM) and intrinsic angular momentum (IAM) of a chiral superconductor with $p$-wave symmetry on a two-dimensional square lattice are discussed on the basis of the Bogoliubov-de Gennes equation. The the IMM and IAM are shown to be on the order of $μ_{\rm B}N$ and $\hbar N$, respectively, $N$ being the total number of particles, without an extra factor $(T_{\rm c}/T_{\rm F})^γ$ ($γ=1,2$), and parallel to the pair angular momentum. They arise from the current in the surface layer with a width on the order of the coherence length $ξ_{0}$, the size of Cooper pairs. However, in a single-band model, they are considerably canceled by the contribution from the Meissner surface current in a layer with the width of the penetration depth $λ$, making it difficult to observe them experimentally. In the case of multi-band metals with both electron-like and hole-like bands, however, considerable cancellation still occurs for the IMM but not for the IAM, making it possible to observe the IAM selectively because the effect of the Meissner current becomes less important. As an example of a multi-band metal, the case of the spin-triplet chiral superconductor Sr$_2$RuO$_4$ is discussed and experiments for observing the IAM are proposed.

cond-mat.supr-con↗
arXiv2015

Ginzburg-Landau Formalism for 2n-Body Condensation

The Ginzburg-Landau formalism is constructed for Fermi superfluidity based on the 2n-body condensation in parallel with the usual Ginzburg-Landau formalism for the Cooper pair condensation. By this formalism, the transition temperature of the 2n-body condensation is given compactly by the zero of coefficient of the quadratic term in the 2n-body condensed order parameter without counting complicated Feynman diagrams for the 2n-body condensation susceptibility. It is shown that the 2n-body condensed state is stabilized in the intermediate- or strong-coupling regime against the BCS state based on the Cooper pair condensation. This theory is applied to the case of the possible superfluid state of cold atomic gases such as $^9$Be and $^{173}$Yb; the quartet state is possible in the former case, while the sextet state is expected in the latter case. It is predicted that the $^{173}$Yb atomic gas so far attained satisfies the condition for the sextet condensed state to be realized.

cond-mat.supr-con↗
arXiv2015

Deformation of the Fermi Surface and Anomalous Mass Renormalization by Critical Spin Fluctuations through Asymmetric Spin-Orbit Interaction

It is shown that an asymmetric spin-orbit interaction is appreciably renormalized by the effect of critical spin fluctuations. As an explicit example, the Rashba-type interaction is predicted to be suppressed by anti-ferromagnetic critical fluctuations near the hot line (or point), leading to a deformation of the Fermi surface near the hot line (or point) around which the band splitting is decreased, while ferromagnetic critical fluctuations are shown to enhance the Rashba-type interaction everywhere on the Fermi surface, leading to an increase in the band splitting. It is also found that the many-body mass renormalization, which diverges towards the magnetic quantum critical point, is in the opposite sign for the two split bands by the Rashba-type interaction. These predictions are observable by the de Haas-van Alphen (dHvA) effect in principle.

cond-mat.str-el↗
arXiv2014

BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model under Magnetic Field

The Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover in the two-dimensional attractive Hubbard model under the magnetic field is discussed at the half-filling at T=0 K on the basis of the formalism of Eagles and Leggett. It is shown that the so-called Fulde-Ferrel-Larkin-Ovchinikov-like state with a non-zero center-of-mass wave vector ${\bf q}\not=0$ is not stabilized in the weak-coupling (BCS) region, while such a state with ${\bf q}\not=0$ is stabilized against that with ${\bf q}=0$ even in a wide strong-coupling (BEC) region where di-fermion molecules are formed. The physical implication of this surprising result is discussed.

cond-mat.supr-con↗
arXiv2014

Wide Quantum Critical Region of Valence Fluctuations: Origin of Robust Quantum Criticality in Quasicrystal Yb15Al34Au51 under Pressure

The mechanism of the emergence of robust quantum criticality in the heavy-electron quasicrystal Yb15Al34Au51 is analyzed theoretically. By constructing a minimal model for the quasicrystal and its crystalline approximant, which contain concentric shell structures with Yb and Al-Au clusters, we show that a set of quantum critical points of the first-order valence transition of Yb appears as spots in the ground-state phase diagram. Their critical regions overlap each other, giving rise to a wide quantum critical region. This well explains the robust criticality observed in Yb15Al34Au51 under pressure, and predicts the emergence of the common criticality in the crystalline approximant under pressure. The wider critical region in the quasicrystal than that in the crystalline approximant in the T-P phase diagram and the field-induced valence-crossover "region" in the T-H phase diagram are predicted to appear.

cond-mat.str-el↗
arXiv2014

T/B Scaling in beta-YbAlB4

The scaling behavior over four decades of the ratio of temperature T to magnetic field B observed in the magnetization in beta-YbAlB4 is theoretically examined. By developing a theoretical framework that exhibits the quantum critical phenomena of Yb-valence fluctuations under a magnetic field, we show that the T/B-scaling behavior can appear near the quantum critical point of the valence transition. The emergence of the T/B scaling indicates the presence of the small characteristic energy scale of critical Yb-valence fluctuations. It is argued that the quantum valence criticality offers a unified explanation for the unconventional quantum criticality as well as the T/B scaling in beta-YbAlB4.

cond-mat.str-el↗
arXiv2014

Theory of Pairing Assisted Spin Polarization in Spin-Triplet Equal Spin Pairing: Origin of Extra Magnetization in Sr_2RuO_4 in Superconducting State

It is shown that an extra magnetization is induced by an onset of the equal-spin-pairing of spin triplet superconductivity if the energy dependence of the density of states of quasiparticles exists in the normal state. It turns out that the effect is observable in Sr_2RuO_4 due to the existence of van Hove singularity in the density of states near the Fermi level, explaining the extra contribution in the Knight shift reported by Ishida et al. It is also quite non-trivial that this effect exists even without external magnetic field, which implies that the time reversal symmetry is spontaneously broken in the spin space.

cond-mat.supr-con↗
arXiv2014

Unconventional Quantum Criticality due to Critical Valence Transition

Quantum criticality due to the valence transition in some Yb-based heavy fermion metals has gradually turned out to play a crucial role to understand the non-Fermi liquid properties that cannot be understood from the conventional quantum criticality theory due to magnetic transitions. Namely, critical exponents giving the temperature (T) dependence of the resistivity ρ(T), the Sommerfeld coefficient, C(T)/T, the magnetic susceptibility, χ(T), and the NMR relaxation rates, 1/(T_{1}T), can be understood as the effect of the critical valence fluctuations of f electrons in Yb ion in a unified way. There also exist a series of Ce-based heavy fermion metals that exhibit anomalies in physical quantities, enhancements of the residual resistivity ρ_{0} and the superconducting critical temperature (T_c) around the pressure where the valence of Ce sharply changes. Here we review the present status of these problems both from experimental and theoretical aspects.

cond-mat.str-el↗
arXiv2013

Robustness of Quantum Criticality of Valence Fluctuations

The mechanism of emergence of robust quantum criticality in Yb- and Ce-based heavy electron systems under pressure is analyzed theoretically. By constructing a minimal model for quasicrystal Yb15Al34Au51 and its approximant, we show that quantum critical points of the first-order valence transition of Yb appear in the ground-state phase diagram with their critical regimes being overlapped to be unified, giving rise to a wide quantum critical regime. This well explains the robust unconventional criticality observed in Yb15Al34Au51 under pressure. We also discuss broader applicability of this mechanism to other Yb- and Ce-based systems such as beta-YbAlB4 showing unconventional quantum criticality.

cond-mat.str-el↗
arXiv2013

Effect of Spin-Orbit Interaction on (4d)^3- and (5d)^3 -Based Transition-Metal Oxides

The effects of a spin-orbit interaction on transition-metal ions of (4d)^3- and (5d)^3 -based oxides in which three electrons occupy t_{2g} orbitals are studied. The amplitude of the magnetic moment of d electrons on the 5d and 4d orbitals is estimated by numerical diagonalization. It is found that the magnetic moment is reduced by the spin-orbit interaction. It is suggested that (4d)^3- and (5d)^3 -based oxides are located in the middle of the L-S and J-J coupling schemes.

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