arXiv subjects

Yutaro Tanaka

Publications and source records attributed to Yutaro Tanaka.

15 recordsLinked to original sources

arXiv2026

Hinge modes of three-dimensional Euler insulators

In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a pair of real bands in the Brillouin zone. In this paper, we study three-dimensional $C_{2z}T$-symmetric insulators characterized by $\bar{e}_2$, defined as the difference in the Euler classes between two $C_{2z}T$-invariant planes in the three-dimensional Brillouin zone. By deriving effective surface Hamiltonians from generic low-energy continuum Hamiltonians characterized by the topological invariant $\bar{e}_2$, we reveal that multiple gapless boundary states exist at the domain walls of the surface mass, which give rise to the multiple chiral hinge modes. We also show that three-dimensional insulators characterized by $\bar{e}_2=N$ support $N$ chiral hinge modes. Notably, due to the constraint of two occupied bands in our system, these phases are distinct from stacked Chern insulators composed of $N$ layers. Furthermore, we construct tight-binding models for $\bar{e}_2=2$ and $3$ and numerically demonstrate the emergence of two and three chiral hinge modes, respectively. These results are consistent with those obtained from the surface theory.

cond-mat.mes-hall↗

arXiv2026

Hopper-Like Growth of Higher-Order Topological Insulators

Understanding crystal growth and morphology is a fundamental issue in condensed matter physics. While crystal morphology due to the distribution and dynamics of the diffusion field has been intensively studied, how the intrinsic material properties affect crystal morphology remains unclear. In this Letter, we demonstrate that higher-order topological phases can give rise to hollowed crystal morphologies, where the corners advance faster than the central regions of the crystal, through an unconventional mechanism originating from topological electronic states. We quantitatively show this connection by analyzing both the fractal dimension $D_f$ and the fractal dimension of coastlines $D_{f,c}$. When we compare the crystals in the normal insulator and higher-order topological insulator phases with the same $D_{f}$ in the case of relatively rapid crystal growth, the former is in the dendritic shape, while the latter is in the hopper-like shape, quantified by the smaller $D_{f,c}$ in the higher-order topological phase.

cond-mat.mes-hall↗

arXiv2025

Spatiotemporal chaos in the interface growth of topological insulators

We demonstrate that topological insulators exhibit an intrinsic interfacial instability that amplifies small interface fluctuations, resulting in chaotic behavior during interface growth. This mechanism is different from conventional interfacial instabilities in crystal growth that are driven by external non-uniformities such as surface diffusion, and instead arises from intrinsic electronic properties of topological materials. We find that the boundary states of topological insulators have a pronounced impact on the surface stiffness, which quantifies how strongly a surface resists changes in its shape or orientation. While trivial insulators possess positive stiffness that smooths out surface roughness, topological insulators exhibit negative stiffness that amplifies small shape fluctuations. We derive an effective equation of the interface growth with this negative stiffness and demonstrate that the interface dynamics is governed by the Kuramoto--Sivashinsky equation, a prototypical nonlinear equation exhibiting spatiotemporal chaos.

cond-mat.mes-hall↗

arXiv2025

Exceptional second-order topological insulators

Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection symmetry. Based on this classification, we propose exceptional second-order topological insulators, exhibiting second-order boundary states stabilized by point-gap topology. As an illustrative example, we uncover a two-dimensional exceptional second-order topological insulator with point-gapless corner states. Furthermore, we identify a three-dimensional exceptional second-order topological insulator that features hinge states with isolated exceptional points, representing second-order topological phases intrinsic to non-Hermitian systems. Our work enlarges the family of point-gap topological phases in non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2025

Dynamic mode decomposition for detecting oscillatory transient activity via sparsity and smoothness regularization

Dynamic mode decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to interpret how these modes contribute to the transient behavior. In this study, we propose a simple extension of DMD that facilitates extraction of oscillatory transient activity by introducing time-varying amplitudes for the DMD modes based on sparsity and smoothness regularization. This approach enables identification of dynamically significant modes and extraction of their transient activities, providing a more interpretable representation of non-steady dynamics. We illustrate the validity of the proposed method using a simple example and then apply it to fluid flow data of a laminar airfoil wake exhibiting transient behavior. We demonstrate that it can capture the temporal structure of mode activations that are not accessible with the standard DMD method.

physics.flu-dyn↗

arXiv2025

Nonsymmorphic Topological Phases of Non-Hermitian Systems

Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice translations, has remained largely unexplored. Here, we systematically classify non-Hermitian topological crystalline phases protected by nonsymmorphic symmetry and reveal unique phases that have no counterparts in either Hermitian topological crystalline phases or non-Hermitian topological phases protected solely by internal symmetry. Specifically, we elucidate the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ non-Hermitian topological phases and their associated anomalous boundary states characterized by distinctive complex-valued energy dispersions.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian skin effect enforced by nonsymmorphic symmetries

Crystal symmetries play an essential role in band structures of non-Hermitian Hamiltonian. In this paper, we propose a non-Hermitian skin effect (NHSE) enforced by nonsymmorphic symmetries. We show that the NHSE inevitably occurs if a two-dimensional non-Hermitian system satisfies conditions derived from the nonsymmorphic symmetry of the doubled Hermitian Hamiltonian. This NHSE occurs in symmetry classes with and without time-reversal symmetry. The NHSE enforced by nonsymmorphic symmetries always occurs simultaneously with the closing of the point gap at zero energy. We also show that such a NHSE can occur in specific three-dimensional space groups with nonsymmorphic symmetries.

cond-mat.mes-hall↗

arXiv2023

Effects of first- and second-order topological phases on equilibrium crystal shapes

We study equilibrium crystal shapes of a topological insulator (TI), a topological crystalline insulator (TCI) protected by mirror symmetry, and a second-order topological insulator (SOTI) protected by inversion symmetry. By adding magnetic fields to the three-dimensional TI, we can realize the mirror-symmetry-protected TCI and the inversion-symmetry-protected SOTI. They each have topological boundary states in different positions: the TCI has gapless states on the surfaces that are invariant under the symmetry operation, and the SOTI has gapless states at the intersections between certain surfaces. In this paper, we discuss how these boundary states affect the surface energies and the equilibrium crystal shapes in terms of the calculations of the simple tight-binding model by using the Wulff construction. By comparing the changes in the shapes of the TI to that of the trivial insulator through the process of applying the magnetic fields, we show that the presence/absence of the topological boundary states affects the emergence of the specific facets in a different way from the trivial insulator.

cond-mat.mes-hall↗

arXiv2023

Systematic study for two-dimensional $Z_2$ topological phase transitions at high-symmetry points in all layer groups

We construct a general theory of $Z_2$ topological phase transitions in two-dimensional systems with time-reversal symmetry. We investigate the possibilities of $Z_2$ topological phase transitions at band inversions at all high-symmetry points in $k$-space in all the 80 layer groups. We exclude the layer groups with inversion symmetry because the $Z_2$ topological phase transition is known to be associated with band inversions with an exchange of parities. Among the other layer groups, we find 21 layer groups with insulator-to-insulator transitions with band inversion, and this problem is finally reduced to five point groups $C_3, C_4, C_6, S_4$, and $C_{3h}$. We show how the change of the $Z_2$ topological invariant at a band inversion is entirely determined by the irreps of occupied and unoccupied bands at the high-symmetry point. For example, in the case of $C_3$, we show that the $Z_2$ topological invariants change whenever the band inversion occurs between two Kramers pairs whose $C_3$ eigenvalues are $\{e^{πi / 3}, e^{-πi / 3}\}$ and $\{-1, -1\}$. These results are not included in the theory of symmetry-based indicators or topological quantum chemistry.

cond-mat.mes-hall↗

arXiv2022

Anomalous Crystal Shapes of Topological Crystalline Insulators

Understanding crystal shapes is a fundamental subject in surface science. It is now well studied how chemical bondings determine crystal shapes via dependence of surface energies on surface orientations. Meanwhile, discoveries of topological materials have led us to a new paradigm in surface science, and one can expect that topological surface states may affect surface energies and crystal facets in an unconventional way. Here we show that the surface energy of glide-symmetric topological crystalline insulators (TCI) depends on the surface orientation in a singular way via the parity of the Miller index. This singular surface energy of the TCI affects equilibrium crystal shapes, resulting in emergence of unique crystal facets of the TCI. This singular dependence of the topological surface states is unique to the TCI protected by the glide symmetry in contrast to a TCI protected by a mirror symmetry. In addition, we show that such singular surface states of the TCI protected by the glide symmetries can be realized in KHgSb with first-principles calculations. Our results provide a basis for designs and manipulations of crystal facets by utilizing symmetry and topology.

cond-mat.mes-hall↗

arXiv2022

Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals

We give a bulk-hinge correspondence for higher-order topological phases protected by rotoinversion $C_{4}\mathcal{I}$ symmetry in magnetic systems. Our approach allows us to show the emergence of the chiral hinge modes only from the information of the $C_{4}\mathcal{I}$ eigenvalues at the high-symmetry points in the Brillouin zone. In addition, based on the bulk-hinge correspondence, we propose a class of higher-order Weyl semimetals (HOWSMs) being Weyl semimetals with hinge modes and Fermi-arc surface states. The HOWSM is characterized by topological invariants for three-dimensional higher-order topological insulators, and the topological invariants are determined by the $C_{4}\mathcal{I}$ symmetry eigenvalues at the high-symmetry points. This HOWSM has chiral hinge modes as a direct consequence of the three-dimensional higher-order topology in the bulk.

cond-mat.mes-hall↗

arXiv2021

Measurement of the temperature dependence of dwell time and spin relaxation probability of Rb atoms on paraffin surfaces using a beam-scattering method

The scattering of Rb atoms on an anti-relaxation coating was studied. No significant change in the spin relaxation probability of Rb atoms by single scattering from a tetracontane surface was observed by cooling the film from 305 to 123 K. The mean surface dwell time was estimated using a time-resolved method.Delay-time spectra, from which mean surface dwell times can be estimated, were measured at 305, 153, and 123 K, with a time window of $9.3\times 10^{-5}$ s. The increase in mean surface dwell time with cooling from 305 to 123 K was smaller than $4.4\times 10^{-6}$ s, which is significantly smaller than the value expected from the mean dwell time at room temperature measured using the Larmor frequency shift. These results can be explained by assuming a small number of scattering components, with a mean surface dwell time at least three orders of magnitude longer than the majority component.

physics.atom-ph↗

arXiv2020

Theory of inversion-$\mathbb{Z}_{4}$ protected topological chiral hinge states and its applications to layered antiferromagnets

We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with inversion symmetry by studying dependence of the sign of the surface Dirac mass on surface orientations. In particular, in the presence of glide symmetry, for particular surface orientations, the surface Dirac mass changes sign by changing the surface terminations. By applying this result to a layered antiferromagnet (AFM), we find a difference in the hinge states between the cases with an even and odd number of layers. In the case of an even number of layers, which does not preserve inversion symmetry, positions of hinge states are not inversion symmetric. Nonetheless, these inversion-asymmetric hinge states result from the bulk topology. We show that their inversion-asymmetric configurations are uniquely determined from the symmetries and the topological invariant.

cond-mat.mes-hall↗

arXiv2020

Appearance of hinge states in second-order topological insulators via the cutting procedure

In recent years, second-order topological insulators have been proposed as a new class of topological insulators. Second-order topological insulators are materials with gapped bulk and surfaces, but with topologically protected gapless states at the intersection of two surfaces. These gapless states are called hinge states. In this paper, we give a general proof that any insulators with inversion symmetry and gapped surface in class A always have hinge states when the $\mathbb{Z}_{4}$ topological index $μ_{1}$ is $μ_{1}=2$. We consider a three-dimensional insulator whose boundary conditions along two directions change by changing the hopping amplitudes across the boundaries. We study behaviors of gapless states through continuously changing boundary conditions along the two directions, and reveal that the behaviors of gapless states result from the $\mathbb{Z}_{4}$ strong topological index. From this discussion, we show that gapless states inevitably appear at the hinge of a three-dimensional insulator with gapped surfaces when the strong topological index is $\mathbb{Z}_{4}=2$ and the weak topological indices are $ν_{1}=ν_{2}=ν_{3}=0$.

cond-mat.mes-hall↗

arXiv2019

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D $Z_2$ topological insulator. We prove it by considering a process of cutting the three-dimensional inversion-symmetric HOTI along a plane, and study the spectral flow in the cutting process. We show that the $Z_4$ indicators, which characterize three-dimensional inversion-symmetric HOTIs in classes A and AII, are directly related to the $Z_2$ indicators for the corresponding two-dimensional slabs with inversion symmetry, i.e. the Chern number parity and the $Z_2$ topological invariant, for classes A and AII respectively. The existence of the gapless hinge states is understood from the conventional bulk-edge correspondence between the slab system and its edge states. Moreover, we also show that the spectral-flow analysis leads to another proof of the bulk-edge correspondence in one- and two-dimensional inversion-symmetric insulators.

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