scholarly journals Observation of Protected Photonic Edge States Induced by Real-Space Topological Lattice Defects

2020 ◽  
Vol 124 (24) ◽  
Author(s):  
Qiang Wang ◽  
Haoran Xue ◽  
Baile Zhang ◽  
Y. D. Chong
Keyword(s):  
Real Space ◽  
Lattice Defects ◽  
Edge States ◽  
Topological Lattice

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

scholarly journals Revealing topology with transformation optics

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lizhen Lu ◽  
Kun Ding ◽  
Emanuele Galiffi ◽  
Xikui Ma ◽  
Tianyu Dong ◽  
...  
Keyword(s):  
Physical Space ◽  
Real Space ◽  
Virtual Space ◽  
Transformation Optics ◽  
Coordinate Space ◽  
Dimensional System ◽  
Edge States ◽  
And Topology ◽  
Higher Dimensional ◽  
Insight Into

AbstractSymmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

scholarly journals Local symmetry theory of resonator structures for the real-space control of edge states in binary aperiodic chains

2019 ◽  
Vol 99 (21) ◽  
Author(s):  
M. Röntgen ◽  
C. V. Morfonios ◽  
R. Wang ◽  
L. Dal Negro ◽  
P. Schmelcher
Keyword(s):  
Local Symmetry ◽  
Real Space ◽  
Edge States ◽  
The Real ◽  
Symmetry Theory

scholarly journals Twisted bulk-boundary correspondence of fragile topology

Science ◽  
2020 ◽  
Vol 367 (6479) ◽  
pp. 794-797 ◽  
Author(s):  
Zhi-Da Song ◽  
Luis Elcoro ◽  
B. Andrei Bernevig
Keyword(s):  
Boundary Conditions ◽  
Topological Insulator ◽  
Experimental Verification ◽  
Real Space ◽  
Two Dimensional ◽  
Edge States ◽  
Quantum Numbers ◽  
Boundary Correspondence ◽  
Topological States ◽  
Twisted Boundary Conditions

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Topologically valley-polarized edge states in elastic phononic plates yielded by lattice defects

2022 ◽  
pp. 111413
Author(s):  
Baizhan Xia ◽  
Jie Zhang ◽  
Liang Tong ◽  
Shengjie Zheng ◽  
Xianfeng Man
Keyword(s):  
Lattice Defects ◽  
Edge States

scholarly journals Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system

2019 ◽  
Vol 5 (7) ◽  
pp. eaav6600 ◽  
Author(s):  
Alexandra Palacio-Morales ◽  
Eric Mascot ◽  
Sagen Cocklin ◽  
Howon Kim ◽  
Stephan Rachel ◽  
...  
Keyword(s):  
Hybrid System ◽  
Theoretical Calculations ◽  
Real Space ◽  
Scanning Tunneling Spectroscopy ◽  
Atomic Scale ◽  
Scanning Tunneling ◽  
Edge States ◽  
Interface Engineering ◽  
New Paradigm ◽  
Topological Quantum

Topological superconductors are predicted to harbor exotic boundary states—Majorana zero-energy modes—whose non-Abelian braiding statistics present a new paradigm for the realization of topological quantum computing. Using low-temperature scanning tunneling spectroscopy, here, we report on the direct real-space visualization of chiral Majorana edge states in a monolayer topological superconductor, a prototypical magnet-superconductor hybrid system composed of nanoscale Fe islands of monoatomic height on a Re(0001)-O(2 × 1) surface. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the hybrid system into a topologically nontrivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.

scholarly journals Observing multifarious topological phase transitions with real-space indicator

Nanophotonics ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yong-Heng Lu ◽  
Yao Wang ◽  
Feng Mei ◽  
Yi-Jun Chang ◽  
Hang Zheng ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Three Dimensional ◽  
Real Space ◽  
Second Order ◽  
Topological Phases ◽  
Topological Phase ◽  
Edge States ◽  
Direct Writing ◽  
Topological Features ◽  
Topological Phase Transitions

Abstract First- and second-order topological phases, capable of inherent protection against disorder of materials, have been recently experimentally demonstrated in various artificial materials through observing the topologically protected edge states. Topological phase transition represents a new class of quantum critical phenomena, which is accompanied by the changes related to the bulk topology of energy band structures instead of symmetry. However, it is still a challenge to directly observe the topological phase transitions defined in terms of bulk states. Here, we theoretically and experimentally demonstrate the direct observation of multifarious topological phase transitions with real-space indicator in a single photonic chip, which is formed by integration of 324 × 33 waveguides supporting both first- and second-order topological phases. The trivial-to-first-order, trivial-to-second-order and first-to-second-order topological phase transitions signified by the band gap closure can all be directly detected via photon evolution in the bulk. We further observe the creation and destruction of gapped topological edge states associated with these topological phase transitions. The bulk-state-based route to investigate the high-dimensional and high-order topological features, together with the platform of freely engineering topological materials by three-dimensional laser direct writing in a single photonic chip, opens up a new avenue to explore the mechanisms and applications of artificial devices.

scholarly journals Real-space effects of a quench in the Su-Schrieffer-Heeger model and elusive dynamical appearance of the topological edge states

2021 ◽  
Author(s):  
Lorenzo Rossi ◽  
Fausto Rossi ◽  
Fabrizio Dolcini
Keyword(s):  
Thermal State ◽  
Real Space ◽  
Time Averaging ◽  
Topological Phase ◽  
Edge States ◽  
Additional Time ◽  
Dynamical Features ◽  
A Chain ◽  
Ssh Model ◽  
Space Effects

Abstract The topological phase of the Su-Schrieffer-Heeger (SSH) model is known to exhibit two edge states that are topologically protected by the chiral symmetry. We demonstrate that, for any parameter quench performed on the half-filled SSH chain, the occupancy of each lattice site remains locked to 1/2 at any time, due to the additional time-reversal and charge conjugation symmetries. In particular, for a quench from the trivial to the topological phase, no signature of the topological edge states appears in real-space occupancies, independently of the quench protocol, the temperature of the pre-quench thermal state or the presence of chiral disorder. However, a suitably designed local quench from/to a SSH ring threaded by a magnetic flux can break these additional symmetries while preserving the chiral one. Then, real-space effects of the quench do appear and exhibit different dynamical features in the topological and in the trivial phases. Moreover, when the particle filling is different from a half and the pre-quench state is not insulating, the dynamical appearance of the topological edge states is visible already in a chain, it survives time averaging and can be observed also in the presence of chiral-breaking disorder and for instantaneous quenches.

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