[Show abstract][Hide abstract] 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 spring-mass model topologically with a particular focus
on the bulk-edge correspondence and new aspects of the symmetry in a classical
system.
[Show abstract][Hide abstract] ABSTRACT: Mechanical graphene, which is a spring-mass 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
bulk-edge 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 three-dimensional (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 inter-atom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we re-formulate the WT model in terms of the overlapping molecular-orbital (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 doubly-degenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triply-degenerate and non-degenerate (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.
New Journal of Physics 02/2015; 17(2). DOI:10.1088/1367-2630/17/2/025009 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We argue that the entanglement Chern number proposed recently is an invariant
under the adiabatic deformation of a gapped many-body 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 particle-hole
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.
Journal of the Physical Society of Japan 01/2015; 84(4). DOI:10.7566/JPSJ.84.043703 · 1.59 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Topological properties of the spin-1/2 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 1/2-plateau 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 bulk-edge 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
bulk-edge 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 time-evolving 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.
Physical Review B 12/2014; 91(21). DOI:10.1103/PhysRevB.91.214410 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In order to analytically capture and look for peculiarities in the electronic
structure of silicene, Weaire-Thorp(WT) model, a standard model for treating
three-dimensional (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 inter-atom hopping, the band
structure can be systematically examined, which contains flat (dispersionless)
bands. If we re-formulate 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 electron-hole symmetric point in
multi-orbital 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 doubly-degenerate flat ones, that in 2D the dipersive bands with
cones are sandwiched by triply-degenerate and non-degenerate (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 (delta-function-like) $n=0$ 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
delta-function-like. This has been shown analytically in terms of the
Aharonov-Casher 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 non-unitary transformation, with which the split,
nonzero-energy $n=0$ wave functions of the massive system can be identified as
a gauge-transformed zero-mode wave functions of the massless system. This is
confirmed from a numerical result for a model tight-binding 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.
Physical Review B 10/2014; 91(8). DOI:10.1103/PhysRevB.91.085112 · 3.74 Impact Factor
[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 Wilson-Dirac 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.
Journal of the Physical Society of Japan 08/2014; 83(11). DOI:10.7566/JPSJ.83.113705 · 1.59 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We propose classification schemes for characterizing two-dimensional
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 so-called Wilson-Dirac model with (i) anisotropic Wilson terms,
(ii) next nearest neighbor hopping terms, and (iii) a superlattice
generalization of the model, here in the tight-binding 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.
Physical Review B 05/2014; 90(15). DOI:10.1103/PhysRevB.90.155443 · 3.74 Impact Factor
[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 bulk-edge correspondence of Dirac
fermions is discussed as well.
Physical Review B 04/2014; 90(8). DOI:10.1103/PhysRevB.90.085132 · 3.74 Impact Factor
[Show abstract][Hide abstract] 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, first-principles 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 tight-binding model.
Proceedings of the 12th Asia Pacific Physics Conference (APPC12); 03/2014
[Show abstract][Hide abstract] ABSTRACT: The fermionic Shastry-Sutherland model has a rich phase diagram, including
phases with massless Dirac fermions, a quadratic band crossing point, and a
pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional 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 bulk-edge correspondence of the
massless Dirac fermion systems.
Physical Review B 07/2013; 88(24). DOI:10.1103/PhysRevB.88.245126 · 3.74 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We explore novel topological phases realized in a superlattice system based
on the Wilson-Dirac model. Our main focus is on a two-dimensional 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.
Journal of the Physical Society of Japan 04/2013; 82(7). DOI:10.7566/JPSJ.82.073708 · 1.59 Impact Factor
[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 particle-like
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 time-dependent Hartree-Fock approximation. In our simulation, the bound states of electrons in the dot are self-consistently 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
Japanese Journal of Applied Physics 04/2013; 52(4S):04CJ06. DOI:10.7567/JJAP.52.04CJ06 · 1.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Chiral symmetry, fundamental in the physics of graphene, guarantees the existence of topologically stable doubled Dirac cones and anomalous behaviors of the zero-energy Landau level in magnetic fields. Its crucial role, especially its manifestation in optical responses and many-body 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.
New Journal of Physics 03/2013; 15(3):035023. DOI:10.1088/1367-2630/15/3/035023 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We have investigated the effect of Coulomb interaction on electron transport in a one-dimensional nanoscale structure using a multi-electron wave packet approach. To study the time evolution, we numerically solve the time-dependent Hartree-Fock 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.
31st International Conference on the Physics of Semiconductors (ICPS); 01/2013
[Show abstract][Hide abstract] ABSTRACT: We study the transport dynamics of semiclassical electrons in graphene in the
Klein tunneling regime by scattering wave packets off a potential step while
taking the full graphene Hamiltonian into account. Besides establishing the
basic transmission characteristics for zigzag and armchair step edges, our
numerical simulation suggests that the wave packet dynamics is substantially
affected by the Berry curvature, which induces lateral shifts near the step
edge reminiscent of the Hall effect of light. This anomalous correction can be
relevant for recent Klein tunneling experiments.