arXiv subjects

Yutaro Nagae

Publications and source records attributed to Yutaro Nagae.

7 recordsLinked to original sources

arXiv2026

Nonlocal Cooper pairs in finite topological superconductors and their relation to Majorana nonlocality

We identify two fundamental properties of the Gor'kov Green's function of finite one-dimensional topological superconductors. In the low-frequency (low-energy) regime, the normal and anomalous Green's functions, which describe single-particle and Cooper-pair correlations, respectively, become identical up to a phase factor. Moreover, they exhibit pronounced nonlocality: correlations between the two ends of the system grow exponentially with system length, whereas local correlations at either end vanish in the zero-frequency limit. These striking features signify the emergence of unconventional nonlocal Cooper pairs associated with a nonlocal fermionic mode composed of hybridized Majorana end modes. The nonlocal Cooper pairs are directly linked to fermion parity and to the nonlocal transport properties of finite topological superconductors. By focusing on pair correlations, our analysis advances the understanding of Majorana nonlocality, a key concept in topological quantum computation.

cond-mat.supr-con↗

arXiv2026

Robust realization of spin-polarized specular Andreev reflection in V$_2$O-based altermagnets

We theoretically investigate charge transport in a junction between a conventional superconductor and a V$_2$O-based altermagnet exhibiting distinctive spin-split quasi-one-dimensional Fermi surfaces. The altermagnet is described by a microscopically motivated six-orbital model that incorporates sublattice degrees of freedom associated with both V and O sites. Based on calculations performed under various boundary conditions, we demonstrate the robust emergence of specular Andreev reflection with a distinctive spin polarization. Furthermore, we propose an efficient multiterminal setup to detect this specular Andreev reflection through nonlocal conductance measurements. Our results establish V$_2$O-based altermagnets as a promising platform for realizing spin-resolved Cooper pair splitting, which is essential for generating energy-entangled electron pairs.

cond-mat.supr-con↗

arXiv2025

Spin-polarized Specular Andreev Reflections in Altermagnets

We show theoretically that specular Andreev reflection occurs stably at altermagnet--superconductor interfaces, which is a phenomenon that has previously been predicted only in a limited range of materials, such as Dirac/Weyl materials with fine-tuned chemical potentials. Furthermore, the characteristic spin-split bands of the altermagnet lead to a distinctive spin polarization in the specular Andreev reflections. By utilizing this feature, we propose a device that integrates the functions of both a Cooper pair splitter and a spin beam splitter, thereby creating energy-entangled electron pairs. The positive nonlocal conductance and the positive noise cross-correlation are unambiguous signatures of specular Andreev reflections in the proposed device.

cond-mat.supr-con↗

arXiv2025

Majorana flat bands and anomalous proximity effects in $p$-wave magnet--superconductor hybrid systems

Flat-band Majorana bound states of nodal $p$-wave superconductors give rise to striking electromagnetic anomalies, reflecting their high degree of degeneracy at the Fermi level. However, experimental investigations of these states have been limited because of the scarcity of materials exhibiting intrinsic $p$-wave superconductivity. In this Letter, we demonstrate that Majorana flat bands can emerge in a hybrid system consisting of a conventional superconductor and a $p$-wave magnet, a recently proposed class of unconventional magnets that possess a unique composite symmetry, the $[C_{2\perp}||\boldsymbol{t}]$ symmetry. The degeneracy of the flat-band Majorana bound states is protected by chiral symmetry from the BDI symmetry class, which originates from the $[C_{2\perp}||\boldsymbol{t}]$ symmetry of the $p$-wave magnet. In addition, we predict the robust appearance of a zero-bias conductance peak in a dirty normal-metal--superconductor junction containing a $p$-wave magnet, which serves as an unambiguous signature of anomalous proximity effects associated with the Majorana flat bands.

cond-mat.supr-con↗

arXiv2024

Multi-locational Majorana Zero Modes

We show the appearance of an unconventional Majorana zero mode whose wave function splits into multiple parts located at different ends of different topological superconductors, hereinafter referred to as a multi-locational Majorana zero mode. Specifically, we discuss the multi-locational Majorana zero modes in a three-terminal Josephson junction consisting of topological superconductors, which forms an elemental qubit of fault-tolerant topological quantum computers. We also demonstrate anomalously long-ranged nonlocal resonant transport phenomena caused by the multi-locational Majorana zero mode.

cond-mat.supr-con↗

arXiv2018

Reduced Dependency Spaces for Existential Parameterised Boolean Equation Systems

A parameterised Boolean equation system (PBES) is a set of equations that defines sets satisfying the equations as the least and/or greatest fixed-points. Thus this system is regarded as a declarative program defining predicates, where a program execution returns whether a given ground atomic formula holds or not. The program execution corresponds to the membership problem of PBESs, which is however undecidable in general. This paper proposes a subclass of PBESs which expresses universal-quantifiers free formulas, and studies a technique to solve the problem on it. We use the fact that the membership problem is reduced to the problem whether a proof graph exists. To check the latter problem, we introduce a so-called dependency space which is a graph containing all of the minimal proof graphs. Dependency spaces are, however, infinite in general. Thus, we propose some conditions for equivalence relations to preserve the result of the membership problem, then we identify two vertices as the same under the relation. In this sense, dependency spaces possibly result in a finite graph. We show some examples having infinite dependency spaces which are reducible to finite graphs by equivalence relations. We provide a procedure to construct finite dependency spaces and show the soundness of the procedure. We also implement the procedure using an SMT solver and experiment on some examples including a downsized McCarthy 91 function.

cs.LO↗

arXiv2017

An Extension of Proof Graphs for Disjunctive Parameterised Boolean Equation Systems

A parameterised Boolean equation system (PBES) is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a datum and returns a Boolean value. The membership problem of PBESs is a problem to decide whether a given element is in the defined set or not, which corresponds to an execution of the program. This paper introduces reduced proof graphs, and studies a technique to solve the membership problem of PBESs, which is undecidable in general, by transforming it into a reduced proof graph. A vertex X(v) in a proof graph represents that the data v is in the set X, if the graph satisfies conditions induced from a given PBES. Proof graphs are, however, infinite in general. Thus we introduce vertices each of which stands for a set of vertices of the original ones, which possibly results in a finite graph. For a subclass of disjunctive PBESs, we clarify some conditions which reduced proof graphs should satisfy. We also show some examples having no finite proof graph except for reduced one. We further propose a reduced dependency space, which contains reduced proof graphs as sub-graphs if a proof graph exists. We provide a procedure to construct finite reduced dependency spaces, and show the soundness and completeness of the procedure.

cs.LO↗