arXiv subjects

Motohiko Ezawa

Publications and source records attributed to Motohiko Ezawa.

At least 163 records · Page 9Linked to original sources

arXiv2014

Symmetry Protected Topological Charge in Symmetry Broken Phase: Spin-Chern, Spin-Valley-Chern and Mirror-Chern Numbers

The Chern number is a genuine topological number. On the other hand, a symmetry protected topological (SPT) charge is a topological number only when a symmetry exists. We propose a formula for the SPT charge as a derivative of the Chern number in terms of the Green function in such a way that it is valid and related to the associated Hall current even when the symmetry is broken. We estimate the amount of deviation from the quantized value as a function of the strength of the broken symmetry. We present two examples. First, we consider Dirac electrons with the spin-orbit coupling on honeycomb lattice, where the SPT charges are given by the spin-Chern, valley-Chern and spin-valley-Chern numbers. Though the spin-Chern charge is not quantized in the presence of the Rashba coupling, the deviation is estimated to be $10^{-7}$ in the case of silicene, a silicon cousin of graphene. Second, we analyze the effect of the mirror-symmetry breaking of the mirror-Chern number in a thin-film of topological crystalline insulator.

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arXiv2013

Charge transport in pn and npn junctions of silicene

We investigate charge transport of pn and npn junctions made from silicene, Si analogue of graphene. The conductance shows the distinct gate-voltage dependences peculiar to the topological and non-topological phases, where the topological phase transition is caused by external electric field. Namely, the conductance is suppressed in the np regime when the both sides are topological, while in the nn regime when one side is topological and the other side is non-topological. Furthermore, we find that the conductance is almost quantized to be 0, 1 and 2. Our findings will open a new way to nanoelectronics based on silicene.

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arXiv2013

Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers

The valley-Chern and spin-valley-Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley-Chern and spin-valley-Chern numbers. The edge state between them is topologically trivial in the tight-binding model but is shown to be as robust as the topological edge. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges are conserved at the junction. We may interpret a Y-junction as a scattering process of particles which have four topological numbers. It would be a milestone of future topological electronics.

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arXiv2013

Single Dirac-Cone State and Quantum Hall Effects in Honeycomb Structure

A honeycomb lattice system has four types of Dirac electrons corresponding to the spin and valley degrees of freedom. We consider a state that contains only one type of massless electrons and three types of massive ones, which we call the single Dirac-cone state. We analyze quantum Hall (QH) effects in this state. We make a detailed investigation of the Chern and spin-Chern numbers. We make clear the origin of unconventional QH effects discovered in graphene. We also show that the single Dirac-cone state may have arbitrary large spin-Chern numbers in magnetic field. Such a state will be generated in antiferromagnetic transition-metal oxides under electric field or silicene with antiferromagnetic order under electric field.

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arXiv2013

Edge States in Silicene Nanodisks

Silicene is a honeycomb-structure silicon atoms, which shares many intriguing properties with graphene. Silicene is expected to be a quantum spin-Hall insulator due to its spin-orbit interactions. We investigate the electronic properties of silicene nanodisks, which are silicene derivatives with closed edge. In case of the simplest model of graphene nanodisks, the number of the zero-energy modes is given by the lower bound of the Lieb theorem. They are standing wave states.When the spin-orbit interaction is introduced and the system becomes a topological insulator, they begin to propagate around a nanodisk. Helical edge currents flow around the edge of a nanodisk though the crystal momentum is ill-defined. We have newly found the counting rule of the zero-energy states, and constructed the low-energy theory of zigzag triangular silicene. We also show the validity of the bulk-edge correspondence in nanodisks with rough edge by calculating the local probability amplitude and current. Finally, the signatures of the topological phase transition in silicene nanodisks under an external electric field are revealed.Our results will be observable by means of STM experiments.

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arXiv2013

Quantum Hall Effects with High Spin-Chern Numbers in Buckled Honeycomb Structure with Magnetic Order

As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. The Chern and spin-Chern numbers are calculated based on the bulk-edge correspondence in the lattice theory and on the Kubo formula in the Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems in coexistence with buckled structure and magnetic order. This is a new type of topological insulators. Samples may be provided by silicene with ferromagnetic order and transition-metal oxide with antiferromagnetic order.

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arXiv2013

Spin-Valleytronics in Silicene: Quantum-Spin-Quantum-Anomalous Hall Insulators and Single-Valley Semimetals

Valley-based electronics, known as valleytronics, is one of the keys to break 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 an 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 characteristic spin-valley structure. The single Dirac-cone semimetal is such a state that one gap is closed while the other three gaps are open, evading the Nielsen-Ninomiya fermion-doubling problem. We have newly discovered a hybrid topological insulator named the quantum-spin-quantum-anomalous Hall insulator, where the quantum anomalous Hall effect occurs at one valley and the quantum spin Hall effect occurs at the other valley. Along its phase boundary, single-valley semimetals emerge, where only one of the two valleys is gapless with degenerated spins. These semimetals are also topologically protected because they appear in the interface of different topological insulators. Such a spin-valley dependent physics will be observed by optical absorption or edge modes.

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arXiv2013

Hexagonally Warped Dirac Cones and Topological Phase Transition in Silicene Superstructure

Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. We investigate the topological properties of a silicene superstructure generated by an external periodic potential. The superstructure is a quantum spin-Hall (QSH) insulator if it is topologically connected to silicene. It is remarkable that two inequivalent K and K' points in the silicene Brillouin zone are identified in certain superstructures. In such a case two Dirac cones coexist at the same Dirac point in the momentum space and they are hexagonally warped by the Coulomb interaction. We carry out a numerical analysis by taking an instance of the ($3\times 3$) superstructure on the ($4\times 4$) structure of the Ag substrate. We show that it is a QSH insulator, that there exists no topological phase transition by external electric field, and that the hexagonally warping occurs in the band structure.

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arXiv2013

Quantized Conductance and Field-Effect Topological Quantum Transistor in Silicene Nanoribbons

Silicene (a monolayer of silicon atoms) is a quantum spin-Hall insulator, which undergoes a topological phase transition into other insulators by applying external field such as electric field, photo-irradiation and antiferromagnetic order. We investigate the electronic and transport properties of silicene nanoribbons based on the Landauer formalism. We propose to determine topological phase transitions by measuring the density of states and conductance. The conductance is quantized and changes its value when the system transforms into different phases. We show that a silicene nanoribbon near the zero energy acts as a field-effect transistor. This transistor is robust though it makes use of the minimum quantized conductance since the zero-energy edge states are topologically protected. Our findings open a new way to future topological quantum devices.

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arXiv2013

Interference of Topologically Protected Edge States in Silicene Nanoribbons

Silicene is a two-dimensional quantum spin-Hall insulator. We study the edge channels of silicene nanoribbons from the viewpoint of the topological protection and the interference between the two edges. It is found that the behaviors of the helical edge channels (HECs) are completely different between the armchair and zigzag edges. The penetration depths $ξ$ of the HEC is antiproportional to the spin-orbit gap for the armchair edge $ξ_{\rm arm} \sim \hbar v_\text{F}/ Δ$ ($v_\text{F}$: the Fermi velocity, $Δ$: the gap due to the spin-orbit interaction), while it remains as short as the lattice constant for the zigzag edge. Zero-energy states disappear in armchair nanoribbons due to an interference of two edge states, while they remains in zigzag nanoribbons even if the width $W$ is quite narrow. The gap $δ$ of HECs behaves as $δ\sim \hbar v_\text{F}/W$ for $Δ=0$, and as $δ\sim Δ\exp[- W/ξ_{\rm arm}]$ for $Δ\not=0$ for armchair nanoribbons, while it remains essentially zero irrespectively of $Δ$ for zigzag nanoribbons.

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arXiv2013

Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene

Silicene (a monolayer of silicon atoms) is a quantum spin Hall insulator (QSHI), which undergoes a topological phase transition to a band insulator under external electric field $E_{z}$. We investigate a photo-induced topological phase transition by irradiating circular polarized light at fixed $E_{z}$. The band structure and also the topological property are modified by photon dressing. By increasing the intensity of light at $E_{z}=0 $, a photo-induced quantum Hall insulator (P-QHI) is realized, where the quantum Hall effect occurs without magnetic field. Its edge modes are anisotropic chiral, in which the velocities of up and down spins are different. There appears a spin polarized metal characterized by topological flat bands at the critical point between the QSHI and P-QHI. At $E_{z}>E_{\text{cr}}$ with a certain critical field $E_{\text{cr}}$, a photo-induced spin-polarized quantum Hall insulator emerge. This is a new state of matter, possessing one Chern number and one half spin-Chern numbers. The edge mode supports a perfectly spin-polarized current, which are different from the chiral or helical edge modes. We newly discovered a single Dirac-cone state along a phase boundary. A distinctive hallmark of the state is that one of the two Dirac valleys is closed with a linear dispersion and the other open with a parabolic dispersion.

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arXiv2012

Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene

Bilayer silicene has richer physical properties than bilayer graphene due to its buckled structure together with its trigonal symmetric structure. The buckled structure arises from a large ionic radius of silicon, and the trigonal symmetry from a particular way of hopping between two silicenes. It is a topologically trivial insulator since it carries a trivial $\mathbb{Z}_{2}$ topological charge. Nevertheless, its physical properties are more akin to those of a topological insulator than those of a band insulator. Indeed, a bilayer silicene nanoribbon has edge modes which are almost gapless and helical. We may call it a quasi-topological insulator. An important observation is that the band structure is controllable by applying the electric field to a bilayer silicene sheet. We investigate the energy spectrum of bilayer silicene under electric field. Just as monolayer silicene undergoes a phase transition from a topological insulator to a band insulator at a certain electric field, bilayer silicene makes a transition from a quasi-topological insulator to a band insulator beyond a certain critical field. Bilayer silicene is a metal while monolayer silicene is a semimetal at the critical field. Furthermore we find that there are several critical electric fields where the gap closes due to the trigonal warping effect in bilayer silicene.

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arXiv2012

Spin-Valley Optical Selection Rule and Strong Circular Dichroism in Silicene

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. The spin polarization is unique and opposite at the K and K' points due to the spin-orbit coupling. Accordingly, silicene exhibits a strong circular dichroism with respect to optical absorption, obeying a certain spin-valley selection rule. It is remarkable that this selection rule is drastically different between these two types of insulators owing to a band inversion taking place at the phase transition point. Hence we can tell experimentally whether silicene is in the topological or band insulator phase by circular dichroism. Furthermore the selection rule enables us to excite electrons with definite spin and valley indices by optical absorption. Photo-induced current is spin polarized, where the spin direction is different between the topological and band insulators. It is useful for future spintronics applications.

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arXiv2012

Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene

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 the electric field to a silicene sheet. We explore the phase diagram of silicene together with exchange field $M$ and by applying electric field $E_{z}$. There appear quantum anomalous Hall (QAH) insulator, valley polarized metal (VPM), marginal valley polarized metal (M-VPM), quantum spin Hall (QSH) insulator and band insulator (BI). They are characterized by the Chern numbers and/or by the edge modes of a nanoribbon. It is intriguing that electrons have been moved from a conduction band at the K point to a valence band at the K' point for $E_{z}>0$ in the VPM. We find in the QAH phase that flat gapless edge modes emerge and that spins form a momentum-space skyrmion to yield the Chern number. It is remarkable that a topological quantum phase transition can be induced simply by changing electric field in a single silicene sheet.

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arXiv2012

Topological Phase Transition and Electrically Tunable Diamagnetism in Silicene

Silicene is a monolayer of silicon atoms forming a honeycomb lattice. The lattice is actually made of two sublattices with a tiny separation. Silicene is a topological insulator, which is characterized by a full insulating gap in the bulk and helical gapless edges. It undergoes a phase transition from a topological insulator to a band insulator by applying external electric field. Analyzing the spin Chern number based on the effective Dirac theory, we find their origin to be a pseudospin meron in the momentum space. The peudospin degree of freedom arises from the two-sublattice structure. Our analysis makes clear the mechanism how a phase transition occurs from a topological insulator to a band insulator under increasing electric field. We propose a method to determine the critical electric field with the aid of diamagnetism of silicene. Diamagnetism is tunable by the external electric field, and exhibits a singular behaviour at the critical electric field. Our result is important also from the viewpoint of cross correlation between electric field and magnetism. Our finding will be important for future electro-magnetic correlated devices.

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arXiv2012

Dirac Theory and Topological Phases of Silicon Nanotube

Silicon nanotube is constructed by rolling up a silicene, i.e., a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. It is a semiconductor or an insulator owing to relatively large spin-orbit interactions induced by its buckled structure. The key observation is that this buckled structure allows us to control the band structure by applying electric field $E_z$. When $E_z$ is larger than a certain critical value $E_{\text{cr}}$, by analyzing the band structure and also on the basis of the effective Dirac theory, we demonstrate the emergence of four helical zero-energy modes propagating along nanotube. Accordingly, a silicon nanotube contains three regions, namely, a topological insulator, a band insulator and a metallic region separating these two types of insulators. The wave function of each zero mode is localized within the metallic region, which may be used as a quantum wire to transport spin currents in future spintronics. We present an analytic expression of the wave function for each helical zero mode. These results are applicable also to germanium nanotube.

cond-mat.mes-hall↗

arXiv2012

Topological Insulator and Helical Zero Mode in Silicene under Inhomogeneous Electric Field

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 the electric field to a silicene sheet. In particular, the gap closes at a certain critical electric field. Examining the band structure of a silicene nanoribbon, we demonstrate that a topological phase transition occurs from a topological insulator to a band insulator with the increase of the electric field. We also show that it is possible to generate helical zero modes anywhere in a silicene sheet by adjusting the electric field locally to this critical value. The region may act as a quantum wire or a quantum dot surrounded by topological and/or band insulators. We explicitly construct the wave functions for some simple geometries based on the low-energy effective Dirac theory. These results are applicable also to germanene, that is a two-dimensional honeycomb structure of germanium.

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arXiv2012

Quantum Hall Effects in Silicene

We investigate quantum Hall effects in silicene by applying electric field $E_z$ parallel to magnetic field. Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, and shares almost every remarkable property with graphene. A new feature is its buckled structure, due to which the band structure can be controlled externally by changing $E_z$. The low energy physics of silicene is described by massive Dirac fermions, where the mass is a function of $E_z$ and becomes zero at the critical field $E_{\text{cr}}$. We show that there are no zero energy states due to the Dirac mass term except at the critical electric field $E_{\text{cr}}$. Furthermore it is shown that the 4-fold degenerate zero-energy states are completely resolved even without considering Coulomb interactions. These features are highly contrasted with those in graphene, demonstrating that silicene has a richer structure. The prominent feature is that, by applying the electric field, we can control the valley degeneracy. As a function of $E_z$, Hall plateaux appear at the filling factors $ν=0,\pm 1,\pm 2,\pm 3,...$ except for the points where level crossings occur.

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