scholarly journals Nonlinear second-order photonic topological insulators

2021 ◽  
Author(s):  
Marco S. Kirsch ◽  
Yiqi Zhang ◽  
Mark Kremer ◽  
Lukas J. Maczewsky ◽  
Sergey K. Ivanov ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Higher Order ◽  
Topological Phase ◽  
Topological Properties ◽  
Linear Evolution ◽  
New Class ◽  
On Demand ◽  
Boundary Correspondence ◽  
Topological States ◽  
The Impact

AbstractHigher-order topological insulators are a novel topological phase beyond the framework of conventional bulk–boundary correspondence1,2. In these peculiar systems, the topologically non-trivial boundary modes are characterized by a co-dimension of at least two3,4. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems5,6, the flourishing field of experimental higher-order topological insulator research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. Here we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.

scholarly journals Non-Abelian Bloch oscillations in higher-order topological insulators

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
M. Di Liberto ◽  
N. Goldman ◽  
G. Palumbo
Keyword(s):  
Quantum Dynamics ◽  
Topological Insulators ◽  
Berry Phase ◽  
Center Of Mass ◽  
Higher Order ◽  
Topological Properties ◽  
Bloch Oscillations ◽  
Abelian Gauge ◽  
Synchronization Mechanism ◽  
Wide Range

AbstractBloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.

scholarly journals Non-Abelian Bloch oscillations in higher-order topological insulators

2020 ◽  
Author(s):  
Marco Di Liberto ◽  
Nathan Goldman ◽  
Giandomenico Palumbo
Keyword(s):  
Topological Insulators ◽  
Berry Phase ◽  
Center Of Mass ◽  
Higher Order ◽  
Topological Properties ◽  
Bloch Oscillations ◽  
Lattice Systems ◽  
Abelian Gauge ◽  
Synchronization Mechanism ◽  
Wide Range

Abstract Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to an external force. Observed in a wide range of synthetic lattice systems, BOs are intrinsically related to the geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift that is synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We identify the origin of this synchronization mechanism through a quantum dance of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties in synthetic matter through the measurement of Berry phases and center-of-mass displacements.

scholarly journals Topological states between inversion symmetric atomic insulators

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Ana Silva ◽  
Jasper van Wezel
Keyword(s):  
Topological Insulators ◽  
Group Representation ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Atomic Lattice ◽  
Space Group ◽  
Topological Materials ◽  
Boundary Correspondence ◽  
Symmetric Band ◽  
Topological States

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary correspondence has been well-tested for strong topological invariants, and forms the basis for all proposed technological applications of topology. Here, we report that a group of weak topological invariants, which depend only on the symmetries of the atomic lattice, also induces a particular type of bulk-boundary correspondence. It predicts the presence or absence of states localised at the interface between two inversion-symmetric band insulators with trivial values for their strong invariants, based on the space group representation of the bands on either side of the junction. We show that this corresponds with symmetry-based classifications of topological materials. The interface modes are protected by the combination of band topology and symmetry of the interface, and may be used for topological transport and signal manipulation in heterojunction-based devices.

scholarly journals Tunable zero modes and quantum interferences in flat-band topological insulators

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 591
Author(s):  
Juan Zurita ◽  
Charles Creffield ◽  
Gloria Platero
Keyword(s):  
Topological Insulators ◽  
Flat Band ◽  
Topological Phase ◽  
Edge States ◽  
One Dimensional ◽  
Zero Modes ◽  
Symmetry Classes ◽  
Boundary Correspondence ◽  
High Degree ◽  
Aharonov Bohm

We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

Keynote

2019 ◽  
Vol 1 (1) ◽  
Author(s):  
Jeanne LIEDTKA
Keyword(s):  
Organizational Performance ◽  
Design Thinking ◽  
Social Systems ◽  
Field Research ◽  
Higher Order ◽  
Lens Design ◽  
Social Sector ◽  
Extensive Field ◽  
Innovative Solutions ◽  
The Impact

The value delivered by design thinking is almost always seen to be improvements in the creativity and usefulness of the solutions produced. This paper takes a broader view of the potential power of design thinking, highlighting its role as a social technology for enhancing the productivity of conversations for change across difference. Examined through this lens, design thinking can be observed to aid diverse sets of stakeholders’ abilities to work together to both produce higher order, more innovative solutions and to implement them more successfully. In this way, it acts as a facilitator of the processes of collectives, by enhancing their ability to learn, align and change together. This paper draws on both the author’s extensive field research on the use of design thinking in social sector organizations, as well as on the literature of complex social systems, to discuss implications for both practitioners and scholars interested in assessing the impact of design thinking on organizational performance.

The Impact of Duplicate Orders on Demand Estimation and Capacity Investment

2005 ◽  
Vol 51 (10) ◽  
pp. 1505-1518 ◽  
Author(s):  
Mor Armony ◽  
Erica L. Plambeck
Keyword(s):  
Demand Estimation ◽  
Capacity Investment ◽  
On Demand ◽  
The Impact

The impact of the COVID-19 pandemic on demand for emergency ambulances in Victoria, Australia

2021 ◽  
pp. 1-8
Author(s):  
Emily Andrew ◽  
Ziad Nehme ◽  
Michael Stephenson ◽  
Tony Walker ◽  
Karen Smith
Keyword(s):  
On Demand ◽  
The Impact

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

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