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.

Two-dimensional ferroelastic topological insulator with tunable topological edge states in single-layer ZrAsX (X = Br and Cl)

2019 ◽  
Vol 7 (31) ◽  
pp. 9743-9747 ◽  
Author(s):  
Xiangting Hu ◽  
Ning Mao ◽  
Hao Wang ◽  
Chengwang Niu ◽  
Baibiao Huang ◽  
...  
Keyword(s):  
Topological Insulator ◽  
Single Layer ◽  
Two Dimensional ◽  
Edge States

Here we predict theoretically that topological edge states can be significantly tuned by switching the ferroelastic ordering in a two-dimensional (2D) topological insulator.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

scholarly journals Dynamic impurities in two-dimensional topological-insulator edge states

2021 ◽  
Vol 104 (20) ◽  
Author(s):  
Simon Wozny ◽  
Martin Leijnse ◽  
Sigurdur I. Erlingsson
Keyword(s):  
Topological Insulator ◽  
Two Dimensional ◽  
Edge States

scholarly journals CONTINUUM AND LATTICE OVERLAP FOR CHIRAL FERMIONS ON THE TORUS

1996 ◽  
Vol 11 (21) ◽  
pp. 3987-4003 ◽  
Author(s):  
C.D. FOSCO
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Effective Action ◽  
Lattice Spacing ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
The Real ◽  
Theory Result ◽  
Twisted Boundary Conditions ◽  
The Continuum

The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We first evaluate the continuum overlap, which is convergent and well-defined, and yields the correct string theory result for both the real and imaginary parts of the effective action. We then show that the lattice version of the overlap gives the continuum overlap results in the limit where the lattice spacing tends to zero, and that the subleading terms in that limit are irrelevant.

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 Antiferromagnetic topological crystalline insulator and mixed Weyl semimetal in two-dimensional NpAs monolayer

2021 ◽  
Author(s):  
Xiaorong Zou ◽  
Ning Mao ◽  
Bingyang Li ◽  
Wenli Sun ◽  
Baibiao Huang ◽  
...  
Keyword(s):  
Anomalous Hall Effect ◽  
Topological Classification ◽  
Two Dimensional ◽  
Edge States ◽  
Magnetization Direction ◽  
Weyl Semimetal ◽  
Potential Applications ◽  
Topological States ◽  
Quantum Phenomena ◽  
Topological Crystalline Insulator

Abstract Magnetic topological states have attracted significant attentions due to their intriguing quantum phenomena and potential applications in topological spintronic devices. Here, we propose a two-dimensional material NpAs monolayer as a candidate for multiple topological states accompanied with the changes of magnetic structures. Under the antiferromagnetic configuration, the long-awaited topological crystalline insulator (TCI) emerges with a nonzero mirror Chern number $\mathcal{C_M} = 1$ and a giant band gap of 630 meV, and remarkably a pair of gapless edge states can be tailored by rotating the magnetization directions while the TCI phase survives. Moreover, we establish the existence of quantum anomalous Hall effect and nontrivial nodal points under the ferromagnetic configuration, thereby giving rise to the mixed Weyl semimetal after adding the magnetization direction to topological classification. Our findings not only provide an ideal candidate for uncovering exotic topological characters with magnetism but also put forward potential applications in topological spintronics.

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