arXiv subjects

Motohiko Ezawa

Publications and source records attributed to Motohiko Ezawa.

At least 19 recordsLinked to original sources

arXiv2026

Topological superconductors and Majorana fermions based on $X$-wave magnets with $X=p,d,f,g,i $

We study superconductors coupled with $X$-wave magnets with $X=p,d,f,g,i$. They are essentially different between altermagnets with $X=d,g,i$ and odd-parity magnets $X=p,f$ due to the compatibility of the spin-singlet formation of the $s$-wave superconductor. The altermagnets and odd-parity magnets show rich superconducting phase diagrams depending on the strength of the magnetic order, the chemical potential and the ratio of the on-site and nearest-neighbor interactions. Especially, we find that the altermagnetic order stabilizes the chiral ($p_{x}+ip_{y}$)-wave superconductor, which is a class D topological superconductor hosting Majorana chiral edge states. It is characterized by the Chern number. Especially, there emerge two chiral edge modes in the $i$-wave altermagnet, which are characterized by the Chern number 2. On the other hand, the $p$ ($f$)-wave odd-parity magnetic order stabilizes the $p$ ($f$)-wave topological superconductor, which is a class DIII topological superconductor hosting Majorana flat bands. It is characterized by the winding number. Majorana flat bands are robust in the presence of the mixing with the $s$-wave superconductivity, which is inevitable for odd-parity magnets although the magnitude of the mixing is tiny.

cond-mat.supr-con↗

arXiv2026

Observation of g-wave altermagnetic multipole

Over the past few years, altermagnets have emerged as a new class of collinear magnets with broken time-reversal symmetry, offering novel opportunities for spintronics beyond conventional magnets. Rather than from net magnetization, as in ferromagnets, the unconventional time-reversal symmetry breaking of altermagnets originates from antiferroic magnetic dipoles locked to higher-order multipoles. Here we report the direct visualization of a $g$-wave altermagnetic multipole in the canonical altermagnet CrSb. Combining high-energy synchrotron X-ray diffraction with valence electron density (VED) analysis, we uncover a pronounced directional anisotropy of the VED distribution alternating between Cr sublattices. This evidences the antiferroic order of electric hexadecapoles predicted in $g$-wave altermagnets. Its coexistence with antiferroic magnetic dipoles induces ferroic magnetic multipoles, as probed by polarized neutron diffraction. We further identify a microscopic model of altermagnetism that directly relates the $g$-wave multipole and the $g$-wave spin splitting. Through direct observation and quantification of multipoles, this study provides a real-space fingerprint of altermagnetism and establishes a general probe of hidden multipole order in quantum materials.

cond-mat.str-el↗

arXiv2026

Magnetization induced by a nonlinear response to temperature gradient in $d^{\prime }$, $g^{\prime }$ and $i^{\prime }$ altermagnets

It is a highly nontrivial question whether magnetization is induced by a nonlinear response to a temperature gradient in systems where the linear response is forbidden by inversion symmetry. In this work, we address this issue and provide explicit examples demonstrating that such a response can indeed arise. The spin-split electron band structures induced by $d$-wave, $g $-wave, $i$-wave altermagnets are characterized by $k^{N_{X}}\sin N_{X}ϕ$ around the band bottom, where $N_{X}=2,4$ and $6$, respectively. In contrast, those of the corresponding $d^{\prime }$-wave, $g^{\prime }$-wave, $i^{\prime }$-wave altermagnets are described by $k^{N_{X}}\cos N_{X}ϕ$. We show that a finite magnetization is induced in the $d^{\prime }$-wave, $g^{\prime }$-wave, $i^{\prime }$-wave altermagnets under a second-order nonlinear response to a temperature gradient $(\partial_{x}T)^2$ when the temperature gradient is linear and along either the $x$ or $y$ direction, whereas no such response occurs in the $d$-wave, $g$-wave and $i$-wave altermagnets. We also study the case where the direction of the temperature gradient is arbitrary. In this case, a finite magnetization is induced also in $d$-wave altermagnets but not in $g $-wave and $i$-wave altermagnets. We discuss the difference in physics between the $X$-wave and $X^{\prime }$-wave altermagnets with $X=d,g,i$ based on the tight-binding model. Furthermore, we show the emergence of the magnetization as a response when the temperature profile is not linear, $\partial _{x}^{2}T\neq 0$.

cond-mat.mes-hall↗

arXiv2026

Fourth-order and six-order nonlinear spin current rectifier in three-dimensional $h$-wave and $j$-wave odd-parity magnet

Higher-order symmetric $X$-wave magnets consist of two groups. One includes $d$-wave, $g$-wave and $i$-wave altermagnets, while the other includes $p$-wave and $f$-wave odd-parity magnets. Recently, the possibility of $h$-wave magnets has been discussed. Motivated by this development, we systematically construct an $X$-wave magnet with $\left( N_{X}+1\right) $ nodes in three dimensions from an $X$-wave magnet with $N_{X}$ nodes in two dimensions by means of a dimensional extension, where $N_X=1,2,3,4,6$ for $X=p,d,f,g,i$, respectively. Based on this method, we predict $j$-wave magnets in three dimensions. Then, we argue how to identify each of these $X$-wave magnets experimentally. We show that the $X$-wave magnet is completely identified by measuring the nonlinear spin currents. In particular, we predict that there are no spin currents other than the fourth-order ones such as $σ_{\text{spin}}^{x^{3}y;z}$ in $h$-wave odd-parity magnets in three dimensions and the sixth-order ones such as $σ_{\text{spin}}^{x^{5}y;z}$ in $j$-wave odd-parity magnets in three dimensions. They function as spin-current rectifier because the spin current exhibits unidirectional flow independent of the applied electric field.

cond-mat.mes-hall↗

arXiv2026

Spin-selective elliptic optical dichroism and perfectly spin-polarized third-order nonlinear photocurrent in altermagnets

We show that the low-energy theory of a $d$-wave altermagnet is characterized by anisotropic Dirac cones with spin-split band structures based on a recently proposed tight-binding model. In this system, spin-selective perfect elliptic dichroism emerges, enabling exclusive excitation of either up-spin or down-spin electrons by tuning the ellipticity of the incident light. We further derive a formula for the third-order photocurrent generated under simultaneous application of elliptically polarized light and a static electric field, expressed in terms of the quantum metric and Berry curvature. Using this formula, we demonstrate that only an up-spin polarized current is induced. This third-order response constitutes the leading photocurrent, as second-order processes such as injection and shift currents are forbidden by the inversion symmetry inherent to altermagnets. They lead to the prediction that, in insulating $d$-wave altermagnets, a spin-polarized third-order photocurrent arises as the leading electric response when elliptically polarized light and a static electric field are applied simultaneously. These findings provide a foundation for future developments in photoinduced spintronics based on altermagnets.

cond-mat.mes-hall↗

arXiv2026

Non-Clifford symmetry protected topological higher-order cluster states in multi-qubit measurement-based quantum computation

A cluster state is a strongly entangled state, which is a source of measurement-based quantum computation. It is generated by applying controlled-Z (CZ) gates to the state $\left\vert ++\cdots +\right\rangle $. It is protected by the $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{ \text{odd}}$ symmetry. By applying general quantum gates to the state $ \left\vert ++\cdots +\right\rangle $, we systematically obtain a general short-range entangled cluster state. If we use a non-Clifford gate such as the controlled phase-shift gate, we obtain a non-Clifford cluster state. Furthermore, if we use the controlled-controlled Z (CCZ) gate instead of the CZ gate, we obtain non-Clifford cluster states with five-body entanglement. We generalize it to the C$^{N}$Z gate, where $(2N+1)$-body entangled states are generated. The $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{\text{odd}}$ symmetry is non-Clifford for $N\geq 3$. We demonstrate that there emerge $2^{2N}$ fold degenerate ground states for an open chain, indicating the emergence of $N$ free spins at each edge. They can be used as an $N$-qubit input and an $N$-qubit output in measurement-based quantum computation. We also study the non-invertible symmetry, the Kennedy-Tasaki transformation and the string-order parameter in addition to the $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{\text{odd}}$ symmetry in these models.

quant-ph↗

arXiv2026

Nonlinear spin-Seebeck diode in $f$-wave magnets, third-order spin-Nernst effects in $g$-wave magnets and spin-Nernst effects in $i$-wave altermagnets

A prominent feature of $d$-wave altermagnets is that spin current is generated by applying temperature gradient, which is known as the spin-Nernst effect. We show in $f$-wave magnets that spin current is generated proportional to the square of the temperature gradient, which we call the nonlinear spin-Seebeck current. It can be used as a spin current diode. In addition, we show in $g$-wave altermagnets that spin current is generated in the third order of the temperature gradient. We also show in $i$-wave altermagnets that spin current is generated perpendicular to the temperature gradient, which is the spin-Nernst current. We have derived analytic formulas for these spin currents. It is interesting that these phenomena occur in the absence of the spin-orbit interaction. On the other hand, we show in $p$-wave magnets that spin current is not generated by temperature gradient.

cond-mat.mes-hall↗

arXiv2026

Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$

Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the spin degrees of freedom. It is related to electromagnetic cross responses. Quantum geometry is generalized to non-Hermitian systems and density matrices. Especially, the latter is quantum information geometry, where the quantum Fisher information naturally arises as quantum metric. We apply these results to the $X$-wave magnets, which include $d$% -wave, $g$-wave and $i$-wave altermagnets as well as $p$-wave and $f$-wave magnets. They have universal physics for anomalous Hall conductivity, tunneling magneto-resistance and planar Hall effect. We also study magneto-optical conductivity, magnetic circular dichroism and Friedel oscillations in the $X$-wave magnets. Various analytic formulas are derived in the case of two-band Hamiltonians. This paper presents a review of recent progress together with some original results.

cond-mat.mes-hall↗

arXiv2025

Almost half-quantized planar Hall effects in $X$-wave magnets with $X=p,d,f,g,i$

The planar Hall effect is a phenomenon that the Hall conductivity emerges perpendicular to the electric field in the presence of an in-plane magnetic field. We investigate the planar Hall effect in two-dimensional metal coupled with higher symmetric $X$-wave magnets with $X=p,d,f,g,i$,\ where those with $X=d,g,i$ are altermagnets. The $X$-wave magnet is characterized by the number $N_{X}$ of the nodes in the band structure, where $N_{X}=1,2,3,4,6$ corresponding to $X=p,d,f,g,i$. Although the system is metallic, provided the Dirac gap is tiny, we demonstrate that the Hall conductivities are almost half quantized and well approximated by the formula $σ_{xy}=\pm (e^{2}/2h)$ sgn$\left( J\sin N_{X}Φ\right) $, where $J$ is the coefficient of the coupling between the $X$-wave magnet and the electrons, and $Φ$ is the direction of the applied magnetic field. Hence, the Hall conductivity is periodic in $Φ$, and the periodicity is equal to the number $N_{X}$ of the nodes. This property may be used to confirm that the target material is indeed an $X $-wave magnet. Furthermore, the sign of $J$ may be used as a bit for antiferromagnetic spintronics.

cond-mat.mes-hall↗

arXiv2025

Tunneling magnetoresistance in a junction made of $X$-wave magnets with $X=p,d,f,g,i$

We investigate the tunneling magnetoresistance (TMR) of a bilayer system made of $X$-wave magnets with $X=p,d,f,g,i$, where $X=d,g,i$ corresponds to altermagnets. A universal analytic formula is derived for the TMR ratio. It is proportional to $\left\vert J\right\vert /\left( N_{X}Γ\right) $ for small $Γ$, where $N_{X}$ is the number of the nodes of the $X$% -wave magnet, $J$ is the strength of the $X$-wave magnet, and $Γ$ is the self-energy. It is contrasted with the TMR ratio made of ferromagnets, where it is proportional to $J^{2}/Γ^{2}$ for small $Γ$. Therefore, the TMR ratio is larger in ferromagnets for $\left\vert J\right\vert >Γ$. However, the $X$-wave magnets are expected to achieve high-speed and ultra-dense memory owing to the zero net magnetization.

cond-mat.mes-hall↗

arXiv2025

Metallic $p$-wave magnet with commensurate spin helix

Antiferromagnetic states with spin-split electronic structure give rise to novel spintronic, magnonic, and electronic phenomena despite (near-) zero net magnetization. The simplest odd-parity spin splitting - $p$-wave - was originally proposed to emerge from a collective instability in interacting electron systems. Recent theory identifies a distinct route to realise $p$-wave spin-split electronic bands without strong correlations, termed $p$-wave magnetism. Here we demonstrate an experimental realisation of a metallic $p$-wave magnet. The odd-parity spin splitting of delocalised conduction electrons arises from their coupling to an antiferromagnetic texture of localised magnetic moments: a coplanar spin helix whose magnetic period is an even multiple of the chemical unit cell, as revealed by X-ray scattering experiments. This texture breaks space inversion symmetry but preserves time-reversal ($T$) symmetry up to a half-unit-cell translation - thereby fulfilling the symmetry conditions for $p$-wave magnetism. Consistent with theoretical predictions, our $p$-wave magnet exhibits a characteristic anisotropy in the electronic conductivity. Relativistic spin-orbit coupling and a tiny spontaneous net magnetization further break $T$ symmetry, resulting in a giant anomalous Hall effect (AHE, $σ_{xy}>600\,$S/cm, Hall angle $>3\,\%$), for an antiferromagnet. Our model calculations show that the spin nodal planes found in the electronic structure of $p$-wave magnets are readily gapped by a small perturbation to induce the AHE.

cond-mat.str-el↗

arXiv2025

Purely electrical detection of the spin-splitting vector in $p$-wave magnets based on linear and nonlinear conductivities

A $p$-wave magnet has a momentum-dependent spin splitting and zero-net magnetization just as in the case of an altermagnet. It will be useful for high-density and ultra-fast memory, where the direction of the spin-splitting vector may be used as a bit. The spin-splitting vector corresponds to the Néel vector in altermagnets. However, it is a nontrivial problem to detect the spin-splitting vector in a $p$-wave magnet because time-reversal symmetry is preserved, while this is not a problem in an altermagnet because the anomalous Hall conductivity is present due to the breaking of time-reversal symmetry. Here, we show that it is possible to detect the in-plane component of the spin-splitting vector in the $p$-wave magnet by measuring the linear transverse and longitudinal Drude conductivity. Remarkably, this measurement is possible without using magnetization. Furthermore, we study the nonlinear Drude conductivity, the quantum-metric and the Berry curvature dipole induced nonlinear conductivity in the presence of tiny magnetization along the $z$\ axis. It is possible to detect the $z$-component of the spin-splitting vector by measuring the above nonlinear conductivities. We obtain analytic formulae for them in the first-order perturbation theory, which agree quite well with numerical results without perturbation.

cond-mat.mes-hall↗

arXiv2025

Higher-order bulk photovoltaic effects, quantum geometry and application to $p$-wave magnets

The injection and shift currents are generalized to the $\ell $th-order injection and shift currents for the longitudinal conductivities in the two-band model, where $\ell $ is the power of the applied electric field. In addition, the formulas for the higher-order injection current are expressed in terms of the quantum metric and the higher-order shift current in terms of the higher-order quantum connection. Then, they are applied to $p$-wave magnets. It is shown that the injection and shift currents are zero. On the other hand, the $\ell $th-order injection and shift currents with odd $\ell $ are nonzero when the direction of the Néel vector of the $p$-wave magnet points to an in-plane direction.

cond-mat.mes-hall↗

arXiv2025

Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model

Recent studies on topological materials are expanding into the nonlinear regime, while the central principle, namely the bulk-edge correspondence, is yet to be elucidated in the strongly nonlinear regime. Here, we reveal that nonlinear topological edge modes can exhibit the transition to spatial chaos by increasing nonlinearity, which can be a universal mechanism of the breakdown of the bulk-edge correspondence. Specifically, we unveil the underlying dynamical system describing the spatial distribution of zero modes and show the emergence of chaos. We also propose the correspondence between the absolute value of the topological invariant and the dimension of the stable manifold under sufficiently weak nonlinearity. Our results provide a general guiding principle to investigate the nonlinear bulk-edge correspondence that can potentially be extended to arbitrary dimensions.

cond-mat.mes-hall↗

arXiv2025

Quantum geometry and elliptic optical dichroism in $p$-wave magnets

The quantum geometric tensor is composed of the Berry curvature and the quantum metric, which is observable by means of optical absorption of elliptically polarized light. Especially, the quantum geometric tensor at the zero-momentum is observable by the optical absorption at the optical band edge. In this context, we study optical absorption of a $p$-wave magnet under irradiation of elliptically polarized light. The $p$-wave magnet has a band splitting along one axis, which we choose the $x$ axis. We obtain analytic formulae for the optical conductivity up to the second order in the magnitude of the Néel vector. In particular, the optical conductivity is exactly obtained when the Néel is along the $x$, $y$ and $z$ axis. It shows strong ellipticity a dependence of the light polarization, which is an elliptic dichroism. Especially, there is a perfect elliptic optical dichroism when the Néel vector is along the $y$ axis. It is possible to determine the Néel vector by measuring the ellipticity of the perfect elliptic dichroism.

cond-mat.mes-hall↗

arXiv2025

Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures

We investigate bilayer and trilayer systems composed of topologically distinct, vertically stacked layers, forming topological heterostructures based on the Benalcazar-Bernevig-Hughes model. We find that a topological phase transition induced by interlayer coupling significantly alters the number of corner states in these topological structures. Furthermore, we find that traditional nested Wilson loop analysis inaccurately classifies certain phases, leading us to evaluate multipole chiral numbers (MCNs) as a more appropriate topological invariant for this scenario. The MCNs not only enable accurate classification of topological phases but also directly correspond to the number of zero-energy corner states, effectively characterizing $\mathbb{Z}$-class HOTI phases. Our study proposes the novel concept of topological heterostructures, providing critical insights into the control of localized corner states within multilayer systems and expanding potential research directions.

cond-mat.mes-hall↗

arXiv2025

Bulk photovoltaic effects in altermagnets

The bulk photovoltaic effect is a photocurrent generation from alternating electric field, which is a promising candidate for future efficient solar cell technology. It is the second-order optical current, which is the injection current or the shift current. We focus on the direct current generation. By employing a simple two-band model of the $d$-wave altermagnet coupled with the Rashba interaction, we show that the linearly polarized light can generate the injection and shift currents when the Néel vector points to an in-plane direction. The magnitude of the injection current is almost constant over a wide range of the frequency $ω$ of the applied light provided it is smaller than a certain critical frequency $ω_{\text{c}}$ and larger than the bulk gap energy $\varepsilon _{\text{gap}}$, $\varepsilon _{\text{gap}}<\hbar ω<\hbar ω_{\text{c}}$. Hence, the use of the injection current is quite efficient for solar cell technology because any photon whose energy is within this range can be equally utilized.

cond-mat.mes-hall↗

arXiv2025

Third-order and fifth-order nonlinear spin-current generation in $g$-wave and $i$-wave altermagnets, and perfectly nonreciprocal spin-current in $f$-wave magnets

A prominent feature of $d$-wave altermagnets is the pure spin current generated in the absence of spin-orbit interactions. In the context of symmetry, there are the $s$-wave, the $p$-wave, the $d$-wave, the $f$-wave, the $g$-wave and the $i$-wave magnets. In this paper, making an analytic study of two-band Hamiltonian systems coupled with electrons, we demonstrate unexpectedly that only the $\ell $-th order nonlinear transverse spin current proportional to $E^{\ell }$ is generated in higher-wave symmetric magnets when the number of the nodes is $\ell +1$. Here $E$ is applied electric field. The nonlinear spin current is essential provided the linear spin current is absent. Indeed, only the third-order nonlinear spin current is generated in $g$-wave altermagnets, while only the fifth-order spin current is generated in $i$-wave altermagnets. In particular, only the second-order nonlinear spin current is generated in $f$-wave magnets, which leads to a perfect nonreciprocal spin current. On the other hand, there is no spin-current generation in $p$-wave magnets.

cond-mat.mes-hall↗