arXiv subjects

Nobuyuki Okuma

Publications and source records attributed to Nobuyuki Okuma.

32 records · Page 2Linked to original sources

arXiv2021

Nontrivial interband effect: applications to magnetic susceptibility, nonlinear optics, and topological degeneracy pressure

The interband effect is an important concept both in traditional and modern solid-state physics. In this paper, we present a theory of the nontrivial interband effect, which cannot be removed without breaking given rules. We define the general nontrivial interband effect by regarding a property of the set of the total bands of a tight-binding Hamiltonian as the triviality. As examples of the source of the nontrivial interband effect, we consider several topological concepts: stable topological insulator, symmetry-based indicator, fragile topological insulator, and multipole/higher-order topological insulator. As an application, we calculate the orbital magnetic susceptibility for tight-binding Hamiltonians with topological properties. In addition, we consider the mechanical properties induced by the nontrivial interband effect. We define interband-induced degeneracy pressure, which tends to take a negative value, and calculate it for the Chern insulator. This calculation demonstrates the importance of topological band structures in mechanical properties of solids. We also discuss the application to nonlinear optics characterized by the polarization difference and the generalization to interacting systems with entanglement. The framework of the nontrivial interband effect, which includes topological concepts as subsets, might be useful for finding unexplored concepts.

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arXiv2020

Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems

We investigate the roles of non-Hermitian topology in spectral properties and entanglement structures of open systems. In terms of spectral theory, we give a unified understanding of two interpretations of non-Hermitian topology: quantum anomaly and non-Hermitian skin effects, in which the bulk spectra extremely depend on the boundary conditions. In this context, the fact that the intrinsic higher-dimensional skin effects under the full open boundary condition need the presence of the topological defects is understood in terms of the anomalous fermion production such as the Rubakov-Callan effect in the presence of the magnetic monopole. In terms of the entanglement structure, we investigate steady states of fermionic open systems whose Liouvillian (rapidity) spectra host non-Hermitian topology. We analyze dissipation-driven Majorana steady states in zero-dimensional open systems and relate them to the Majorana edge modes of topological superconductors by using the entanglement entropy. We also analyze a steady state of a one-dimensional open Fermi system with a non-Hermitian topological spectrum and relate it to the chiral edge states of the Chern insulator on the basis of the trace index defined from the entanglement spectrum. These correspondences indicate that the entanglement generates circular nonreciprocal currents under the periodic boundary condition and the skin-effect voltage with fermion accumulation under the open boundary condition. Finally, we discuss several related topics such as pseudospectral behaviors of Liouvillian dynamics and skin effects in interacting systems.

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arXiv2020

Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number

There is a common belief in the condensed matter community that bulk quantities become insensitive to the boundary condition in the infinite-volume limit. Here we reconsider this statement in terms of recent arguments of non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for the non-Hermitian Hamiltonians-, in the traditional Green's function formalism. We find the criterion for quantities to be sensitive/insensitive against the boundary condition in Hermitian correlated/disordered systems, which is characterized by the residue theorem. We also discuss the uncertainty of the quasiparticle energy under the skin effects in terms of nonnormal pseudospectra, which can be tested via the sharp optical absorption from the bulk-surface coupling. Our result indicates that "pseudo quantum number" emerges as a consequence of large nonnormality.

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arXiv2020

Hermitian zero modes protected by nonnormality: Application of pseudospectra

Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological insulators. On the other hand, in terms of the spectral theory, the skin effects can also be interpreted as instability of spectra for nonnormal (non-Hermitian) Hamiltonians. Applying the latter interpretation to the former relation, we develop a theory of zero modes with quantum anomaly for general Hermitian lattice systems. Our theory is applicable to a wide range of systems: Majorana chains, non-periodic lattices, and long-range hopping systems. We relate exact zero modes and quasi-zero modes of a Hermitian system to spectra and pseudospectra of a non-Hermitian system, respectively. These zero and quasi-zero modes of a Hermitian system are robust against a class of perturbations even if there is no topological protection. The robustness is measured by nonnormality of the corresponding non-Hermitian system. We also present explicit construction of such zero modes by using a graphical representation of lattice systems. Our theory reveals the presence of nonnormality-protected zero modes, as well as the usefulness of the nonnormality and pseudospectra as tools for topological and/or non-Hermitian physics.

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arXiv2020

Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class

Non-Hermitian Hamiltonians are generally sensitive to boundary conditions, and their spectra and wave functions under open boundary conditions are not necessarily predicted by the Bloch band theory for periodic boundary conditions. To elucidate such a non-Bloch feature, recent works have developed a non-Bloch band theory that works even under arbitrary boundary conditions. Here, it is demonstrated that the standard non-Bloch band theory breaks down in the symplectic class, in which non-Hermitian Hamiltonians exhibit Kramers degeneracy because of reciprocity. Instead, a modified non-Bloch band theory for the symplectic class is developed in a general manner, as well as illustrative examples. This nonstandard non-Bloch band theory underlies the $\mathbb{Z}_{2}$ non-Hermitian skin effect protected by reciprocity.

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arXiv2020

Topological Origin of Non-Hermitian Skin Effects

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non-Hermitian topology. Such a topological origin not merely explains the universal feature of the known skin effect, but also leads to new types of the skin effects---symmetry-protected skin effects. In particular, we discover the $\mathbb{Z}_{2}$ skin effect protected by time-reversal symmetry. On the basis of topological classification, we also discuss possible other skin effects in arbitrary dimensions. Our work provides a unified understanding about the bulk-boundary correspondence and the skin effects in non-Hermitian systems.

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arXiv2019

Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics

Quantum phase transitions are intriguing and fundamental cooperative phenomena in physics. Analyzing a superconducting nanowire with spin-dependent non-Hermitian hopping, we discover a topological quantum phase transition driven by infinitesimal cascade instability. The anomalous phase transition is complementary to the universal non-Bloch wave behavior of non-Hermitian systems. We show that an infinite small magnetic field drastically suppresses the non-Hermitian skin effect, inducing a topological phase with Majorana boundary states. Furthermore, by identifying the bulk topological invariant, we establish the non-Hermitian bulk-boundary correspondence that does not have a Hermitian counterpart. We also discuss an experimental realization of the system by using the spin-current injection to a quantum wire.

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arXiv2019

Nonreciprocal superposition state in antiferromagnetic optospintronics

The absence of net magnetization, which forbids any stray magnetic fields, is one of the greatest advantages of antiferromagnets in device applications. In conventional antiferromagnets, however, spin current cannot be extracted without the aid of a static magnetic field. Here, we develop a theory of antiferromagnetic opto-spintronics to resolve this fundamental dilemma. By coupling a linearly polarized photon and nonreciprocal magnon bands, we construct a superposition state of left- and right-handed magnon states with opposite group velocities. We numerically demonstrate that by using this superposition state, an antiferromagnetic spin current can be efficiently generated without a net magnetic field including net magnetization. We also find that the breakdown of the superposition state induces the stripe superfluid phase of a two-component Bose-Einstein condensate. Our results lay the foundation for manipulating the superposition states of emergent particles in devices.

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arXiv2019

Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology

We classify time-reversal breaking (class A) spinful topological crystalline insulators with crystallographic non-magnetic (32 types) and magnetic (58 types) point groups. The classification includes all possible magnetic topological crystalline insulators protected by point group symmetry. Whereas the classification of topological insulators is known to be given by the $K$-theory in the momentum space, computation of the $K$-theory has been a difficult task in the presence of complicated crystallographic symmetry. Here we consider the $K$-homology in the real space for this problem, instead of the $K$-theory in the momentum space, both of which give the same topological classification. We apply the Atiyah-Hirzebruch spectral sequence (AHSS) for computation of the $K$-homology, which is a mathematical tool for generalized (co)homology. In the real space picture, the AHSS naturally gives the classification of higher-order topological insulators at the same time. By solving the group extension problem in the AHSS on the basis of physical arguments, we completely determine possible topological phases including higher-order ones for each point group. Relationships among different higher-order topological phases are argued in terms of the AHSS in the $K$-homology. We find that in some nonmagnetic and magnetic point groups, a stack of two $\mathbb{Z}_2$ second-order topological insulators can be smoothly deformed into non-trivial fourth-order topological insulators, which implies non-trivial group extensions in the AHSS.

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arXiv2017

Magnon Spin-Momentum Locking: Various Spin Vortices and Dirac Magnons in Noncollinear Antiferromagnets

We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120$^\circ$ structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can be explained in the context of a singular band point or a $U(1)$ symmetry breaking. A spin vortex in momentum space generated in a kagome lattice antiferromagnet has the winding number $Q=-2$, while the typical one observed in topological insulator surface states is characterized by $Q=+1$. A magnonic analogue of the surface states, the Dirac magnon with $Q=+1$, is found in another kagome lattice antiferromagnet. We also derive the sum rule for $Q$ by using the Poincaré-Hopf index theorem.

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arXiv2017

Microscopic derivation of magnon spin current in a topological insulator/ferromagnet heterostructure

We investigate a spin-electricity conversion effect in a topological insulator/ferromagnet heterostructure. In the spin-momentum-locked surface state, an electric current generates nonequilibrium spin accumulation, which causes a spin-orbit torque that acts on the ferromagnet. When spins in the ferromagnet are completely parallel to the accumulated spin, this spin-orbit torque is zero. In the presence of spin excitations, however, a coupling between magnons and electrons enables us to obtain a nonvanishing torque. In this paper, we consider a model of the heterostructure in which a three-dimensional magnon gas is coupled with a two-dimensional massless Dirac electron system at the interface. We calculate the torque induced by an electric field, which can be interpreted as a magnon spin current, up to the lowest order of the electron-magnon interaction. We derive the expressions for high and low temperatures and estimate the order of magnitude of the induced spin current for realistic materials at room temperature.

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arXiv2017

Theory of the Spin Seebeck Effect at a Topological-Insulator/Ferromagnetic-Insulator Interface

The spin-Seebeck effect refers to voltage signals induced in metals by thermally driven spin currents in adjacent magnetic systems. We present a theory of the spin-Seebeck signal in the case where the conductor that supports the voltage signal is the topologically protected two-dimensional surface-state system at the interface between a ferromagnetic insulator (FI) and a topological insulator (TI). Our theory uses a Dirac model for the TI surface-states and assumes Heisenberg exchange coupling between the TI quasiparticles and the FI magnetization. The spin-Seebeck voltage is induced by the TI surface states scattering off the nonequilibrium magnon population at the surface of the semi-infinite thermally driven FI. Our theory is readily generalized to spin-Seebeck voltages in any two-dimensional conductor that is exchange-coupled to the surface of a FI. Surface-state carrier-density-dependent signal strengths calculated using Bi$_2$Te$_3$ and yttrium iron garnet material parameters are consistent with recent experiments.

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arXiv2016

Unconventional Spin Hall Effect and Axial Current Generation in a Dirac Semimetal

We investigate electrical transport in a three-dimensional massless Dirac fermion model that describes a Dirac semimetal state realized in topological materials. We derive a set of interdependent diffusion equations with eight local degrees of freedom, including the electric charge density and the spin density, that respond to an external electric field. By solving the diffusion equations for a system with a boundary, we demonstrate that a spin Hall effect with spin accumulation occurs even though the conventional spin current operator is zero. The Noether current associated with chiral symmetry, known as the axial current, is also discussed. We demonstrate that the axial current flows near the boundary and that it is perpendicular to the electric current.

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arXiv2014

Long-range Coulomb interaction effects on the surface Dirac electron system of a three-dimensional topological insulator

The surface state of a three-dimensional topological insulator forms a two-dimensional massless Dirac electron system. In Dirac electron systems, Coulomb interaction is not screened due to the small density of states at the Fermi energy and thus the long-range Coulomb interaction (LRCI) plays a crucial role. In this paper, we investigate the surface state with chemical potential $μ=0$ in the presence of the LRCI using the Wilsonian renormalization group. We first check the Fermi velocity enhancement in the surface Dirac system, which also occurs in a usual Dirac electron system. The most remarkable feature of the surface Dirac system is that the Dirac Hamiltonian contains not pseudo spin but real spin Pauli matrices. Because of this feature, we find the g-factor enhancement, which is a unique property of the surface Dirac system. We also investigate the explicit form of the spin susceptibility and find that the spin susceptibility is enhanced in the presence of the LRCI.

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