scholarly journals Bulk-edge correspondence of classical diffusion phenomena

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tsuneya Yoshida ◽  
Yasuhiro Hatsugai
Keyword(s):  
Temperature Field ◽  
Diffusion Equation ◽  
Edge State ◽  
Lattice System ◽  
Honeycomb Lattice ◽  
Two Dimensional ◽  
Winding Number ◽  
Edge States ◽  
Diffusive Dynamics ◽  
Diffusion Phenomena

AbstractWe elucidate that diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring diffusive dynamics at edges. Furthermore, we discover a novel diffusion phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $$\pi $$ π cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.

Dual modulation of topological edge states from two-dimensional photonic crystals with lattice shrink

2021 ◽  
pp. 2150236
Author(s):  
Xiao-Xue Li ◽  
Yun-Tuan Fang ◽  
Li-Xia Yang
Keyword(s):  
Photonic Crystals ◽  
Edge State ◽  
Wide Bandgap ◽  
Two Dimensional ◽  
Edge States ◽  
Source Position ◽  
State Structure ◽  
Intense Field ◽  
Flat Edge ◽  
Field Localization

The current topological edge states lack dynamical modulation and the intense field localization effect. To solve these problems, we construct a topological edge state structure based on two-dimensional photonic crystals with lattice shrink. Through the optimization of structure parameters, a nearly flat edge state dispersion curve occurs in a wide bandgap. The topological edge states with intense field localization take on some unique properties such that the transport directions can be controlled by both the source spin and the source position. The transport modes can be dynamically switched between the two opposite unidirectional channels just through moving the source position.

Ferromagnetic dual topological insulator in a two-dimensional honeycomb lattice

2020 ◽  
Vol 7 (9) ◽  
pp. 2431-2438
Author(s):  
Hao Wang ◽  
Ning Mao ◽  
Chengwang Niu ◽  
Shiying Shen ◽  
Myung-Hwan Whangbo ◽  
...  
Keyword(s):  
Hall Effect ◽  
Topological Insulator ◽  
Topological Insulators ◽  
Anomalous Hall Effect ◽  
Topological Invariant ◽  
Honeycomb Lattice ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Anomalous Hall Effect ◽  
Significant Attention

Magnetic topological insulators (TIs), including the quantum anomalous Hall effect and antiferromagnetic TIs, have attracted significant attention owing to the exotic properties they give rise to, however, ferromagnetic TIs with gapless surface/edge states and a nonzero topological invariant have not been reported so far.

scholarly journals Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

Photonics ◽  
2020 ◽  
Vol 7 (4) ◽  
pp. 81
Author(s):  
Matthew Proctor ◽  
Xiaofei Xiao ◽  
Richard V. Craster ◽  
Stefan A. Maier ◽  
Vincenzo Giannini ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Honeycomb Lattice ◽  
Far Field ◽  
Two Dimensional ◽  
Edge States ◽  
Source Position ◽  
Magnetic Dipoles ◽  
Classical Wave ◽  
Field Excitation ◽  
Crystalline Symmetry

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

scholarly journals Strain-Induced Quantum Spin Hall Effect in Two-Dimensional Methyl-Functionalized Silicene SiCH3

Nanomaterials ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 698 ◽  
Author(s):  
Ceng-Ceng Ren ◽  
Wei-Xiao Ji ◽  
Shu-Feng Zhang ◽  
Chang-Wen Zhang ◽  
Ping Li ◽  
...  
Keyword(s):  
Hexagonal Boron Nitride ◽  
Quantum Spin ◽  
Honeycomb Lattice ◽  
Potential Candidate ◽  
Two Dimensional ◽  
Edge States ◽  
Spin Orbital ◽  
Spintronic Devices ◽  
Potential Applications ◽  
Quantum Spin Hall

Quantum Spin Hall (QSH) has potential applications in low energy consuming spintronic devices and has become a researching hotspot recently. It benefits from insulators feature edge states, topologically protected from backscattering by time-reversal symmetry. The properties of methyl functionalized silicene (SiCH3) have been investigated using first-principles calculations, which show QSH effect under reasonable strain. The origin of the topological characteristic of SiCH3, is mainly associated with the s-pxy orbitals band inversion at Γ point, whilst the band gap appears under the effect of spin-orbital coupling (SOC). The QSH phase of SiCH3 is confirmed by the topological invariant Z2 = 1, as well as helical edge states. The SiCH3 supported by hexagonal boron nitride (BN) film makes it possible to observe its non-trivial topological phase experimentally, due to the weak interlayer interaction. The results of this work provide a new potential candidate for two-dimensional honeycomb lattice spintronic devices in spintronics.

Topological Lifshitz Transition and Novel Edge States Induced by Non-Abelian SU(2) Gauge Field on Bilayer Honeycomb Lattice

2021 ◽  
Author(s):  
Wen-Xiang Guo ◽  
Wu-Ming Liu
Keyword(s):  
Secular Equation ◽  
Universality Class ◽  
Gauge Potential ◽  
Honeycomb Lattice ◽  
The Novel ◽  
Winding Number ◽  
Edge States ◽  
Abelian Gauge ◽  
Fermi Surfaces ◽  
Lifshitz Transition

Abstract We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

Edge states, band structure, and the Hall effect in two-dimensional lattice structures: quantum dot arrays and the tight-binding model

1995 ◽  
Vol 73 (3-4) ◽  
pp. 147-162 ◽  
Author(s):  
R. Akis ◽  
C. Barnes ◽  
G. Kirczenow
Keyword(s):  
Quantum Dots ◽  
Tight Binding ◽  
Transmission Probability ◽  
Edge State ◽  
Matrix Formalism ◽  
Two Dimensional ◽  
Tight Binding Model ◽  
Edge States ◽  
Binding Model ◽  
Hall Conductance

Using a model that is based on a transfer matrix formalism, we study the electronic structure and transport in two dimensional periodic arrays of quantum dots in magnetic fields. The quantum dots in our model are connected to each other via ballistic constrictions. The spectrum for this system has much in common with that with the tight-binding model. In particular, q bulk bands arise if the normalized magnetic flux per unit cell is p/q, where p and q are coprime integers. Working within an edge-state picture, we investigate if these similarities translate to a correspondence in the transport properties of the two systems. As we shall show, the answer to this question depends very much on the transmission probability of the constrictions. Our analysis also shows that, under certain circumstances, the Hall conductance within the context of the tight-binding model may take on fractional values.

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