arXiv subjects

Kazushige Machida

Publications and source records attributed to Kazushige Machida.

At least 19 recordsLinked to original sources

arXiv2026

Nodal Superconductivity of UTe$_2$ Probed by Field-Angle-Resolved Specific Heat on a Crystal with $T_{\rm c}=2.1$ K

Field-angle-resolved specific-heat measurements were performed on a clean single crystal of a spin-triplet superconductor UTe$_2$ with $T_{\rm c}=2.1$ K and a low residual electronic specific heat. At low temperatures, the specific heat exhibits a linear dependence on the magnetic field when the field is applied precisely along the $b$ axis, in stark contrast to its rapid increase at low fields for other orientations. This pronounced anisotropy suggests the presence of nodal quasiparticle excitations with the Fermi velocity predominantly aligned along the $b$ axis. Considering the characteristic field-angle dependences of both the specific heat and the upper critical field, these observations are broadly compatible with theoretical models that assume a superconducting gap structure featuring either point nodes consistent with $B_{\rm 2u}$ symmetry, allowed in the infinitely strong spin-orbit coupling scheme, or line nodes confined to flat regions of the quasi-two-dimensional Fermi surface, consistent with $^3B_{\rm 3u}$ symmetry in the finite spin-orbit classification scheme. These results yield crucial hints for resolving the pairing symmetry of UTe$_2$, paving the way for a deeper understanding of its spin-triplet superconductivity.

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arXiv2025

Field-induced anomaly in the anisotropic non-Fermi-liquid normal state of UBe$_{13}$

We report the results of high-resolution dc magnetization and specific-heat measurements at very low temperatures for a single crystal \color{black} of UBe$_{13}$ in magnetic fields applied along the [001] and [111] directions, in both the normal and superconducting states. In the normal state, magnetic susceptibility $\chi(T) = M/H$ exhibits a logarithmic temperature dependence over a wide temperature range (1-20 K). However, with increasing field, this non-Fermi-liquid (NFL) behavior of $\chi(T) $ at low temperatures is suppressed. Moreover, a susceptibility maximum occurs below 4 T, whereas Fermi-liquid coherence is recovered above 8 T. In addition, thermodynamic anomalies ($T_{\rm A}$ and $H_{\rm A}$) occur in both magnetic susceptibility and specific heat at intermediate fields (6--10 T) along the [111] direction. Furthermore, a nontrivial fifth-order nonlinear susceptibility is observed in the normal-state magnetization of UBe$_{13}$. These results suggest a close relationship between the field-induced multipolar correlations of $5f$-electron degrees of freedom and the Fermi-surface reconstruction accompanying the crossover from the NFL state to the Fermi-liquid state in UBe$_{13}$.

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arXiv2025

High-resolution magnetostriction measurements of the Pauli-limited superconductor Sr2RuO4

We performed high-resolution magnetostriction measurements on the Pauli-limited superconductor Sr$_2$RuO$_4$ using high-quality single crystals. A first-order superconducting transition, accompanied by pronounced hysteresis, was observed under in-plane magnetic fields, where the relative length change of the sample, $\Delta L/L$, was on the order of $10^{-8}$. To ensure the reliability of the measurements, particular attention was paid to minimizing the influence of magnetic torque, which can significantly affect data under in-plane field configurations, via field-angle-resolved magnetostriction. Within the hysteresis regime, slightly below the Pauli-limited upper critical field, a hump-like anomaly in the magnetostriction coefficient was identified. Furthermore, a characteristic double-peak structure in the field-angle derivative of the magnetostriction provides additional support for this anomaly. Although these findings may reflect a lattice response associated with the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in Sr$_2$RuO$_4$, the possibility of a broadened first-order transition cannot be excluded. Notably, this magnetostriction anomaly qualitatively deviates from the FFLO phase boundary suggested by previous NMR measurements, highlighting the necessity for further experimental and theoretical investigations to elucidate the nature of the FFLO state in this material.

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arXiv2025

Novel $H_{\rm c2}$ suppression mechanism in a spin triplet superconductor -- Application to UTe$_2$--

A novel $H_{\rm c2}$ suppression mechanism is theoretically proposed in a spin triplet superconductor (SC) with equal spin pairs. We show that the upper critical field $H_{\rm c2}$ can be reduced from the orbital depairing limit $H^{\rm orb}_{\rm c2}$ to arbitrarily small value, keeping the second order phase transition nature. This mechanism is sharply different from the known Pauli-Clogston limit for a spin singlet SC where the reduction is limited to $\sim$0.3$H^{\rm orb}_{\rm c2}$ with the first order transition when the Maki parameter goes infinity. This novel $H_{\rm c2}$ suppression mechanism is applied to UTe$_2$, which is a prime candidate for a spin triplet SC, to successfully analyze the $H_{\rm c2}$ data for various crystalline orientations both under ambient and applied pressure, and to identify the pairing symmetry. It is concluded that the non-unitary spin triplet state with equal spin pairs is realized in UTe$_2$, namely $(\hat b+i\hat c)k_a$ in $^3$B$_{\rm 3u}$ which is classified under finite spin orbit coupling scheme.

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arXiv2024

Theoretical studies on off-axis phase diagrams and Knight shifts in UTe$_2$ -- Tetra-critical point, d-vector rotation, and multiple phases

Inspired by recent remarkable sets of experiments on UTe$_2$: discoveries of the fourth horizontal internal transition line running toward a tetra-critical point (TCP) at $H$=15T, the off-axis high field phases, and abnormally large Knight shift (KS) drop below $T_{\rm c}$ for $H$$\parallel$$a$-magnetic easy axis, we advance further our theoretical work on the field ($H$)-temperature ($T$) phase diagram for $H$$\parallel$$b$-magnetic hard axis which contains a positive sloped $H_{\rm c2}$ departing from TCP. A nonunitary spin-triplet pairing with three components explains these experimental facts simultaneously and consistently by assuming that the underlying normal electron system with a narrow bandwidth characteristic to the Kondo temperature $\sim$60K unsurprisingly breaks the particle-hole symmetry. This causes a special invariant term in Ginzburg-Landau (GL) free energy functional which couples directly with the 5f magnetic system, giving rise to the $T_{\rm c}$ splitting and ultimately to the positive sloped $H_{\rm c2}$ and the horizontal internal transition line connected to TCP. The large KS drop can be understood in terms of this GL invariance whose coefficient is negative and leads to a diamagnetic response where the Cooper pair spin is antiparallel to the applied field direction. The present scenario also accounts for the observed d-vector rotation phenomena and off-axis phase diagrams with extremely high $H_{\rm c2}$$\gtrsim$70T found at angles in between the $b$ and $c$-axes and between the $bc$ plane and $a$-axis, making UTe$_2$ a fertile playground for a topological superconductor.

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arXiv2023

Topological spin texture and d-vector rotation in spin-triplet superconductors: A case of UTe2

A novel spin texture formed by Cooper pair spins is found theoretically with a phase string attached by half-quantized vortices at both ends in a unit cell and characterized by its topologically rich vortex structure in a spin-triplet pairing. It is stable at an intermediate field region sandwiched by two conventional singular vortex phases below and above it. The d-vector direction of this spin texture is tilted from the principal crystal axes, whose spin susceptibility is neither the normal Pauli one \c{hi}N nor zero, describing microscopically the process of the d-vector rotation phenomena observed recently in UTe2. We compare the spin texture and singular vortex state in relation to the quasi-particle structure with Majorana zero modes for STM, the nuclear spin resonance spectral line width for NMR and {\mu}SR, and the vortex form factors for SANS to facilitate the identification of the pairing symmetry in UTe2.

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arXiv2023

Modulation vector of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn5 revealed by high-resolution magnetostriction measurements

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is an exotic superconducting phase formed by Cooper pairs with finite center-of-mass momentum $q$. On theoretical grounds, the superconducting order parameter in the FFLO state is spatially modulated along the $q$ vector, and the emergence of an associated anisotropy is expected at the phase transition from the Abrikosov state to the FFLO state. Here, we report the results of high-resolution magnetostriction measurements for a single crystal of CeCoIn$_5$ around $B \parallel c$. We find two anomalies in the magnetostriction along the $c$ axis, parallel to the magnetic-field orientation. In sharp contrast, this $B_{\rm K}$ anomaly disappears in the magnetostriction along the $a$-axis direction, perpendicular to the magnetic-field orientation. To explain this uniaxial expansion, we suggest a possibility that the FFLO transition occurs slightly below the upper critical field, and the FFLO modulation vector parallel to the applied magnetic field gives rise to the anisotropic response.

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arXiv2023

Violation of the orbital depairing limit in a non-unitary state --on the high field phase in the heavy Fermion superconductor UTe$_2$--

A theoretical study is reported on the origin of extremely high upper critical field $\sim$70T observed in UTe$_2$ with the transition temperature T$_{\rm c}$=1.6K-2K, far exceeding the conventional orbital depairing limit set by the Fermi velocity and T$_{\rm c}$ for a superconductor (SC) in the clean limit. We investigate possible violation of the orbital limit in terms of a spin-triplet nonunitary state, which is effectively coupled to the underlying magnetization induced by external field. This in turn produces the reduced internal field by cancelling it via magnetization. We formulate a theory within Ginzburg-Landau framework to describe this orbital limit violation and analyze experimental data on the upper critical fields for various field orientations in UTe$_2$. It is pointed out that the orbital limit violation for a spin-triplet SC together with the Pauli-Clogston limit violation for a spin-singlet SC constitutes a complete and useful framework to examine the high field physics in superconductors in the clean limit.

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arXiv2022

Anisotropic field response of specific heat for a ferromagnetic superconductor UCoGe in magnetic fields

Magnetic-field-angle-resolved specific heat and magnetization measurements were conducted on a ferromagnetic superconductor UCoGe with remarkable anisotropic upper critical field $H_{\rm c2}$. Although $H_{\rm c2}$ reaches a high magnetic field ($\sim 20$~T) along the $b$ axis, it is small ($\sim~0.6$~T) when a magnetic field is applied along the magnetic easy $c$-axis. This study indicates that the specific heat is abruptly suppressed when the magnetic field is applied toward the $c$ axis from the $a$ and $b$ axes in the ferromagnetic state. The field response of density of states (DOS) is anisotropic, relative to the $c$ axis, and its angle dependence is slightly singular. The Ising-type magnetic anisotropy of the ferromagnetic state is dominant even in the anisotropic reinforced superconducting state. These facts indicate that the suppression of DOS may closely relate to the superconducting state. We theoretically analyze these findings together with URhGe and UTe$_2$ by highlighting the common and distinctive features among three compounds.

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arXiv2022

Violation of the Pauli-Clogston limit in a heavy Fermion superconductor CeRh$_2$As$_2$ --Duality of itinerant and localized 4f electrons--

We theoretically propose a mechanism to understand the violation of the Pauli-Clogston limit for the upper critical field H$_{\rm c2}$ observed in the Ce bearing heavy Fermion material CeRh$_2$As$_2$ from the view point of spin singlet pairing. It is based on a duality concept, the dual simultaneous aspects of an electron: the itinerant part and localized part of quasi-particles (QPs) originated from the 4f electrons of the Ce atoms. While the itinerant QPs directly participate in forming the Cooper pairs, the localized QPs exert the internal field so as to oppose the applied field through the antiferromagnetic exchange interaction between them. This is inherent in the dense Kondo lattice system in general. We argue that this mechanism can be applied not only to the locally noncentrosymmetric material CeRh$_2$As$_2$, but also to globally inversion symmetry broken Ce-based materials such as CePt$_3$Si. Moreover, we point out that it also works for strongly Pauli limit violated spin triplet pairing systems, such as UTe$_2$.

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arXiv2021

Non-unitary triplet superconductivity tuned by field-controlled magnetization --URhGe, UCoGe and UTe$_2$--

We report on theoretical studies on ferromagnetic superconductors, URhGe, and UCoGe and identifies the pairing state as a non-unitary spin-triplet one, analogous to superfluid $^3$He-A phase. A recently found superconductor UTe$_2$ with almost ferromagnet is analyzed by the same manner. Through investigating their peculiar upper critical field $H_{\rm c2}$ shapes, it is shown that the pairing symmetry realized in all three compounds can be tuned by their magnetization curves under applied fields. This leads to the reentrant $H_{\rm c2}$ in URhGe, an S-shaped in UCoGe and an L-shaped $H_{\rm c2}$ in UTe$_2$ observed under the field direction parallel to the magnetic hard axis in orthorhombic crystals in common. The identification with double chiral form: ${\bf d}(k)=(\hat{b}+i\hat{c})(k_b+ik_c)$ in UTe$_2$ naturally enables us to understand (1) multiple phases with A$_1$, A$_2$, and A$_0$ phases observed under pressure, (2) the enhanced reentrant $H_{\rm c2}$ for the off-axis direction fields associated with first order meta-magnetic transition, and (3) Weyl point nodes oriented along the $a$-axis. All three compounds are found to be topologically rich solid-state materials worth further investigation.

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arXiv2020

Fully gapped superconductivity without sign reversal in the topological superconductor PbTaSe$_2$

We investigate the superconducting gap function of topological superconductor PbTaSe$_2$. Temperature, magnetic field, and three-dimensional (3D) field-angle dependences of the specific heat prove that the superconductivity of PbTaSe$_2$ is fully-gapped, with two isotropic $s$-wave gaps. The pair-breaking effect is probed by systematically increasing non-magnetic disorders through H$^+$-irradiations. The superconducting transition temperature, $T_{\rm{c}}$, is found to be robust against disorders, which suggests that the pairing should be sign-preserved rather than sign-reversed.

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arXiv2020

Notes on multiple superconducting phases in UTe$_2$ ---Third transition---

A three-component Ginzburg-Landau theory for a triplet pairing is developed to understand the observed multiple phases in a new superconductor UTe$_2$ under pressure. Near the critical pressure $P_{\rm cr}$=0.2GPa where all components are perfectly degenerate the three successive superconducting transitions are predicted to occur. The $p$-wave pairing symmetry realized in UTe$_2$ is characterized by non-unitarity and chirality with point nodes, thus time reversal symmetry spontaneously broken.

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arXiv2020

Microscopic Eilenberger theory of Fulde-Ferrell-Larkin-Ovchinnikov states in the presence of vortices

We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entropy, and the zero-energy density of states are calculated. Those quantities are shown to start quickly growing upon entering the LO state. We also evaluate the wave length of the LO modulation, the flux line lattice form factors for small angle neutron scattering, and the NMR spectra to facilitate the identification of the LO state. Two cases of strong and intermediate Pauli paramagnetic effect are studied comparatively. The possibility of the LO phase in Sr$_2$RuO$_4$, CeCoIn$_5$, CeCu$_2$Si$_2$, and the organic superconductors is critically examined and crucial experiments to identify it are proposed.

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arXiv2020

Orientation of point nodes and nonunitary triplet pairing tuned by the easy-axis magnetization in UTe2

The gap structure of a novel uranium-based superconductor UTe$_2$, situated in the vicinity of ferromagnetic quantum criticality, has been investigated via specific-heat $C(T,H,\Omega)$ measurements in various field orientations. Its angular $\Omega(\phi,\theta)$ variation shows a characteristic shoulder anomaly with a local minimum in $H \parallel a$ at moderate fields rotated within the $ab$ and $ac$ planes. Based on the theoretical calculations, these features can be attributed to the presence of point nodes in the superconducting gap along the $a$ direction. Under the field orientation along the easy-magnetization $a$ axis, an unusual temperature dependence of the upper critical field at low fields together with a convex downward curvature in $C(H)$ were observed. These anomalous behaviors can be explained on the basis of a nonunitary triplet state model with equal-spin pairing whose $T_{\rm c}$ is tuned by the magnetization along the $a$ axis. From these results, the gap symmetry of UTe$_2$ is most likely described by a vector order parameter of $d(k)=(b + ic)(k_b + ik_c)$.

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arXiv2020

Theory of spin-polarized superconductors -- an analogue of superfluid $^3$He A-phase

It is shown theoretically that ferromagnetic superconductors, UGe$_2$, URhGe, and UCoGe can be described in terms of the A-phase like triplet pairing similar to superfluid $^3$He in a unified way, including peculiar reentrant, S-shape, or L-shape $H_{\rm c2}$ curves. The associated double transition inevitable between the A$_1$ and A$_2$-phases in the $H$-$T$ plane is predicted, both of which are characterized by non-unitary state with broken time reversal symmetry and the half-gap. UTe$_2$, which has been discovered quite recently to be a spin-polarized superconductor, is analyzed successively in the same view point, pointing out that the expected A$_1$-A$_2$ transition is indeed emerging experimentally. Thus the four heavy Fermion compounds all together are entitled to be topologically rich solid state materials worth further investigating together with superfluid $^3$He A-phase.

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arXiv2019

Spin gap and L modulated intensity at the low-energy incommensurate magnetic fluctuations in the superconducting state of Sr2RuO4

Low-energy incommensurate (IC) magnetic fluctuations in the multiband superconductor Sr$_2$RuO$_4$ is investigated by high-resolution inelastic neutron scattering measurements and random phase approximation (RPA) calculations. Below $T_\text{c}$, the substantial spin gap is observed at $\mathbf{Q}_\text{IC}=(0.3, 0.3, L)$ where the quasi-one-dimensional $\alpha$ and $\beta$ sheets consisting of the Fermi surfaces are in good nesting conditions. $L$ modulated intensity of the low-energy IC magnetic fluctuations and our RPA calculations indicate that the superconducting gaps regarding the $\alpha$ and $\beta$ sheets have the horizontal line nodes.

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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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