scholarly journals Structural buckling induced higher-order topology

2021 ◽  
Author(s):  
Huaqing Huang ◽  
Feng Liu
Keyword(s):  
Mirror Symmetry ◽  
Physical Mechanism ◽  
Higher Order ◽  
Order Topology ◽  
First Principles Calculations ◽  
Rotation Symmetry ◽  
Mechanistic Approach ◽  
Fundamental Understanding ◽  
Plane Displacement ◽  
Topological Crystalline Insulators

ABSTRACT The higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry preserves in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled $\beta $-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.

scholarly journals A fractional corner anomaly reveals higher-order topology

Science ◽  
2020 ◽  
Vol 368 (6495) ◽  
pp. 1114-1118 ◽  
Author(s):  
Christopher W. Peterson ◽  
Tianhe Li ◽  
Wladimir A. Benalcazar ◽  
Taylor L. Hughes ◽  
Gaurav Bahl
Keyword(s):  
Charge Density ◽  
Higher Order ◽  
Order Topology ◽  
Two Dimensional ◽  
Spectral Measurements ◽  
Fractional Charge ◽  
Boundary Correspondence ◽  
Rotationally Symmetric ◽  
Topological Crystalline Insulators ◽  
Gap States

Spectral measurements of boundary-localized topological modes are commonly used to identify topological insulators. For high-order insulators, these modes appear at boundaries of higher codimension, such as the corners of a two-dimensional material. Unfortunately, this spectroscopic approach is only viable if the energies of the topological modes lie within the bulk bandgap, which is not required for many topological crystalline insulators. The key topological feature in these insulators is instead fractional charge density arising from filled bulk bands, but measurements of such charge distributions have not been accessible to date. We experimentally measure boundary-localized fractional charge density in rotationally symmetric two-dimensional metamaterials and find one-fourth and one-third fractionalization. We then introduce a topological indicator that allows for the unambiguous identification of higher-order topology, even without in-gap states, and we demonstrate the associated higher-order bulk-boundary correspondence.

scholarly journals Two-dimensional higher-order topology in monolayer graphdiyne

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Eunwoo Lee ◽  
Rokyeon Kim ◽  
Junyeong Ahn ◽  
Bohm-Jung Yang
Keyword(s):  
Tight Binding ◽  
Three Dimensional ◽  
Higher Order ◽  
Order Topology ◽  
Two Dimensional ◽  
First Principles Calculations ◽  
Charge Accumulation ◽  
Binding Model ◽  
Nodal Lines ◽  
Bulk Band

AbstractBased on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the pz orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from px,y and s orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.

scholarly journals Non-Hermitian route to higher-order topology in an acoustic crystal

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
He Gao ◽  
Haoran Xue ◽  
Zhongming Gu ◽  
Tuo Liu ◽  
Jie Zhu ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Topology ◽  
Topological Phases ◽  
Edge States ◽  
Experimental Realization ◽  
Artificial Materials ◽  
Intrinsic Loss ◽  
Topological Phases Of Matter ◽  
Hierarchical Features ◽  
Nontrivial Topology

AbstractTopological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

scholarly journals Mirror symmetry of higher order aberrations between right and left eyes

2014 ◽  
Vol 73 (1) ◽  
Author(s):  
M. Oberholzer ◽  
W.D.H. Gillan ◽  
A. Rubin
Keyword(s):  
Wave Front ◽  
South African ◽  
Visual Function ◽  
Mirror Symmetry ◽  
Correlation Coefficients ◽  
Higher Order ◽  
Pearson Product Moment Correlation ◽  
Scatter Plots ◽  
The Right ◽  
High Order Aberrations

Introduction: There is evidence that certain measures of visual function show some type of relationship between right and left eyes in the same individual.  Similarly, particular ocular maladies may be related, or be symmetric, in the right and left eyes of the same person. There is also evidence to suggest that certain relationships do not exist between eyes in an individual. For example, diseases such as glaucoma are often asymmetric in their progression in the two eyes of an afflicted individual. Inter-ocular mirror symmetry between right and left eyes, when considering ocular wave-front aberrations (WAs), has been shown to exist by some authors. This study investigates whether mirror symmetry of high order aberrations (HOAs) exists between the right and left eyes in a cohort of South African subjects. Method: Third to 5th order Zernike coefficients (HOAs) were measured on both eyes of 66 subjects (132 eyes) using a Zywave aberrometer. A total of 15 Zernike coefficients for each eye were obtained. Mirror symmetry was investigated using correlation coefficients between the various measurements obtained from each eye. Results: Pearson product-moment correlation coefficients provide evidence that the majority of the 15 Zernike coefficients suggest the presence of mirror symmetry between right and left eyes of the 66 subjects. Examples of individual scatter plots comparing right and left eyes are presented.  Conclusion: The results of this study suggest that mirror symmetry exists in the HOAs obtained from the 132 eyes measured and thus care should be exercised when combining eyes of individuals for analysis. (S Afr Optom 2013 73(1) 39-44)

scholarly journals Three-dimensional superconductors with hybrid higher-order topology

2019 ◽  
Vol 99 (12) ◽  
Author(s):  
Nick Bultinck ◽  
B. Andrei Bernevig ◽  
Michael P. Zaletel
Keyword(s):  
Three Dimensional ◽  
Higher Order ◽  
Order Topology

Predicted Weyl fermions in magnetic GdBi and GdSb

2017 ◽  
Vol 31 (29) ◽  
pp. 1750217 ◽  
Author(s):  
Zhi Li ◽  
Dan-Dan Xu ◽  
Shu-Yu Ning ◽  
Haibin Su ◽  
Toshiaki Iitaka ◽  
...  
Keyword(s):  
First Principles ◽  
Electronic Structures ◽  
Topological Charge ◽  
Local Density ◽  
Chiral Anomaly ◽  
First Principles Calculations ◽  
Rotation Symmetry ◽  
Band Crossing ◽  
Crossing Point ◽  
Weyl Fermions

Motivated by the chiral anomaly steering negative longitudinal magnetoresistance in GdBiPt under external magnetic field, we studied the electronic structures of GdBi with paramagnetism, antiferromagnetism and ferromagnetism by first-principles calculations with modified Becke and Johnson local density approximation plus Hubbard [Formula: see text]. Our calculated results reveal that paramagnetic GdBi is semiconducting, while the antiferromagnetic GdBi is a topological nontrivial compensation metal. We also predict the presence of a pair of Weyl fermions in ferromagnetic GdBi and GdSb. The band crossing along the direction of magnetization is protected by the fourfold rotation symmetry, and the topological charge associating with each [Formula: see text] band crossing point is [Formula: see text].

Warpage of Flip Chip BGA Package

2006 ◽  
Author(s):  
Milena Vujosevic
Keyword(s):  
Flip Chip ◽  
Plate Theory ◽  
Contour Plot ◽  
Thermally Induced ◽  
Ball Grid Arrays ◽  
Fundamental Understanding ◽  
Out Of Plane ◽  
Bga Package ◽  
Plane Displacement ◽  
Analytical Expressions

The work focuses on the thermally induced out of plane displacement of Flip Chip Ball Grid Arrays (FCBGA). Analytical expressions for substrate displacements are derived based on the Plate Theory and Suhir's solution for stresses in tri-material assembly. The validity of the model is established by comparing the analytical solution to the finite element results as well as to the experimental data. The benefits of the model are twofold: 1) it provides a tool for fundamental understanding of the parameters that influence warpage, and 2) has a predictive capability. With respect to 1) an analysis is presented on the nature and degree of influence that different geometric and material parameters have on the FCBGA warpage. With respect to 2) the "Warpage Contour Plot" is proposed as a tool for warpage prediction that can be easily utilized in the early stages of the design process.

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