arXiv subjects

Kazushige Machida

Publications and source records attributed to Kazushige Machida.

At least 37 records · Page 2Linked to original sources

arXiv2019

Quasi-particle evidence for the nematic state above $T_{\rm{c}}$ in Sr$_x$Bi$_2$Se$_3$

In the electronic nematic state, an electronic system has a lower symmetry than the crystal structure of the same system. Electronic nematic states have been observed in various unconventional superconductors such as cuprate- and iron-based, heavy-fermion, and topological superconductors. The relation between nematicity and superconductivity is a major unsolved problem in condensed matter physics. By angle-resolved specific heat measurements, we report bulk quasi-particle evidence of nematicity in the topological superconductor Sr$_x$Bi$_2$Se$_3$. The specific heat exhibited a clear 2-fold symmetry despite the 6-fold symmetric lattice. Most importantly, the 2-fold symmetry appeared in the normal state above the superconducting transition temperature. This is explained by the angle-dependent Zeeman effect due to the anisotropic density of states in the nematic phase. Such results highlight the interrelation between nematicity and unconventional superconductivity.

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arXiv2019

Theoretical studies for identifying horizontal line nodes via angle-resolved density of states measurements ---Application to Sr$_2$RuO$_{4}$---

On the basis of the microscopic quasi-classical Eilenberger theory, we analyze the recent angle-resolved specific heat experiment carried out at low temperature for Sr$_2$RuO$_{4}$ to identify the superconducting gap symmetry, comprising either horizontal or vertical line nodes relative to the tetragonal crystal symmetry. Several characteristics, in particular, the landscape of the in-plane oscillation amplitude $A_4(B, T)$ with a definite sign for almost the entire $B$-$T$ plane are best explained by the horizontal line node symmetry, especially when the multiband effect and Pauli paramagnetic effect are taken into account. The present analysis of $A_4(B,T)$ with definite sign points to the presence of an anomalous field region at a lower temperature in the experimental data, whose origin is investigated. Our theory demonstrates the application and uniqueness of the field-rotating thermodynamic measurements in uncovering the precise gap structure for target materials.

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arXiv2018

Disorder-sensitive node-like small gap in FeSe

We investigate the band structure, nematic state and superconducting gap structure of two selected FeSe single crystals containing different amount of disorder. Transport and angle-resolved photoemission spectroscopy measurements show that the small amount of disorder has little effect to the band structure and the nematic state of FeSe. However, temperature and magnetic field dependencies of specific heat for the two samples are quite different. Wave-vector-dependent gap structure are obtained from the three dimensional field-angle-resolved specific heat measurements. A small gap with two vertical-line nodes or gap minima along the $k_z$ direction is found only in the sample with higher quality. Such symmetry-unprotected nodes or gap minima are found to be smeared out by small amount of disorder, and the gap becomes isotropic in the sample of lower quality. Our study reveals that the reported controversy on the gap structure of FeSe is due to the disorder-sensitive node-like small gap.

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arXiv2018

Searching for gap zeros in Sr2RuO4 via field-angle-dependent specific-heat measurement

The gap structure of Sr$_2$RuO$_4$, which is a longstanding candidate for a chiral p-wave superconductor, has been investigated from the perspective of the dependence of its specific heat on magnetic field angles at temperatures as low as 0.06 K ($\sim 0.04T_{\rm c}$). Except near $H_{\rm c2}$, its fourfold specific-heat oscillation under an in-plane rotating magnetic field is unlikely to change its sign down to the lowest temperature of 0.06 K. This feature is qualitatively different from nodal quasiparticle excitations of a quasi-two-dimensional superconductor possessing vertical lines of gap minima. The overall specific-heat behavior of Sr$_2$RuO$_4$ can be explained by Doppler-shifted quasiparticles around horizontal line nodes on the Fermi surface, whose in-plane Fermi velocity is highly anisotropic, along with the occurrence of the Pauli-paramagnetic effect. These findings, in particular, the presence of horizontal line nodes in the gap, call for a reconsideration of the order parameter of Sr$_2$RuO$_4$.

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arXiv2018

Multifaceted properties of Andreev bound states: Interplay of symmetry and topology

Andreev bound states ubiquitously emerge as a consequence of nontrivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties as Majorana fermions and odd-frequency pairing. A unified concept behind Andreev bound states originates from a soliton state in the one-dimensional Dirac equation with mass domain wall, and the interplay of ABSs with symmetry and topology enriches their physical characteristics. We make an overview of Andreev bound states with a special focus on superfluid $^3$He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity, and the anomalous magnetic response. The marriage of the superfluid $^3$He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with Andreev bound states.

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arXiv2017

Gap structure of FeSe determined by field-angle-resolved specific heat measurements

Quasiparticle excitations in FeSe were studied by means of specific heat ($C$) measurements on a high-quality single crystal under rotating magnetic fields. The field dependence of $C$ shows three-stage behavior with different slopes, indicating the existence of three gaps ($Δ_1$, $Δ_2$, and $Δ_3$). In the low-temperature and low-field region, the azimuthal-angle ($ϕ$) dependence of $C$ shows a four-fold symmetric oscillation with sign change. On the other hand, the polar-angle ($θ$) dependence manifests as an anisotropy-inverted two-fold symmetry with unusual shoulder behavior. Combining the angle-resolved results and the theoretical calculation, the smaller gap $Δ_1$ is proved to have two vertical-line nodes or gap minima along the $k_z$ direction, and is determined to reside on the electron-type $\varepsilon$ band. $Δ_2$ is found to be related to the electron-type $δ$ band, and is isotropic in the $ab$-plane but largely anisotropic out of the plane. $Δ_3$ residing on the hole-type $α$ band shows a small out-of-plane anisotropy with a strong Pauli-paramagnetic effect.

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arXiv2017

Spin triplet nematic pairing symmetry and superconducting double transition in U$_{1-x}$Th$_{x}$Be$_{13}$

Motivated by a recent experiment on U$_{1-x}$Th$_{x}$Be$_{13}$ with $x=3\%$, we develop a theory to narrow down the possible pair symmetry to consistently describe the double transition utilizing various theoretical tools; group theory and Ginzburg-Landau theory. It is explained in terms of the two dimensional representation E$_{\rm u}$ with spin triplet. A symmetry breaking causes the degenerate $T_{\rm c}$ to split into the two. The low temperature phase is identified as the cyclic $p$ wave: $\vec {d}({\bf k})={\hat x}k_x+\varepsilon{\hat y}k_y+\varepsilon^2{\hat z}k_z$ with $\varepsilon^3=1$ while the biaxial nematic phase: ${\vec d}({\bf k})={\sqrt 3}({\hat x}k_x-{\hat y}k_y$) is the high temperature one. This allows us to simultaneously identify the uniaxial nematic phase: ${\vec d}({\bf k})=2{\hat z}k_z-{\hat x}k_x-{\hat y}k_y$ for UBe$_{13}$, which breaks spontaneously cubic symmetry of the system. Those pair functions are fully consistent with the above and existing data. We comment on the accidental scenario in addition to this degeneracy scenario and the intriguing topological nature hidden in this long-known material.

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arXiv2017

Quasiparticle Excitations and Evidence for Superconducting Double Transitions in Monocrystalline U0.97Th0.03Be13

Superconducting (SC) gap symmetry and magnetic response of cubic U0.97Th0.03Be13 are studied by means of high-precision heat-capacity and dc magnetization measurements using a single crystal, in order to address the long-standing question of its second phase transition at Tc2 in the SC state below Tc1. The absence (presence) of an anomaly at Tc2 in the field-cooling (zero-field-cooling) magnetization indicates that this transition is between two different SC states. There is a qualitative difference in the field variation of the transition temperatures; Tc2(H) is isotropic whereas Tc1(H) exhibits a weak anisotropy between [001] and [111] directions. In the low temperature phase below Tc2(H), the angle-resolved heat-capacity $C(T,H, ϕ)$ reveals that the gap is fully opened over the Fermi surface, narrowing down the possible gap symmetry.

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arXiv2016

Nodal gap detection through polar angle-resolved density of states measurements in uniaxial superconductors

We propose a spectroscopic method to identify the nodal gap structure in unconventional superconductors. This method best suits for locating the horizontal line node and for pinpointing the isolated point nodes by measuring polar angle ($θ$) resolved zero energy density of states $N(θ)$. This is measured by specific heat or thermal conductivity at low temperatures under a magnetic field. We examine a variety of uniaxially symmetric nodal structure, including point and/or line nodes with linear and quadratic dispersions, by solving Eilenberger equation in vortex states. It is found that (A) the maxima of $N(θ)$ continuously shift from the anti-nodal to the nodal direction ($θ_{\rm n}$) as a field increases accompanying the oscillation pattern reversal at low and high fields. Furthermore, (B) local minima emerge next to $θ_{\rm n}$ on both sides except for the case of linear point node. These features are robust and detectable experimentally. Experimental results of $N(θ)$ performed on several superconductors, UPd$_2$Al$_3$, URu$_2$Si$_2$, Cu$_x$Bi$_2$Se$_3$, and UPt$_3$, are examined and commented in light of the present theory.

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arXiv2016

Thermodynamic study of gap structure and pair-breaking effect by magnetic field in the heavy-fermion superconductor CeCu2Si2

This paper presents the results of specific-heat and magnetization measurements, in particular their field-orientation dependence, on the first discovered heavy-fermion superconductor CeCu$_2$Si$_2$ ($T_{\rm c} \sim 0.6$ K). We discuss the superconducting gap structure and the origin of the anomalous pair-breaking phenomena, leading e.g., to the suppression of the upper critical field $H_{\rm c2}$, found in the high-field region. The data show that the anomalous pair breaking becomes prominent below about 0.15 K in any field direction, but occurs closer to $H_{\rm c2}$ for $H \parallel c$. The presence of this anomaly is confirmed by the fact that the specific-heat and magnetization data satisfy standard thermodynamic relations. Concerning the gap structure, field-angle dependences of the low-temperature specific heat within the $ab$ and $ac$ planes do not show any evidence for gap nodes. From microscopic calculations in the framework of a two-band full-gap model, the power-law-like temperature dependences of $C$ and $1/T_1$, reminiscent of nodal superconductivity, have been reproduced reasonably. These facts further support multiband full-gap superconductivity in CeCu$_2$Si$_2$.

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arXiv2016

Evidence for chiral d-wave superconductivity in URu2Si2 from the field-angle variation of its specific heat

Low-energy quasiparticle (QP) excitations in the heavy-fermion superconductor URu$_2$Si$_2$ were investigated by specific-heat $C(T, H, ϕ, θ)$ measurements of a high-quality single crystal. The occurrence of QP excitations due to the Doppler-shift effect was detected regardless of the field direction in $C(H)$ of the present clean sample, which is in sharp contrast to a previous report. Furthermore, the polar-angle-dependent $C(θ)$ measured under a rotating magnetic field within the ac plane exhibits a shoulder-like anomaly at $θ\sim 45$ deg and a sharp dip at $θ= 90$ deg ($H \parallel a$) in the moderate-field region. These features are supported by theoretical analyses based on microscopic calculations assuming the gap symmetry of $k_z(k_x+ik_y)$, whose gap structure is characterized by a combination of a horizontal line node at the equator and point nodes at the poles. The present results have settled the previous controversy over the gap structure of URu$_2$Si$_2$ and have authenticated its chiral $d$-wave superconductivity.

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arXiv2016

Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to $^3$He ---

In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid $^3$He, which serves as a rich repository of novel topological quantum phenomena originating from the intertwining of symmetries and topologies. In particular, it is emphasized that the quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase, the A-phase as a Weyl superfluid, the nodal planar and polar phases, and the crystalline ordered stripe phase. All these phases generate noteworthy topological phenomena, including topological phase transitions concomitant with spontaneous symmetry breaking, Majorana fermions, Weyl superfluidity, emergent supersymmetry, spontaneous edge mass and spin currents, topological Fermi arcs, and exotic quasiparticles bound to topological defects. In relation to the mass current carried by gapless edge states, we also briefly review a longstanding issue on the intrinsic angular momentum paradox in $^3$He-A. Moreover, we share the current status of our knowledge on the topological aspects of unconventional superconductors, such as the heavy-fermion superconductor UPt$_3$ and superconducting doped topological insulators, in connection with the superfluid $^3$He.

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arXiv2015

Interplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor--Application to Sr2RuO4--

We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($\sim$60) and the $H_{\rm c2}$ anisotropy ($\sim$20). Among the three bands; $γ$ with the effective mass anisotropy $\sim$180, $α$ with $\sim$120, and $β$ with $\sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $γ$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $β$ band has a full gap and the minor $γ$ band has a $d_{x^2-y^2}$ like gap.

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arXiv2015

Hidden Crossover Phenomena in Strongly Pauli Limited Multiband Superconductors ---Application to CeCu$_2$Si$_2$

Motivated by recent experiments on heavy fermion materials CeCu$_2$Si$_2$ and UBe$_{13}$, we develop a framework to capture generic properties of multiband superconductors with strong Pauli paramagnetic effect (PPE). In contrast to the single band case, the upper critical field $H_{\rm c2}$ can remain second order transition even for strong PPE cases. The expected first order transition is hidden inside $H_{\rm c2}$ and becomes a crossover due to the interplay of multibandness. The present theory based on full self-consistent solutions of the microscopic Eilenberger theory explains several mysterious anomalies associated with the crossover and the "empty" vortex core state which is observed by recent STM experiment on CeCu$_2$Si$_2$.

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arXiv2015

Pauli-paramagnetic effects on mixed state properties in a strongly anisotropic superconductor ---Application to Sr_2_RuO_4_---

We study theoretically the mixed state properties of a strong uniaxially-anisotropic type II superconductor with the Pauli paramagnetic effect, focusing on their behaviors when the magnetic field orientation is tilted from the conduction layer ab plane. On the basis of Eilenberger theory, we quantitatively estimate significant contributions of the Pauli paramagnetic effects on a variety of physical observables, including transverse and longitudinal components of the flux line lattice form factors, magnetization curves, Sommerfeld coefficient, field distributions and magnetic torques. We apply these studies to Sr_2_RuO_4_ and quantitatively explain several seemingly curious behaviors, including the H_c2_ suppression for the ab plane direction, the larger anisotropy ratio and intensity found by the spin-flip small angle neutron scattering, and the first order transition observed recently in magneto-caloric, specific heat and magnetization measurements in a coherent and consistent manner. Those lead us to conclude that Sr_2_RuO_4_ is either a spin-singlet or a spin-triplet pairing with the d-vector components in the ab plane.

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arXiv2015

Symmetry protected vortex bound state in superfluid $^3$He B-phase

The superfluid $^3$He formed by spin-triplet $p$-wave Cooper pairs is a typical topological superfluid. In the superfluid $^3$He B-phase, several kinds of vortices classified by spatial symmetries $P_1$, $P_2$, and $P_3$ are produced, where $P_1$ is inversion symmetry, $P_2$ is magnetic reflection symmetry, and $P_3$ is magnetic $π$-rotation symmetry. We have calculated the vortex bound states by the Bogoliubov-de Gennes theory and the quasiclassical Eilenberger theory, and also clarified symmetry protection of the low energy excitations by the spatial symmetries. On the symmetry protection, $P_3$ symmetry plays a key role which gives two-fold degenerate Majorana zero modes. Then, the bound states in the most symmetric $o$ vortex with $P_1$, $P_2$, and $P_3$ symmetries and in $w$ vortex with $P_3$ symmetry have the symmetry protected degenerate Majorana zero modes. On the other hand, zero energy modes in $v$ vortex, which is believed to be realized in the actual B-phase, are not protected, and in consequence become gapped by breaking axial symmetry. The excitation gap may have been observed as the variation of critical velocity. We have also suggested an experimental setup to create $o$ vortex with Majorana zero modes by a confinement and a magnetic field.

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arXiv2014

Sharp magnetization jump at the first-order superconducting transition in Sr2RuO4

The magnetization and magnetic torque of a high-quality single crystal of Sr$_2$RuO$_4$ have been measured down to 0.1 K under a precise control of the magnetic-field orientation. When the magnetic field is applied exactly parallel to the $ab$ plane, a sharp magnetization jump $4πδM$ of $(0.74 \pm 0.15)$ G at the upper critical field $H_{{\rm c2},{ab}} \sim 15$ kOe with a field hysteresis of 100 Oe is observed at low temperatures, evidencing a first-order superconducting-normal transition. A strong magnetic torque appearing when $H$ is slightly tilted away from the $ab$ plane confirms an intrinsic anisotropy $\varGamma=ξ_a/ξ_c$ of as large as 60 even at 100 mK, in contrast with the observed $H_{\rm c2}$ anisotropy of $\sim 20$. The present results raise fundamental issues in both the existing spin-triplet and spin-singlet scenarios, providing, in turn, crucial hints toward the resolution of the superconducting nature of Sr$_2$RuO$_4$.

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arXiv2014

Field-Orientation Dependence of Low-Energy Quasiparticle Excitations in the Heavy-Electron Superconductor UBe13

Low-energy quasiparticle excitations in the superconducting (SC) state of UBe$_{13}$ were studied by means of specific-heat ($C$) measurements in a rotating field. Quite unexpectedly, the magnetic-field dependence of $C(H)$ is linear in $H$ with no angular dependence at low fields in the SC state, implying that the gap is fully open over the Fermi surfaces, in stark contrast to the previous expectation. In addition, a characteristic cubic anisotropy of $C(H)$ was observed above 2~T with a maximum (minimum) for $H$ $||$ $[001]$ ($[111]$) within the $(1\bar{1}0)$ plane, both in the normal as well as in the SC states. This oscillation possibly originates from the anisotropic response of the heavy quasiparticle bands, and might be a key to understand the unusual properties of UBe$_{13}$.

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