arXiv subjects

Takashi Hotta

Publications and source records attributed to Takashi Hotta.

At least 19 recordsLinked to original sources

arXiv2025

Effect of $Γ_7$ and $Γ_8$ Hybridizations on Three-Channel Kondo Phase Emerging from Ho Ions

By employing a numerical renormalization group method, we analyze a seven-orbital impurity Anderson model for Ho$^{3+}$ ion with ten $4f$ electrons. This model includes both $V_7$ and $V_8$, which are hybridizations between localized $4f$- and conduction electrons in $Γ_7$ and $Γ_8$ orbitals, respectively. For the case of $V_7=V_8$ with the local $Γ_5$ triplet ground state, we have reported the discovery of a three-channel Kondo (TCK) phase, characterized by a residual entropy of $\log ϕ$ with the golden ratio $ϕ=(1+\sqrt{5})/2$. In this research, by depicting the ground-state phase diagram on the $(V_8, V_7)$ plane, we attempt to unveil the effect of $V_7$ and $V_8$ on the emergence of the TCK phase. After performing a lot of numerical calculations, we find that the TCK phase appears in a relatively wide region on the $(V_8, V_7)$ plane. The boundary curves surrounding the TCK phase are determined by the variation of the temperature dependence in entropy and the abrupt change in energy spectra. We consider that most of the phases surrounding the TCK phase are Fermi liquids, but the non-Fermi liquid two-channel Kondo phase is unexpectedly found to exist next to the TCK phase. Finally, we briefly comment on the actual material concerning the detection of the TCK phase.

cond-mat.str-el↗

arXiv2021

Three-Channel Kondo Effect Emerging from Ho Ions

We illustrate the emergence of the three-channel Kondo effect in a seven-orbital impurity Anderson model hybridized with $Γ_7$ and $Γ_8$ conduction electron bands employing a numerical renormalization group method. In particular, we focus on the case with ten local $f$ electrons corresponding to a Ho$^{3+}$ ion. By investigating the dependence of the low-temperature behavior of the $f$-electron entropy on the crystalline electric field potential and hybridization, we found a residual entropy of $\log ϕ$ with the golden ratio $ϕ=(1+\sqrt{5})/2$, characteristic of the three-channel Kondo effect, for the wide range of parameters of the local $Γ_5$ triplet ground state. To improve our insight of local impurity spin, we explored a quantum critical point between three-channel Kondo and Fermi-liquid phases. Finally, we briefly discussed the cubic Ho compound as a candidate to observe experimentally the three-channel Kondo effect.

cond-mat.str-el↗

arXiv2020

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($Γ_7$ and $Γ_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $Γ_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $Γ_3$ doublet to $Γ_1$ singlet or $Γ_5$ triplet, we commonly observe a residual entropy of $\log ϕ$ with the golden ratio $ϕ=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $Γ_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log ϕ$ generally appears between two-channel Kondo and Fermi-liquid phases.

cond-mat.str-el↗

arXiv2019

Two-Channel Kondo Effect Emerging from Np and Pu Ions

On the basis of an idea of the electron-hole relation between $f^2$ and $f^4$ states in a $j$-$j$ coupling scheme, we point out a possibility that two-channel Kondo phenomena can be observed even in cubic transuranium compounds including Np and Pu ions with local $Γ_3$ non-Kramers doublet ground state. For the purpose, we analyze a seven-orbital impurity Anderson model hybridized with degenerate $Γ_8$ conduction electron bands by employing a numerical renormalization group method. From the numerical results for the case of four local $f$ electrons, corresponding to Np$^{3+}$ and Pu$^{4+}$ ions, we confirm that a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena, appears for the case with the local $Γ_3$ doublet ground state.

cond-mat.str-el↗

arXiv2019

Microscopic Theory of $Γ_3$ Quadrupole Ordering in Pr Compounds on the Basis of a $j$-$j$ Coupling Scheme

Toward the understanding of incommensurate $Γ_3$ quadrupole ordering in PrPb$_3$, we develop a microscopic theory of multipole ordering in $f^2$-electron systems from an itinerant picture on the basis of a $j$-$j$ coupling scheme. For this purpose, we introduce the $Γ_7$-$Γ_8$ Hubbard model on a simple cubic lattice with the effective interactions that induce local $Γ_3$ states. By evaluating multipole susceptibility in a random phase approximation, we find that the hybridization between $Γ_7$ and $Γ_8$ orbitals plays a key role in the emergence of $Γ_3$ quadrupole ordering. We also emphasize that $Γ_3$ quadrupole ordering can be understood from the concept of {\it multipole nesting}, in which the Fermi surface region with large $Γ_8$ orbital density should be nested on the area with a significant $Γ_7$ component when the positions of the Fermi surfaces are shifted by the ordering vector. This concept cab be intuitively understood from the fact that local $Γ_3$ doublets are mainly composed of two singlets between $Γ_8$ and $Γ_7$ orbitals. Finally, we discuss the possible relevance of the present theory to the experimental results of PrPb$_3$ and point out some future problems in this direction of research.

cond-mat.str-el↗

arXiv2018

Impurity Effects in Nodal Extended $s$- and Nodeless $d$-Wave Superconductors: Gap Symmetry of BiS$_2$-Based Layered Superconductors

In BiS$_2$-based layered superconductors,the existence of gap nodes on Fermi-surface curves has been suggested from angle-resolved photoemission spectroscopy measurements, whereas the conventional $s$-wave gap has been proposed from measurements of superfluid density and thermal conductivity. To reconcile these two distinct experimental results of the gap node, we investigate nonmagnetic impurity effects in the superconductor with a disconnected pocketlike Fermi-surface structure. Then, we claim that the seemingly contradictory situation concerning the gap node is resolved by a concept of dirty nodal extended $s$-wave superconductivity. Provided that it is unnecessary to consider the nodes of the gap, at first glance, the conventional $s$-wave gap seems to be a unique solution, but in the pocketlike Fermi-surface topology, a nontrivial possibility of a nodeless $d$-wave superconductor is pointed out. To clarify the gap symmetry, we propose to perform experiments on nuclear magnetic relaxation rate $T_{1}^{-1}$ in BiS$_2$-based layered superconductors.

cond-mat.supr-con↗

arXiv2017

Local nodal Cooper pairs in multiorbital systems

We show the emergence of a new class of superconductivity in multiorbital systems, focusing on non-Kramers f$^2$ states. The Cooper pairs in this class of superconductivity mainly consist of local pairs with the same symmetry as the local f$^2$ ground states. When the local ground state is an anisotropic representation, the superconducting gap has nodes on the Fermi surface. This nodal superconductivity is mediated by the strong onsite inter-orbital attractions as a consequence of negative-$U$ physics generalized to multiorbital systems. We show that this is indeed realized in a simple two-orbital model with antiferro Hund's coupling and enhanced inter-orbital interaction derived via a systematic local down folding. Finally, we briefly discuss superconductivity in Pr-1-2-20 compounds, UBe$_{13}$, and PrOs$_4$Sb$_{12}$ in view of the present mechanism.

cond-mat.supr-con↗

arXiv2017

Kondo effect in the seven-orbital Anderson model hybridized with $Γ_8$ conduction electrons

We clarify the two-channel Kondo effect in the seven-orbital Anderson model hybridized with $Γ_8$ conduction electrons by employing a numerical renormalization group method.From the numerical analysis for the case with two local $f$ electrons, corresponding to Pr$^{3+}$ or U$^{4+}$ ion, we confirm that a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena,appears for the local $Γ_3$ non-Kramers doublet state. For further understanding on the $Γ_3$ state, the effective model is constructed on the basis of a $j$-$j$ coupling scheme. Then, we rediscover the two-channel $s$-$d$ model concerning quadrupole degrees of freedom. Finally, we briefly introduce our recent result on the two-channel Kondo effect for the case with three local $f$ electrons.

cond-mat.str-el↗

arXiv2017

Two-channel Kondo Effect Emerging from Nd Ions

We discuss Kondo phenomena in a seven-orbital impurity Anderson model hybridized with $Γ_8$ conduction electrons by employing a numerical renormalization group method. In particular, we focus on the case with three local $f$ electrons, corresponding to a Nd$^{3+}$ ion. For realistic values of Coulomb interactions, spin-orbit coupling, cubic crystalline electric field potentials, and hybridization, we find a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena, for the wide range of parameters of the local $Γ_6$ ground state. This is considered to be the magnetic two-channel Kondo effect, consistent with the result from an extended $s$-$d$ model constructed on the basis of the $j$-$j$ coupling scheme. Finally, we briefly discuss candidates of Nd compounds to observe the two-channel Kondo effect.

cond-mat.str-el↗

arXiv2017

Influence of lattice structure on multipole interactions in $Γ_3$ non-Kramers doublet systems

We study the multipole interactions between $f^2$ ions with the $Γ_3$ non-Kramers doublet ground state under a cubic crystalline electric field. We construct the $Γ_3$ doublet state of the electrons with the total angular momentum $j=5/2$. By applying the second-order perturbation theory with respect to the intersite hopping, we derive the multipole interactions. We obtain a quadrupole interaction for a simple cubic lattice, an octupole interaction for a bcc lattice, and both quadrupole and octupole interactions for an fcc lattice. We also discuss general tendencies of the multipole interactions depending on the lattice structure by comparing the results with those for the $Γ_8$ quartet systems of $f^1$ ions.

cond-mat.str-el↗

arXiv2016

Valence Imbalance of Manganese Ions between Surface and Bulk Enhanced by Fermi-Surface Structure in Layered Manganites

To investigate valence imbalance phenomena between the surface and bulk in layered manganites, we analyze an eg-orbital degenerate double-exchange model with surfaces for two types of t2g spin structures. We reconfirm that the surface-induced Friedel oscillations occur in the charged structure and that the number of Mn4+ ions on the surface is larger than that in the bulk. This tendency is found to be more significant, when the eg-electron system has Fermi-surface structures with better nesting properties. The behavior of the Friedel oscillations depends on the nesting properties of the Fermi-surface curves along the direction of the oscillations, and not on the dimension of the system itself. We believe that these results will be useful for the development of high-efficiency cathodes in Li-ion batteries and catalysts.

cond-mat.str-el↗

arXiv2015

Quantum Interference of Surface-Induced Friedel Oscillations Enhanced by Fermi-Surface Nesting in Layered Manganites

Imbalance of Mn3+ and Mn4+ ions between surface and bulk in layered manganites is investigated on the basis of an orbital degenerate double-exchange model with surfaces. For two types of t2g spin structures, the number of Mn4+ ions on the surface is found to be larger than that in the bulk, explained by the surface-induced Friedel oscillation. In particular, for the sheet-type antiferromagnetic state, quantum beat phenomenon appears due to the interference among Friedel oscillations and the number of Mn4+ ions tends to increase on the surface. The present results are believed to be useful to develop high-efficient cathodes in Li-ion batteries and catalysts.

cond-mat.str-el↗

arXiv2015

Fermi-Surface Topology and Pairing Symmetry in BiS$_2$-Based Layered Superconductors

In order to clarify superconducting properties of BiS$_2$-based layered superconductors LaO$_{1-x}$F$_x$BiS$_2$, we evaluate the superconducting transition temperature $T_{\rm c}$ and analyze the gap function in a weak-coupling limit on the basis of the two-dimensional two-orbital Hubbard model. It is found that $T_{\rm c}$ becomes maximum at $x=0.6$ in the present calculations. For $x<0.45$, we obtain the $d$-wave gap of which line nodes do not cross the pocket-like Fermi-surface curves with the centers at X and Y points. On the other hand, for $x>0.45$, the extended $s$-wave gap is found for a couple of large Fermi-surface curves with the centers at M and X points. The variation of the Fermi-surface topology plays a key role for the gap symmetry in BiS$_2$-based superconductors.

cond-mat.supr-con↗

arXiv2015

Effect of Spin-Orbit Coupling on Kondo Phenomena in $f^7$-Electron Systems

In order to promote our basic understanding on the Kondo behavior recently observed in europium compounds, we analyze an impurity Anderson model with seven $f$ electrons at an impurity site by employing a numerical renormalization group method. The local part of the model consists of Coulomb interactions among $f$ electrons, spin-orbit coupling $λ$, and crystalline electric field (CEF) potentials, while we consider the hybridization $V$ between local $f$ electrons and single-band conduction electrons with $a_{\rm u}$ symmetry. For $λ=0$, we observe the underscreening Kondo behavior for appropriate values of $V$, characterized by the entropy change from $\ln 8$ to $\ln 7$, in which one of seven $f$ electrons is screened by conduction electrons. When $λ$ is increased, we obtain two types of behavior depending on the values of $V$. For large $V$, we find the entropy release of $\ln 7$ at low temperatures, determined by the level splitting energy due to the hybridization. For small $V$, we also observe the entropy change from $\ln 8$ to $\ln 2$ by the level splitting due to the hybridization, but at low temperatures, $\ln 2$ entropy is found to be released, leading to the Kondo effect. We emphasize that the Kondo behavior for small $V$ is observed for realistic values of $λ$ in the order of $0.1$ eV. We also discuss the effect of CEF potentials and the multipole properties in the Kondo behavior found in this paper.

cond-mat.str-el↗

arXiv2014

Chaos in Jahn-Teller Rattling

We unveil chaotic behavior hidden in the energy spectrum of a Jahn-Teller ion vibrating in a cubic anharmonic potential as a typical model for rattling in cage-structure materials. When we evaluate the nearest-neighbor level-spacing distribution $P(s)$ of eigenenergies of the present oscillator system, we observe the transition of $P(s)$ from the Poisson to the Wigner distribution with the increase of cubic anharmonicity, showing the occurrence of chaos in the anharmonic Jahn-Teller vibration. The energy scale of the chaotic region is specified from the analysis of $P(s)$ and we discuss a possible way to observe chaotic behavior in the experiment of specific heat. It is an intriguing possibility that chaos in nonlinear physics could be detected by a standard experiment in condensed matter physics.

cond-mat.mtrl-sci↗

arXiv2014

Kondo Effect of a Jahn-Teller Ion Vibrating in a Cubic Anharmonic Potential

We discuss the Kondo effect in a spinless two-orbital conduction electron system coupled with anharmonic Jahn-Teller vibration by employing a numerical renormalization group technique. When a temperature $T$ is decreased, we encounter a plateau of $\log 3$ entropy due to quasi-triple degeneracy of local low-energy states, composed of vibronic ground states and the first excited state with an excitation energy of $ΔE$. Around at $T$$\approx$$ΔE$, we observe an entropy change from $\log 3$ to $\log 2$. This $\log 2$ entropy originates from the rotational degree of freedom of the vibronic state and it is eventually released due to the screening by orbital moments of conduction electrons, leading to the Kondo effect of a Jahn-Teller ion. The Kondo temperature is explained by the effective $s$-$d$ model with anisotropic exchange interactions.

cond-mat.mtrl-sci↗

arXiv2013

Key role of hybridization between actinide 5f and oxygen 2p orbitals for electronic structure of actinide dioxides

In order to promote our understanding on electronic structure of actinide dioxides, we construct a tight-binding model composed of actinide $5f$ and oxygen $2p$ electrons, which is called $f$-$p$ model. After the diagonalization of the $f$-$p$ model, we compare the eigenenergies in the first Brillouin zone with the results of relativistic band-structure calculations. Here we emphasize a key role of $f$-$p$ hybridization in order to understand the electronic structure of actinide dioxides. In particular, it is found that the position of energy levels of $Γ_7$ and $Γ_8$ states determined from crystalline electric field potentials depends on the $f$-$p$ hybridization. We clarify the condition on the $f$-$p$ hybridization to explain the electronic structure which is consistent with the local crystalline electric field state. We briefly discuss the region of the absolute values of the Slater-Koster integrals for $f$-$p$ hybridization concerning the appearance of octupole ordering in NpO$_2$.

cond-mat.str-el↗

arXiv2012

Quadrupole Susceptibility of Gd-Based Filled Skutterudite Compounds

It is shown that quadrupole susceptibility can be detected in Gd compounds contrary to our textbook knowledge that Gd$^{3+}$ ion induces pure spin moment due to the Hund's rules in an $LS$ coupling scheme. The ground-state multiplet of Gd$^{3+}$ is always characterized by $J$=7/2, where $J$ denotes total angular momentum, but in a $j$-$j$ coupling scheme, one $f$ electron in $j$=7/2 octet carries quadrupole moment, while other six electrons fully occupy $j$=5/2 sextet, where $j$ denotes one-electron total angular momentum. For realistic values of Coulomb interaction and spin-orbit coupling, the ground-state wavefunction is found to contain significant amount of the $j$-$j$ coupling component. From the evaluation of quadrupole susceptibility in a simple mean-field approximation, we point out a possibility to detect the softening of elastic constant in Gd-based filled skutterudites.

cond-mat.str-el↗