scholarly journals Topological edge and corner states in a two-dimensional photonic Su-Schrieffer-Heeger lattice

Nanophotonics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 3227-3234 ◽  
Author(s):  
Minkyung Kim ◽  
Junsuk Rho
Keyword(s):  
Rotational Symmetry ◽  
Polarization Degree ◽  
Open Boundary ◽  
Topological Phase ◽  
Two Dimensional ◽  
Topological Properties ◽  
Open Boundary Condition ◽  
Metallic Nanoparticle ◽  
Topological Features ◽  
Longitudinal Edge

AbstractImplementation of topology on photonics has opened new functionalities of photonic systems such as topologically protected boundary modes. We theoretically present polarization-dependent topological properties in a 2D Su-Schrieffer-Heeger lattice by using a metallic nanoparticle array and considering the polarization degree of freedom. We demonstrate that when eigenmodes are polarized parallel to the plane of the 2D lattice, it supports longitudinal edge modes that are isolated from the bulk states and transverse edge modes that are overlapped with the bulk states. Also, the in-plane polarized modes support a second-order topological phase under an open boundary condition by breaking the four-fold rotational symmetry. This work will offer polarization-based multifunctionality in compact photonic systems that have topological features.

scholarly journals Topological Edge States of a Majorana BBH Model

2021 ◽  
Vol 6 (2) ◽  
pp. 15
Author(s):  
Alfonso Maiellaro ◽  
Roberta Citro
Keyword(s):  
2D Materials ◽  
Finite Size ◽  
Majorana Fermions ◽  
Topological Phase ◽  
Two Dimensional ◽  
Edge States ◽  
Finite Size Scaling ◽  
Topological Properties ◽  
Berry Curvature ◽  
Topological Superconductors

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

scholarly journals What do we see when we look at networks: Visual network analysis, relational ambiguity, and force-directed layouts

2021 ◽  
Vol 8 (1) ◽  
pp. 205395172110184
Author(s):  
Tommaso Venturini ◽  
Mathieu Jacomy ◽  
Pablo Jensen
Keyword(s):  
Social Sciences ◽  
Network Analysis ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Project Networks ◽  
Topological Features ◽  
Exploratory Data ◽  
Inherent Ambiguity ◽  
Visual Network ◽  
Visual Ambiguity

It is increasingly common in natural and social sciences to rely on network visualizations to explore relational datasets and illustrate findings. Such practices have been around long enough to prove that scholars find it useful to project networks in a two-dimensional space and to use their visual qualities as proxies for their topological features. Yet these practices remain based on intuition, and the foundations and limits of this type of exploration are still implicit. To fill this lack of formalization, this paper offers explicit documentation for the kind of visual network analysis encouraged by force-directed layouts. Using the example of a network of Jazz performers, band and record labels extracted from Wikipedia, the paper provides guidelines on how to make networks readable and how to interpret their visual features. It discusses how the inherent ambiguity of network visualizations can be exploited for exploratory data analysis. Acknowledging that vagueness is a feature of many relational datasets in the humanities and social sciences, the paper contends that visual ambiguity, if properly interpreted, can be an asset for the analysis. Finally, we propose two attempts to distinguish the ambiguity inherited from the represented phenomenon from the distortions coming from fitting a multidimensional object in a two-dimensional space. We discuss why these attempts are only partially successful, and we propose further steps towards a metric of spatialization quality.

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