arXiv subjects

Manabu Sato

Publications and source records attributed to Manabu Sato.

4 recordsLinked to original sources

arXiv2025

Euler band topology in superfluids and superconductors

Real band topology often appears in systems with space-time inversion symmetry and is characterized by invariants such as the Euler and second Stiefel-Whitney classes. Here, we examine the generic band topology of Bogoliubov de-Gennes (BdG) Hamiltonians with $C_{2z}T$ symmetry, where $C_{2z}$ and $T$ are twofold rotation about the $z$ axis and time-reversal symmetries, respectively. We discuss the Euler band topology of superfluids and superconductors in the DIII and CI Altland-Zirnbauer symmetry classes, where the Euler class serves as an integer-valued topological invariant of the $4\times4$ BdG Hamiltonian. Using expressions for the Euler class under $n$-fold rotational symmetry, we derive formulas relating the Euler class to previously known topological invariants of class DIII and CI systems. We demonstrate that three-dimensional class DIII topological phases with an odd winding number, including the B phase of superfluid Helium 3, are topological superconductors or superfluids with a nontrivial Euler class. We refer to these as Euler superconductors or superfluids. Specifically, the $^3$He-B superfluid in a magnetic field is identified as an Euler superfluid. Three-dimensional class CI topological phases with twice an odd winding number are also Euler superconductors or superfluids. When spatial inversion symmetry is present, class CI superconductors with a nontrivial Euler class exhibit superconducting nodal lines with a linking structure. This phenomenon is demonstrated using a model of a three-dimensional $s_\pm$-wave superconductor. These findings provide a unified framework for exploring Euler band topology in superfluids and superconductors, connecting various phenomena associated with $T$-breaking perturbations, including Majorana Ising susceptibility and higher-order topology.

cond-mat.supr-con↗

arXiv2025

Three-dimensional spinless Euler insulators with rotational symmetry

The Euler class is a $\mathbb{Z}$-valued topological invariant that characterizes a pair of real bands in a two-dimensional Brillouin zone. One of the symmetries that permits its definition is $C_{2z}T$, where $C_{2z}$ denotes a twofold rotation about the $z$ axis and $T$ denotes time-reversal symmetry. Here, we study three-dimensional spinless insulators characterized by the Euler class, focusing on the case where additional $C_{4z}$ or $C_{6z}$ rotational symmetry is present, and investigate the relationship between the Euler class of the occupied bands and their rotation eigenvalues. We first consider two-dimensional systems and clarify the transformation rules for the real Berry connection and curvature under point group operations, using the corresponding sewing matrices. Applying these rules to $C_{4z}$ and $C_{6z}$ operations, we obtain explicit formulas that relate the Euler class to the rotation eigenvalues at high-symmetry points. We then extend our analysis to three-dimensional systems, focusing on the difference in the Euler class between the two $C_{2z}T$-invariant planes. We derive analytic expressions that relate the difference in the Euler class to two types of representation-protected invariants and analyze their phase transitions. We further construct tight-binding models and perform numerical calculations to support our analysis and elucidate the bulk-boundary correspondence.

cond-mat.mes-hall↗

arXiv2025

Material realization of spinless, covalent-type Dirac semimetals in three dimensions

Realization of a three-dimensional (3D) analogue of graphene has been a central challenge in topological materials science. Graphene is stabilized by covalent bonding unlike conventional spin-orbit type 3D Dirac semimetals (DSMs). In this study, we demonstrate the material realization of covalent-type 3D DSMs $R_8$Co$X_3$ stabilized by covalent bonding. We observe that the carrier mobility $\mu$ of Dirac fermions reaches 3,000$\,\mathrm{cm^2/Vs}$ even in polycrystalline samples, and $\mu$ increases with the inverse of the Fermi energy, evidencing significant contributions to charge transport from Dirac electrons. $R_8$Co$X_3$ provides a material platform for exploration of Dirac electrons in three dimensions with wide chemical tunability.

cond-mat.mes-hall↗

arXiv2024

Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr$_8$CoGa$_3$ Family

Topological semimetals, known for their intriguing properties arising from band degeneracies, have garnered significant attention. However, the discovery of a material realization and the detailed characterization of spinless Dirac semimetals have not yet been accomplished. Here, we propose from first-principles calculations that the $RE_8\mathrm{Co}X_3$ group ($RE$ = rare earth elements, $X$ = Al, Ga, or In) contains ideal spinless Dirac semimetals whose Fermi surfaces are fourfold degenerate band-crossing points (without including spin degeneracy). Despite the lack of space inversion symmetry in these materials, Dirac points are formed on the rotation-symmetry axis due to accidental degeneracies of two bands corresponding to different 2-dimensional irreducible representations of $C_{6v}$ group. We also investigate, through first-principles calculations and effective model analysis, various phase transitions caused by lattice distortion or elemental substitutions from the Dirac semimetal phase to distinct topological semimetallic phases such as nonmagnetic linked-nodal-line and Weyl semimetals (characterized by the second Stiefel-Whitney class) and ferromagnetic Weyl semimetals.

cond-mat.mtrl-sci↗