arXiv subjects

Masatoshi Sato

Publications and source records attributed to Masatoshi Sato.

At least 37 records · Page 2Linked to original sources

arXiv2024

Intrinsic spin Nernst effect in topological Dirac and magnetic Weyl semimetals

We investigate the intrinsic spin Nernst effect (SNE), a transverse spin current induced by temperature gradients, in topological Dirac semimetals (TDSMs) and magnetic Weyl semimetals (MWSMs) with Ising spin-orbit coupling. The intrinsic SNE is described by the spin Berry curvature, which reflects the geometric nature of TDSMs and MWSMs. We clarified that the intrinsic SNE becomes significant when the Fermi energy is near, but slightly deviates from, the energy of the point nodes. In this situation, Bloch electrons with strong spin Berry curvature contribute to the SNE while avoiding carrier compensation between electrons and holes. We found that in TDSMs with small Fermi surfaces, the spin Nernst angle, which measures the efficiency of the SNE, is larger than that observed in heavy metals. This suggests that TDSMs with small Fermi surfaces can achieve efficient heat-to-spin current conversion. In MWSMs, variation in the magnitude of the exchange coupling with magnetic moments significantly changes the SNE, affecting both the direction and magnitude of the spin Nernst current. This implies that ferromagnetic transitions can be used to reverse the spin Nernst current. These results provide the fundamentals for future topological spin caloritronics.

cond-mat.mtrl-sci↗

arXiv2024

Universal platform of point-gap topological phases from topological materials

Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.

cond-mat.mes-hall↗

arXiv2024

Electromagnetic response of spinful Majorana fermions

A remarkable feature of topological superconductors is the emergence of Majorana fermions in electron systems. Whereas the emergent Majorana fermions share the self-anti-particle property with Majorana fermions in particle physics, they may have essentially different electromagnetic properties. In this paper, we argue the electromagnetic response of spinful Majorana fermions in topological superconductors. We present a general theory of the electromagnetic response of spinful Majorana fermions in topological superconductors and clarify how the pairing symmetry is encoded in the electromagnetic response. As an application, we predict the sublattice-dependent dipole (Ising)-type magnetic response of corner Majorana fermions in iron-based superconductors.

cond-mat.supr-con↗

arXiv2024

Bulk-boundary correspondence in point-gap topological phases

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the $K$-theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.

cond-mat.mes-hall↗

arXiv2024

Topological enhancement of non-normality in non-Hermitian skin effects

The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.

cond-mat.mes-hall↗

arXiv2023

Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups

We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant K-theory in the context of band theory. Various notions in the band theory such as irreducible representations at high-symmetric points, the compatibility relation, topological gapless and singular points naturally fits into the AHSS. As an application of the AHSS, we get the complete list of topological invariants for 230 space groups without time-reversal or particle-hole invariance. We find that a lot of torsion topological invariants appear even for symmorphic space groups.

cond-mat.str-el↗

arXiv2023

A non-commutative Reidemeister-Turaev torsion of homology cylinders

We compute the Reidemeister-Turaev torsion of homology cylinders which takes values in the $K_1$-group of the $I$-adic completion of the group ring $\mathbb{Q}π_1Σ_{g,1}$, and prove that its reduction to $\widehat{\mathbb{Q}π_1Σ_{g,1}}/\hat{I}^{d+1}$ is a finite-type invariant of degree $d$. We also show that the $1$-loop part of the LMO homomorphism and the Enomoto-Satoh trace can be recovered from the leading term of our torsion.

math.GT↗

arXiv2022

Exactly Solvable Spin Tri-Junctions

We present a class of exactly solvable tri-junctions of one- and two-dimensional spin systems. Based on the geometric criterion for solvability, we clarify the sufficient condition for the junctions so that the spin Hamiltonian becomes equivalent to Majorana quadratic forms. Then we examine spin tri-junctions using the obtained solvable models. We consider the transverse magnetic field Ising spin chains and reveal how Majorana zero modes appear at the tri-junctions of the chains. Local terms of the tri-junction crucially affect the appearance of Majorna zero modes, and the tri-junction may support Majorana zero mode even if the bulk spin chains do not have Majorana end states. We also examine tri-junctions of two-dimensional SO(5)-spin lattices and discuss Majorana fermions along the junctions.

cond-mat.stat-mech↗

arXiv2022

Correspondence of topological classification between quantum graph extra dimension and topological matter

In this paper, we study five-dimensional Dirac fermions of which extra-dimension is compactified on quantum graphs. We find that there is a non-trivial correspondence between matrices specifying boundary conditions at the vertex of the quantum graphs and zero-dimensional Hamiltonians in gapped free-fermion systems. Based on the correspondence, we provide a complete topological classification of the boundary conditions in terms of non-interacting fermionic topological phases. The ten symmetry classes of topological phases are fully identified in the language of five-dimensional Dirac fermions, and topological numbers of the boundary conditions are given. In analogy with the bulk-boundary correspondence in non-interacting fermionic topological phases, the boundary condition topological numbers predict four-dimensional massless fermions localized at the vertex of the quantum graphs and thus govern the low energy physics in four dimensions.

hep-th↗

arXiv2022

Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems

The Thouless pump is a phenomenon in which $\mathrm{U}(1)$ charges are pumped from an edge of a fermionic system to another edge. The Thouless pump has been generalized in various dimensions and for various charges. In this paper, we investigate the generalized Thouless pumps of fermion parity in both trivial and non-trivial phases of $1+1$-dimensional interacting fermionic short range entangled (SRE) states. For this purpose, we use matrix product states (MPSs). MPSs describe many-body systems in $1+1$ dimensions, and can characterize SRE states algebraically. We prove fundamental theorems for fermionic MPSs (fMPSs) and use them to investigate the generalized Thouless pumps. We construct non-trivial pumps in both the trivial and non-trivial phases and we show the stability of the pumps against interactions. Furthermore, we define topological invariants for the generalized Thouless pumps in terms of fMPSs and establish consistency with existing results. These are invariants of the family of SRE states that are not captured by the higher dimensional Berry curvature. We also argue a relation between the topological invariants of the generalized Thouless pump and the twist of the $K$-theory in the Donovan-Karoubi formulation.

cond-mat.str-el↗

arXiv2022

Non-Hermitian topological phenomena: A review

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

cond-mat.mes-hall↗

arXiv2022

Extrinsic topology of Floquet anomalous boundary states in quantum walks

Bulk-boundary correspondence is a fundamental principle for topological phases where bulk topology determines gapless boundary states. On the other hand, it has been known that corner or hinge modes in higher order topological insulators may appear due to "extrinsic" topology of the boundaries even when the bulk topological numbers are trivial. In this paper, we find that Floquet anomalous boundary states in quantum walks have similar extrinsic topological natures. In contrast to higher order topological insulators, the extrinsic topology in quantum walks is manifest even for first-order topological phases. We present the topological table for extrinsic topology in quantum walks and illustrate extrinsic natures of Floquet anomalous boundary states in concrete examples.

cond-mat.mes-hall↗

arXiv2022

Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr$_2$RuO$_4$ superconductor

We study the spin susceptibility of the orbital-singlet pairings, including the spin-triplet/orbital-singlet/$s$-wave $E_g$ representation proposed by Suh \textit{et al}., [H.\ G.\ Suh \textit{et al}., Phys.\ Rev.\ Research \textbf{2}, 032023 (2020)], for a three-orbital model of superconducting Sr$_2$RuO$_4$ in three dimensions. For the pseudospin-singlet states represented in the band basis, the spin susceptibility decreases when reducing the temperature, irrespective of the direction of the applied magnetic fields, even if they are spin-triplet/orbital-singlet pairings in the spin-orbital space. However, because the pseudospin-triplet \textbf{d}-vector in the band basis is not completely aligned in the $xy$-plane (along $z$-axis) owing to the strong atomic spin-orbit coupling, the spin susceptibility for spin-singlet/orbital-singlet/odd-parity pairings is reduced around $5$-$10$ percent with the decrease of the temperature along the $z$ ($x$) axis. We can determine the symmetry of the pseudospin structure of the Cooper pair by the temperature dependence of the spin susceptibility measured by nuclear magnetic resonance experiments. Our obtained results serve as a guide to determine the pairing symmetry of Sr$_2$RuO$_4$.

cond-mat.supr-con↗

arXiv2022

On the kernel of the surgery map restricted to the 1-loop part

Every homology cylinder is obtained from Jacobi diagrams by clasper surgery. The surgery map $\mathfrak{s} \colon \mathcal{A}_n^c \to Y_n\mathcal{IC}_{g,1}/Y_{n+1}$ is surjective for $n \geq 2$, and its kernel is closely related to the symmetry of Jacobi diagrams. We determine the kernel of $\mathfrak{s}$ restricted to the 1-loop part after taking a certain quotient of the target. Also, we introduce refined versions of the AS and STU relations among claspers and study the abelian group $Y_n\mathcal{IC}_{g,1}/Y_{n+2}$ for $n \geq 2$.

math.GT↗

arXiv2021

Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems

The Nielsen-Ninomiya theorem is a fundamental theorem on the realization of chiral fermions in static lattice systems in high-energy and condensed matter physics. Here we extend the theorem in dynamical systems, which include the original Nielsen-Ninomiya theorem in the static limit. In contrast to the original theorem, which is a no-go theorem for bulk chiral fermions, the new theorem permits them due to bulk topology intrinsic to dynamical systems. The theorem is based on duality enabling a unified treatment of periodically driven systems and non-Hermitian ones. We also present the extended theorem for non-chiral gapless fermions protected by symmetry. Finally, as an application of our theorem and duality, we predict a new type of chiral magnetic effect -- the non-Hermitian chiral magnetic skin effect.

cond-mat.mes-hall↗

arXiv2021

Non-Hermitian Higher-Order Weyl Semimetals

We study non-Hermitian higher-order Weyl semimetals (NHHOWSMs) possessing real spectra and having inversion $\mathcal{I}$ ($\mathcal{I}$-NHHOWSM) or time-reversal symmetry $\mathcal{T}$ ($\mathcal{T}$-NHHOWSM). When the reality of bulk spectra is lost, the NHHOWSMs exhibit various configurations of surface Fermi Arcs (FAs) and Exceptional Fermi Rings (EFRs), providing a setup to investigate them on an equal footing. The EFRs only appear in the region between 2nd-order WNs. We also discover Weyl nodes originating from non-Hermicity, called non-Hermitian Weyl nodes (NHWNs). Remarkably, we find T-NHHOWSMs which host only 2nd-order NHWNs, having both surface and hinge FAs protected by the quantized biorthogonal Chern number and quadrupole moment, respectively. We call this intrinsically non-Hermitian phase exceptional HOWSM. In contrast to ordinary WNs, the NHWNs can instantly deform to line nodes, forming a monopole comet. The NHWNs also show exceptional tilt-rigidity, which is a strong resistance towards titling due to attachment to exceptional structures. This phenomenon can be a promising experimental knob. Finally, we reveal the exceptional stability of FAs called exceptional helicity. Surface FAs having opposite chirality can live on the same surface without gapping out each other due to the complex nature of the spectrum. Our work motivates an immediate experimental realization of NHHOWSMs.

cond-mat.mes-hall↗

arXiv2021

Non-Hermitian Higher-Order Dirac Semimetals

In this article we study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on $C_4$-symmetric non-Hermitian systems where we investigate inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetric models of NHHODSMs having real bulk spectra. We show that they exhibit the striking property that the bulk and surfaces are anti-PT and PT symmetric, respectively, and so belong to two different topological classes realizing a novel non-Hermitian topological phase which we call a \emph{hybrid-PT topological phases}. Interestingly, while the bulk spectrum is still fully real, we find that exceptional Fermi-rings (EFRs) appear connecting the two Dirac nodes on the surface. This provides a route to probe and utilize both the bulk Dirac physics and exceptional rings/points on equal footing. Moreover, particularly for $\mathcal{T}$-NHHODSMs, we also find real hinge-arcs connecting the surface EFRs. We show that this higher-order topology can be characterized using a biorthogonal real-space formula of the quadrupole moment. Furthermore, by applying Hermitian $C_4$-symmetric perturbations, we discover various novel phases, particularly: (i) an intrinsic $\mathcal{I}$-NHHODSM having hinge arcs and gapped surfaces, and (ii) a novel $\mathcal{T}$-symmetric skin-topological HODSM which possesses both topological and skin hinge modes. The interplay between non-Hermition and higher-order topology in this work paves the way toward uncovering rich phenomena and hybrid functionality that can be readily realized in experiment.

cond-mat.mes-hall↗

arXiv2021

Majorana multipole response: General theory and application to wallpaper groups

Whereas identification of Cooper pair symmetry is the first and crucial step in the investigation of unconventional superconductors, only a few have been established so far because of its own difficulties. To solve this problem, we develop a theory for identification of pairing symmetry using knowledge of topological superconductivity. Establishing the multipole theory of emergent Majorana fermions in time-reversal-invariant topological superconductors, we discover a one-to-one correspondence between the electromagnetic response of Majorana fermions and Cooper pair symmetry. The emergent Majorana fermions host magnetic structures that share the same irreducible representation with Cooper pairs under crystalline symmetry. We furthermore reveal that Majorana fermions in high-spin or nonsymmorphic superconductors may exhibit magnetic octupole responses, which give a direct evidence of these exotic superconducting states. Electric responses of multiple Majorana Kramers pairs are also clarified. Our theory provides the fundamentals for identification of unconventional Cooper pairings through surface-spin-sensitive measurements as well as that for manipulation of Majorana fermions by external electromagnetic fields.

cond-mat.supr-con↗