Publications (94)240.26 Total impact

Article: Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
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ABSTRACT: Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schr\"{o}dinger type equation. The Hannay angle is then used to characterize a simple springmass model topologically with a particular focus on the bulkedge correspondence and new aspects of the symmetry in a classical system.  [Show abstract] [Hide abstract]
ABSTRACT: Mechanical graphene, which is a springmass model with the honeycomb structure, is investigated. The vibration spectrum is dramatically changed by controlling only one parameter, spring tension at equilibrium. In the spectrum, there always exist Dirac cones at K and K'points. As the tension is modified, extra Dirac cones are created and annihilated in pairs. When the time reversal symmetry is broken by uniform rotation of the system, creation and annihilation of the Dirac cones result in a jump of the appropriately defined Chern number. Then, a flip of the propagation direction of the chiral edge modes takes place, which gives an experimental way to detect the topological transition. This is a bulkedge correspondence of the classical system. We also demonstrate the other important concept, symmetry protection of the topological states, is at work in the classical system. For the time reversal invariant case, the topological edge modes exist for the fixed boundary condition but not for the free boundary condition. This contrast originates from the symmetry breaking at the free boundary.  [Show abstract] [Hide abstract]
ABSTRACT: In order to analytically capture and identify peculiarities in the electronic structure of silicene, the Weaire–Thorpe (WT) model, a standard model for treating threedimensional (3D) silicon, is applied to silicene with a buckled 2D structure. In the original WT model for four hybridized sp 3 orbitals on each atom along with interatom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we reformulate the WT model in terms of the overlapping molecularorbital (MO) method which enables us to describe flat bands away from the electron–hole symmetric point. The overlapping MO formalism indeed enables us to reveal an important difference: while in 3D the dipersive bands with cones are sandwiched by doublydegenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triplydegenerate and nondegenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. Thus there emerges a picture for why the whole band structure of silicene comprises a pair of dispersive bands with Dirac cones with each of the bands touching a nearly flat (narrow) band at Γ. We can also recognize that, for band engineering, the bonds perpendicular to the atomic plane are crucial, and that ferromagnetism or structural instabilities are expected if we can shift the chemical potential close to the flat bands.  [Show abstract] [Hide abstract]
ABSTRACT: We argue that the entanglement Chern number proposed recently is an invariant under the adiabatic deformation of a gapped manybody groundstate into {\it disentangled/purified} one, which means a partition of the Chern number (disentangled Chern number) into subsystems. We generalize the idea to another topological number, the Z$_2$ Berry phase for a system with particlehole symmetry, and apply it to a groundstate in a weak topological phase where the Chern number is vanishing but it has, nevertheless, edge states. This entanglement Berry phase is especially useful for characterizing random systems with non trivial edge states.  [Show abstract] [Hide abstract]
ABSTRACT: Topological properties of the spin1/2 dimerized Heisenberg ladder are investigated focusing on the plateau phase whose magnetization is a half of the saturation value that appears in the applied magnetic field. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry protected topological phase supported by the spatial inversion symmetry in the 1/2plateau phase. The Z2 Berry phase that is associated with a symmetry respecting boundary and is quantized into 0 and \pi is used to give a symmetry protected topological order parameter. Edge states are also analyzed to confirm the bulkedge correspondence. In addition, a symmetry breaking boundary is considered. Then, we observe a unique type of quantization of the Berry phase, a quantization into +\pi/2 of the Berry phase. In this case, the bulkedge correspondence is also unique, namely, there emerge "polarized" edge states for the case with +\pi/2 quantization. We also evaluate the entanglement entropy by the infinite timeevolving block decimation (iTEBD) to complement the Berry phase based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD.  [Show abstract] [Hide abstract]
ABSTRACT: In order to analytically capture and look for peculiarities in the electronic structure of silicene, WeaireThorp(WT) model, a standard model for treating threedimensional (3D) silicon, is applied to silicene with the buckled 2D structure. A particular interest is that in the original WT model for four hybridized $sp^3$ orbitals on each atom and interatom hopping, the band structure can be systematically examined, which contains flat (dispersionless) bands. If we reformulate the model in terms of the more general "overlapping molecular orbital" theory due to Hatsugai and Maruyama, we can generically treat the flat bands away from the electronhole symmetric point in multiorbital models for the first time. This enables us to newly interpret why the whole band structure of silicene comprises dispersive bands with Dirac cones and (nearly) flat bands. The algebraic formulation enables us to pin point an important difference from 3D, where the dipersive bands with cones are sandwiched by doublydegenerate flat ones, that in 2D the dipersive bands with cones are sandwiched by triplydegenerate and nondegenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. For the band engineering the bonds perpendicular to the atomic plane are crucial. A ferromagnetism is expected if we can shift the chemical potential close to the flat bands.  [Show abstract] [Hide abstract]
ABSTRACT: Anomalously sharp (deltafunctionlike) $n=0$ Landau level in the presence of disorder is usually considered to be a manifestation of the massless Dirac fermions in magnetic fields. This property persists even when the Dirac cone is tilted, which has been shown by Kawarabayashi et al. [Phys. Rev. B {\bf 83}, 153414 (2011)] to be a consequence of a "generalized chiral symmetry". Here we pose a question whether this property will be washed out when the tilted Dirac fermion becomes massive. Surprisingly, while the massive case with split $n=0$ Landau levels may seem to degrade the anomalous sharpness, the levels do remain deltafunctionlike. This has been shown analytically in terms of the AharonovCasher argument extended to the massive tilted Dirac ferimions. A key observation is that the conventional and generalized chiral operators are related with each other via a nonunitary transformation, with which the split, nonzeroenergy $n=0$ wave functions of the massive system can be identified as a gaugetransformed zeromode wave functions of the massless system. This is confirmed from a numerical result for a model tightbinding system. A message is that the chiral symmetry, rather than a simpler notion of the sublattice symmetry, is essential for the robustness of the $n=0$ Landau level, which is why the chiral symmetry remains applicable even to massive case.  [Show abstract] [Hide abstract]
ABSTRACT: If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an entanglement Chern number as a useful, natural, and calculable topological invariant, which is potentially relevant to various kinds of topological ground states. We show that it serves as an alternative topological invariant for time reversal invariant systems, and as a new topological invariant for a weak topological phase of a superlattice WilsonDirac model. In principle, the entanglement Chern number can be also effective for interacting systems such as topological insulators in contrast to the $Z_2$ invariants.  [Show abstract] [Hide abstract]
ABSTRACT: We propose classification schemes for characterizing twodimensional topological phases with nontrivial weak indices. Here, "weak" implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along specific boundaries. As concrete examples, we analyze different versions of the socalled WilsonDirac model with (i) anisotropic Wilson terms, (ii) next nearest neighbor hopping terms, and (iii) a superlattice generalization of the model, here in the tightbinding implementation. For types (i) and (ii) a graphic classification of strong properties is successfully generalized for classifying weak properties. As for type (iii), weak properties are attributed to quantized Berry phase pi along a Wilson loop.  [Show abstract] [Hide abstract]
ABSTRACT: Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming an existence of some adiabatic process which protects quantization of the Berry phase, non trivial Berry phase $\gamma=\pm 2\pi\rho$ ($\rho$ is a local filling of particles) for the bulk suggests appearance of edge states with boundaries. We have applied this generic consideration for Bloch states of some two dimensional model with massless Dirac fermions where $\gamma=\pm\pi/2$ implies the edge states. Entanglement entropy is evaluated for the models and its relation to the bulkedge correspondence of Dirac fermions is discussed as well. 
Conference Paper: Characterization of Dimers in Graphene Flakes

Conference Paper: Sharp ZeroEnergy Landau Levels in Multilayer Graphene

Conference Paper: Emergence of Topologically Stable Dirac Dispersions in a Fermionic Shastry–Sutherland Model
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ABSTRACT: Electronic structure of fermionic Shastry–Sutherland model, which is recently revealed to have a rich phase diagram, is investigated further in detail. We find that if the spin–orbit coupling exists, the quantum spin Hall insulator phase is also possible, in addition to the phases discovered in the previous study. Furthermore, firstprinciples calculation is performed for an existing material SrCu2(BO3)2 that has Shastry–Sutherland type lattice network, and the obtained results confirm those established with the tightbinding model.  [Show abstract] [Hide abstract]
ABSTRACT: Silicene is a two dimensional material of silicon and has zerogap semiconductor characteristics as is garaphene, where nnergy dispersion reveals DiracFermion nature. Moreover, silicene is expected to be very sensitive to electric field due to its buckled structure. In this paper, we discuss the DiracFermion nature of silicene and propose a recipe for synthesis for freestanding silicene by the theoretical approaches.  [Show abstract] [Hide abstract]
ABSTRACT: The fermionic ShastrySutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin1 Weyl fermion. Berry phases defined by the onedimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulkedge correspondence of the massless Dirac fermion systems.  [Show abstract] [Hide abstract]
ABSTRACT: We explore novel topological phases realized in a superlattice system based on the WilsonDirac model. Our main focus is on a twodimensional analogue of weak topological insulator phases. We find such phases as those characterized by gapless edge states that are protected by symmetry but sensitive to the orientation of the edge relative to the superlattice structure. We show that manifest and hidden reflection symmetries protect such weak topological phases, and propose bulk Z2 indices responsible for the topological protection of the edge states.  [Show abstract] [Hide abstract]
ABSTRACT: Classical and quantum dynamics are important limits for the understanding of the transport characteristics of interacting electrons in nanodevices. Here we apply an intermediate semiclassical approach to investigate the dynamics of two interacting electrons in a planar nanochannel as a function of Coulomb repulsion and electric field. We find that charge is mostly redistributed to the channel edges and that an electric field enhances the particlelike character of electrons. These results may have significant implications for the design and study of future nanodevices.  [Show abstract] [Hide abstract]
ABSTRACT: Influence of Coulomb blockade on electron scattering by a quantum dot has been theoretically investigated using a multielectron wave packet simulation technique based on the timedependent HartreeFock approximation. In our simulation, the bound states of electrons in the dot are selfconsistently determined. We confirmed that Koopman's theorem keeps its validity only for weak Coulomb interactions. Moreover, we show that the maximum number of electrons trapped in the dot does depend on the strength of Coulomb interactions. Consequently, the transmission and reflection probabilities of an incident wave packet toward the dot are strongly influenced by the number of trapped electrons in the dot. (C) 2013 The Japan Society of Applied Physics 
Article: Chiral symmetry and its manifestation in optical responses in graphene: Interaction and multilayers
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ABSTRACT: Chiral symmetry, fundamental in the physics of graphene, guarantees the existence of topologically stable doubled Dirac cones and anomalous behaviors of the zeroenergy Landau level in magnetic fields. Its crucial role, especially its manifestation in optical responses and manybody physics in graphene, is explained in this paper. We also give an overview of multilayer graphene from the viewpoint of the optical properties and their relation with chiral symmetry. 
Conference Paper: Effect of Coulomb Interaction on MultiElectron Wave Packet Dynamics
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ABSTRACT: We have investigated the effect of Coulomb interaction on electron transport in a onedimensional nanoscale structure using a multielectron wave packet approach. To study the time evolution, we numerically solve the timedependent HartreeFock equation, finding that the electron wave packet dynamics strongly depends on the Coulomb interaction strength. When the Coulomb interaction is large, each electron wave packet moves separately in the presence of an electric field. With weak Coulomb interaction, however, the electron wave packets overlap, forming and moving as one collective wave packet.
Publication Stats
2k  Citations  
240.26  Total Impact Points  
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Institutions

20082015

University of Tsukuba
 Centre for Computational Sciences
Tsukuba, Ibaraki, Japan


19902007

The University of Tokyo
 • Department of Applied Physics
 • Institute for Solid State Physics
Tokyo, Tokyoto, Japan


1993

University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, California, United States 
Massachusetts Institute of Technology
 Department of Physics
Cambridge, Massachusetts, United States
