arXiv subjects

Masatoshi Sato

Publications and source records attributed to Masatoshi Sato.

At least 19 recordsLinked to original sources

arXiv2026

Andreev exceptional points in Josephson junctions formed by minimal Kitaev chains

We consider Josephson junctions formed by two minimal Kitaev chains and investigate how the interplay between non-Hermiticity and superconducting phase difference enables the realization of stable topological states that do not exist in the Hermitian realm. In particular, we focus on non-Hermiticity produced by coupling the minimal Kitaev chain Josephson junction to normal reservoirs, which renders the system open and characterized by a complex Andreev spectrum. Interestingly, we find that this complex spectrum hosts second order exceptional points, where a pair of eigenvalues and their respective eigenvectors coalesce, and are fully controlled by the superconducting phase difference. Depending on the spatial unequal distribution of non-Hermiticity, these Andreev exceptional points can appear at zero or finite energies connecting stable energy lines protected by non-Hermitian topology. Moreover, tuning the system parameters, such as onsite energies, non-Hermiticity, or electron cotunneling, the Andreev exceptional points give rise to Andreev exceptional lines enclosing protected two-dimensional zero real energy areas. We also discuss potential detection schemes of Andreev exceptional points by using local and nonlocal conductance signatures. Our results demonstrate the utility of non-Hermiticity from normal reservoirs as a useful resource for engineering non-Hermitian topological phases in minimal Kitaev chain Josephson junctions.

cond-mat.mes-hall↗

arXiv2026

Quantum higher-spin Hall insulators

We develop a theory of quantum spin Hall insulators with arbitrary spin $J$. Our analysis demonstrates that such systems support $J+\tfrac{1}{2}$ pairs of helical edge modes protected by nontrivial mirror Chern numbers. We establish that the corresponding edge theory is described by a generalized Dirac fermion with higher-order dispersion. These modes produce unique transport responses that are non-linear with voltage. An in-plane magnetic field opens a mass gap in the edge spectrum, and magnetic domain walls host $(J+\tfrac{1}{2})$-fold degenerate bound states characterized by nontrivial winding numbers. Our results extend quantum spin Hall physics to higher-spin systems and suggest possible realizations in ultracold atomic gases.

cond-mat.mes-hall↗

arXiv2025

Nonlocal Josephson diode effect in minimal Kitaev chains

We study the emergence of the nonlocal Josephson effect in a system composed of three laterally coupled minimal Kitaev chains and exploit it to realize the nonlocal Josephson diode effect. We find that an imbalance between crossed Andreev reflections and electron cotunneling in the middle Kitaev chain gives rise to an asymmetric $2\pi$-periodic phase-dependent Andreev spectrum, controlled by the superconducting phases across the left and right junctions. We then show that the asymmetric Andreev spectrum, formed by hybridized Andreev bound states at the left and right junctions, enables a supercurrent across one junction via the phase difference at the other junction, thereby signaling the nonlocal Josephson effect. Notably, these nonlocal Josephson supercurrents exhibit distinct positive and negative critical currents, demonstrating the realization of the nonlocal Josephson diode effect with highly tunable polarity and efficiencies exceeding $50\%$. The nonlocal Josephson diode effect requires breaking local time-reversal and local charge-conjugation symmetries, with the latter being unique to minimal Kitaev chains. Our results establish minimal Kitaev chains as a highly controllable platform for engineering nonlocal Josephson phenomena.

cond-mat.supr-con↗

arXiv2025

Subspace-Protected Topological Phases and Bulk-Boundary Correspondence

While tremendous research has revealed that symmetry enriches topological phases of matter, more general principles that protect topological phases have yet to be explored. In this Letter, we elucidate the roles of subspaces in free-fermionic topological phases. A subspace property for Hamiltonians enables us to define new topological invariants. It results in peculiar topological boundary phenomena, i.e., the emergence of an unpaired zero mode or zero-winding skin modes, characterizing subspace-protected topological phases. We establish and demonstrate the bulk-boundary correspondence in subspace-protected topological phases. We further discuss the interplay of the subspace property and internal symmetries. Toward application, we also propose possible platforms possessing the subspace property.

cond-mat.mes-hall↗

arXiv2025

$K$-theory classification of Wannier localizability and detachable topological boundary states

A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions. Remarkably, such Wannier-localizable topological insulators can host boundary states that are detachable from the bulk bands. In our accompanying Letter [D. Nakamura {\it et al.}, Phys. Rev. Lett. 135, 096601 (2025), arXiv:2407.09458], we demonstrate that non-Hermitian topology underlies detachable boundary states in Hermitian topological insulators and superconductors, thereby establishing their tenfold classification based on internal symmetry. Here, using $K$-theory, we elucidate the relationship between Wannier localizability and detachability of topological boundary states. From the boundary perspective, we classify intrinsic and extrinsic non-Hermitian topology, corresponding to nondetachable and detachable topological boundary states, respectively. From the bulk perspective, on the other hand, we classify Wannier localizability through the homomorphisms of topological phases from the tenfold Altland-Zirnbauer symmetry classes to the threefold Wigner-Dyson symmetry classes. Notably, these two approaches from the boundary and bulk perspectives lead to the same classification. We clarify this agreement and develop a unified understanding of the bulk-boundary correspondence on the basis of $K$-theory.

cond-mat.mes-hall↗

arXiv2025

Non-Hermitian Origin of Detachable Boundary States in Topological Insulators

While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non-Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. Based on this connection and $K$-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states.

cond-mat.mes-hall↗

arXiv2025

On the 2-loop part of the Johnson cokernel

We study stable Sp-decompositions of the cokernel of the Johnson homomorphism. Continuing the work of Conant in 2016, which identified the 1-loop part of the Johnson cokernel as the Enomoto-Satoh obstruction, we study the 2-loop part. Using the corresponding 2-loop trace map, we capture all the components of the Johnson cokernels in degree 6 that cannot be detected by the Enomoto-Satoh trace.

math.GT↗

arXiv2025

Non-Hermitian Josephson junctions with four Majorana zero modes

Josephson junctions formed by finite-length topological superconductors host four Majorana zero modes when the phase difference between the superconductors is $\varphi=\pi$ and their length is larger than the Majorana localization length. While this picture is understood in terms of a Hermitian description of isolated junctions, unavoidable transport conditions due to coupling to reservoirs make them open and ground for non-Hermitian effects that still remain largely unexplored. In this work, we investigate the impact of non-Hermiticity on Josephson junctions hosting four Majorana zero modes when they are coupled to normal leads. We demonstrate that, depending on whether inner or outer Majorana zero modes are subjected to non-Hermiticity, Andreev exceptional points can form between lowest (higher energy) Andreev bound states connected by stable zero real energy lines. We further find that the Andreev exceptional points give rise to strong local and nonlocal spectral weights, thus providing a way for their identification via, e.g., conductance measurements. Our findings unveil non-Hermiticity for designing non-Hermitian topological phases and for operating Andreev bound states in Josephson junctions hosting Majorana zero modes.

cond-mat.supr-con↗

arXiv2025

Topological Reality Switch: Towards Bulk-Boundary Selective Lasing

The emergence of complex spectra in non-Hermitian systems causes dramatic changes even under weak perturbations, significantly hindering their precise control for study and integration into practical applications. Achieving a controlled method to generate a real spectrum in non-Hermitian systems has long been a key objective in the field. In this study, we explore the 2D non-Hermitian Su-Schrieffer-Heeger (SSH) model and introduce a reality switch that allows for the controllable induction of a real spectrum depending on the imposed boundary condition. We show that a topological phase transition in the complex gap accompanies the switching process. Our work lays the cornerstone for developing a selective bulk-boundary control mechanism for the gain and lasing behaviors in non-Hermitian systems.

quant-ph↗

arXiv2025

Torsion elements in the associated graded of the $Y$-filtration of the monoid of homology cylinders

Clasper surgery induces the $Y$-filtration $\{Y_n\mathcal{IC}\}_n$ over the monoid of homology cylinders, which serves as a $3$-dimensional analogue of the lower central series of the Torelli group of a surface. In this paper, we investigate the torsion submodules of the associated graded modules of these filtrations. To detect torsion elements, we introduce a homomorphism on $Y_n\mathcal{IC}/Y_{n+1}$ induced by the degree $n+2$ part of the LMO functor. Additionally, we provide a formula that computes this homomorphism under clasper surgery, and use it to demonstrate that every non-trivial torsion element in $Y_6\mathcal{IC}/Y_7$ has order $3$.

math.GT↗

arXiv2025

Exceptional deficiency of non-Hermitian systems

Exceptional points (EPs) are non-Hermitian singularities associated with the coalescence of individual eigenvectors accompanied by the degeneracy of their complex energies. Here, we report the discovery of a generalization to the concept of EP called exceptional deficiency (ED), which features the complete coalescence of two eigenspaces with identical but arbitrarily large dimensions and the coincidence of entire spectral continua. The characteristics of the ED are studied using one-way coupled Hermitian and non-Hermitian lattices. The ED can induce an anomalous absence and presence of non-Hermitian skin effect (NHSE) that transcends the topological bulk-edge correspondence of NHSE, resulting in unexpected synergistic skin-propagative dynamics. The conditions of the ED are also explored for unprecedented control of localization and propagation in non-Hermitian systems. These effects are experimentally observed using active mechanical lattices. The discovery of ED opens multiple new frontiers in non-Hermitian physics and can potentially resolve long-standing challenges in related applications.

quant-ph↗

arXiv2025

Callan-Rubakov effects in topological insulators

The Callan-Rubakov effect describes monopole-catalyzed proton decay. While this effect is fundamental for quantum field theories, its experimental observation has remained far from reality. Here, we reveal a similar, but experimentally reachable, defect-catalysis of the quantum anomaly in topological materials. In particular, surface Dirac fermions on topological insulators develop a distinct localized state at the position of dislocations or $π$-fluxes, which mediates spin-flip time-reversal breaking scattering or absorption of electrons. Despite the Hermiticity of topological insulators, a non-Hermitian topological number guarantees the robust existence of the localized state. Our finding implies that non-magnetic defects may behave like magnetic impurities on surfaces of topological insulators. Using the K-theory classification, we generalize this condensed-matter version of the Callan-Rubakov effect to other classes of topological materials.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian multiterminal phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by multiple superconductors and discover the emergence of exceptional points entirely determined by the interplay of the distinct superconducting phases and non-Hermiticity due to normal reservoirs. In particular, in Josephson junctions with three and four superconductors, we find stable lines and surfaces of exceptional points protected by non-Hermitian topology and highly tuneable by the superconducting phases. We also discover that, in Josephson junctions formed by laterally coupled superconductors, exceptional points can result from hybridized Andreev bound states and lead to the enhancement of supercurrents controlled by dissipation. Our work unveils the potential of multi-terminal Josephson junctions for realizing higher dimensional topological non-Hermitian superconducting phenomena.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian phase-biased Josephson junctions

We study non-Hermitian Josephson junctions formed by superconductors with a finite phase difference under non-Hermiticity, which naturally appears due to coupling to normal reservoirs. Depending on the structure of non-Hermiticity, captured in terms of retarded self-energies, the low-energy spectrum hosts topologically stable exceptional points either at zero or finite real energies as a function of the superconducting phase difference. Interestingly, the corresponding phase-biased supercurrents may acquire divergent profiles at such exceptional points. This instance is a natural and unique non-Hermitian effect that signals a possible way to enhance the sensitivity of Josephson junctions. Our work opens a way for realizing unique non-Hermitian phenomena due to the interplay between non-Hermitian topology and the Josephson effect.

cond-mat.supr-con↗

arXiv2024

General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems

Non-Hermiticity enables macroscopic accumulation of bulk states, named non-Hermitian skin effects. The non-Hermitian skin effects are well-established for single-particle systems, but their proper characterization for general systems is elusive. Here, we propose a general criterion of non-Hermitian skin effects, which works for any finite-dimensional system evolved by a linear operator. The applicable systems include many-body systems and network systems. A system meeting the criterion exhibits enhanced non-normality of the evolution operator, accompanied by exceptional characteristics intrinsic to non-Hermitian systems. Applying the criterion, we discover a new type of non-Hermitian skin effect in many-body systems, which we dub the Fock space skin effect. We also discuss the Fock space skin effect-induced slow dynamics, which gives an experimental signal for the Fock space skin effect.

quant-ph↗

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

Origin of Robust $\mathbb{Z}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion

Quantum spin Hall insulators, which possess a non-trivial $\mathbb{Z}_2$ topological phase, have attracted great attention for two decades. It is generally believed that when an even number of layers of the quantum spin Hall insulators are stacked, the $\mathbb{Z}_2$ topological phase becomes unstable due to $\mathbb{Z}_2$ nature. While the counterexamples of the instability were observed in several literates, there is no systematic understanding. In this work, we provide a systematic understanding that the robust $\mathbb{Z}_2$ topological phase in a Hermitian system with chiral symmetry against stacking. We clarify that the robustness generally originates from level repulsion in the corresponding non-Hermitian system derived from Hermitization. We demonstrate this by treating a class DIII superconductor in 1D with $\mathbb{Z}_2$ topology and the corresponding non-Hermitian 1D system in class AII$^\dagger$ with $\mathbb{Z}_2$ point-gap topology.

cond-mat.mes-hall↗