Motohiko Ezawa

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low-energy structure of silicene is described by Dirac electrons with relatively large spin-orbit interactions due to its buckled structure. The key observation is that the band structure is controllable by applying electric field to silicene. We explore the phase diagram of silicene together with exchange field M and by applying electric field E(

A second-order topological insulator in d dimensions is an insulator which has no d-1 dimensional topological boundary states but has d-2 dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this Letter, we generalize them to breathing kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lat

Nanoribbons (nanographite ribbons) are carbon systems analogous to carbon nanotubes. We characterize a wide class of nanoribbons by a set of two integers $⟨p,q⟩$, and then define the width $w$ in terms of $p$ and $q$. Electronic properties are explored for this class of nanoribbons. Zigzag (armchair) nanoribbons have similar electronic properties to armchair (zigzag) nanotubes. The band gap structure of nanoribbons exhibits a valley structure with streamlike sequences of metallic or almost metal

Silicene (a monolayer of silicon atoms) is a two-dimensional topological insulator (TI) that undergoes a topological phase transition to a band insulator under external electric field E(z). We investigate a photoinduced topological phase transition from a TI to another TI by changing its topological class by irradiating circular polarized light at fixed E(z). The band structure is modified by photon dressing with a new dispersion, where the topological property is altered. By increasing the inte

Valley-based electronics, known as valleytronics, is one of the keys to breaking through to a new stage of electronics. The valley degree of freedom is ubiquitous in the honeycomb lattice system. The honeycomb lattice structure of silicon, called silicene, is a fascinating playground of valleytronics. We investigate topological phases of silicene by introducing different exchange fields on the $A$ and $B$ sites. There emerges a rich variety of topologically protected states, each of which has a

We explore the electronic properties of finite-length graphene nanoribbons as well as graphene nanodisks with various sizes and shapes in quest of metallic ones. For this purpose, it is sufficient to search zero-energy states. We find that no zero-energy states exist in finite-length zigzag nanoribbons though all infinite-length zigzag nanoribbons have zero-energy states. The occurrence of zero-energy states is surprisingly rare. Among typical nanodisks, only trigonal zigzag nanodisks have degen

Phosphorene, a honeycomb structure of black phosphorus, was isolated recently. The band structure is highly anisotropic, where the k _x direction is Dirac-like and the k _y direction is Schrödinger-like. A prominent feature is the presence of a quasi-flat edge band entirely detached from the bulk band in phosphorene nanoribbons. We explore the mechanism of the emergence of the quasi-flat band by employing the topological argument invented to explain successfully the flat band familiar in graphen

A higher-order topological insulator (HOTI) is an extended notion of the conventional topological insulator. It belongs to a special class of topological insulators to which the conventional bulk-boundary correspondence is not applicable. Provided the mirror symmetries are present, the bulk topological number is described by the quantized Wannier center located at a high-symmetry point of the crystal. The emergence of corner states is a manifestation of nontrivial topology in the bulk. In this p

A meron is a controversial topological excitation because it carries just one-half of the skyrmion number. A vortex in thin magnetic films has been argued to be a half-skyrmion, i.e., a meron. We present another type of merons, investigating the two-dimensional nonlinear sigma model together with the Dzyaloshinskii-Moriya interaction. Here, the vortex number of a meron is zero. Basic topological excitations are merons and skyrmions. They behave as if they were free particles. A prominent feature

Nonreciprocal non-Hermitian higher-order topological skin states are realized in $L\phantom{\rule{0}{0ex}}C$ electric circuits with diodes. Here, the authors give examples with rhombus geometry of the nonreciprocal honeycomb system and rhombohedron geometry of the diamond lattice system. In the accompanying image, red balls represent zero-energy topological corner states.

Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing kagome and pyrochlore lattices. They are known to possess three phases (trivial insulator, higher-order topological insulator, and metallic phases) in the tight-binding model, where the topological phase is characterized by the emergence of zero-energy corner states. A topological phase transition is induced by tuning continuously the capac

Non-Hermitian skin-edge states emerge only at one edge in one-dimensional nonreciprocal chains, where all states are localized at the edge irrespective of eigenvalues. The bulk topological number is the winding number associated with the complex energy spectrum, which is well defined for metals. We study non-Hermitian nonreciprocal systems in higher dimensions, and propose to realize them with the use of electric diode circuits. We first investigate one-dimensional interface states between two d

Silicene (a monolayer of silicon atoms) is a topological insulator which undergoes a topological phase transition to a band insulator under an external electric field. We propose a way of detecting the topological phase transition by way of optical absorption. We demonstrate that silicene exhibits a strong circular dichroism with respect to optical absorption and obeys a certain spin-valley selection rule. The selection rule is drastically different between the topological and trivial sectors be

We propose a type of Hopf semimetal indexed by a pair of numbers $(p,q)$, where the Hopf number is given by $pq$. The Fermi surface is given by a preimage of the Hopf map, which consists of loops nontrivially linked for a nonzero Hopf number. The Fermi surface forms a torus link, whose examples are a Hopf link indexed by $(1,1)$, Solomon's knot $(2,1)$, a double Hopf link $(2,2)$, and a double trefoil knot $(3,2)$. We may choose $p$ or $q$ to be a half integer, where the Fermi surface is a torus