Introducing Topological Insulators: Mind the Time Reversal

2015 ◽  
pp. 1-12
Keyword(s):  
Time Reversal ◽  
Topological Insulators

scholarly journals Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kyungchan Lee ◽  
Gunnar F. Lange ◽  
Lin-Lin Wang ◽  
Brinda Kuthanazhi ◽  
Thaís V. Trevisan ◽  
...  
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Dirac Point ◽  
Saddle Points ◽  
Surface States ◽  
Van Hove Singularity ◽  
Space Group ◽  
Topological Materials ◽  
Topological Surface ◽  
Optimal Space

AbstractTime reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected strong TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficult to match the experimental success of strong TIs. We here report on the discovery of a WTI state in RhBi2 that belongs to the optimal space group P$$\bar{1}$$ 1 ¯ , which is the only space group where symmetry indicated eigenvalues enumerate all possible invariants due to absence of additional constraining crystalline symmetries. Our ARPES, DFT calculations, and effective model reveal topological surface states with saddle points that are located in the vicinity of a Dirac point resulting in a van Hove singularity (VHS) along the (100) direction close to the Fermi energy (EF). Due to the combination of exotic features, this material offers great potential as a material platform for novel quantum effects.

scholarly journals Chiral Anomaly, Topological Field Theory, and Novel States of Matter

2018 ◽  
Vol 30 (06) ◽  
pp. 1840007 ◽  
Author(s):  
Jürg Fröhlich
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Time Reversal ◽  
Topological Insulators ◽  
Large Scale ◽  
Quantum Hall ◽  
Chiral Anomaly ◽  
Open Problems ◽  
Spin Currents ◽  
Spin Orbit Interactions

Starting with a description of the motivation underlying the analysis presented in this paper and a brief survey of the chiral anomaly, I proceed to review some basic elements of the theory of the quantum Hall effect in 2D incompressible electron gases in an external magnetic field, (“Hall insulators”). I discuss the origin and role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly or spontaneously broken time reversal, i.e. in Hall insulators and “Chern insulators”. The topological Chern–Simons action yielding the large-scale response equations for the 2D bulk of such states of matter is displayed. A classification of Hall insulators featuring quasi-particles with abelian braid statistics is sketched. Subsequently, the chiral edge spin currents encountered in some time-reversal invariant 2D topological insulators with spin-orbit interactions and the bulk response equations of such materials are described. A short digression into the theory of 3D topological insulators, including “axionic insulators”, follows next. To conclude, some open problems are described and a problem in cosmology related to axionic insulators is mentioned. As far as the quantum Hall effect and the spin currents in time-reversal invariant 2D topological insulators are concerned, this review is based on extensive work my collaborators and I carried out in the early 1990’s. Dedicated to the memory of Ludvig Dmitrievich Faddeev — a great scientist who will be remembered

scholarly journals Quantitative robustness analysis of topological edge modes in C6 and valley-Hall metamaterial waveguides

Nanophotonics ◽  
2019 ◽  
Vol 8 (8) ◽  
pp. 1433-1441 ◽  
Author(s):  
Bakhtiyar Orazbayev ◽  
Romain Fleury
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Statistical Study ◽  
Robustness Analysis ◽  
Ensemble Average ◽  
Edge States ◽  
Edge Mode ◽  
Metamaterial Waveguide ◽  
Recent Advances ◽  
First Time

AbstractRecent advances in designing time-reversal-invariant photonic topological insulators have been extended down to the deep subwavelength scale, by employing synthetic photonic matter made of dense periodic arrangements of subwavelength resonant scatterers. Interestingly, such topological metamaterial crystals support edge states that are localized in subwavelength volumes at topological boundaries, providing a unique way to design subwavelength waveguides based on engineering the topology of bulk metamaterial insulators. While the existence of these edge modes is guaranteed by topology, their robustness to backscattering is often incomplete, as time-reversed photonic modes can always be coupled to each other by virtue of reciprocity. Unlike electronic spins which are protected by Kramers theorem, photonic spins are mostly protected by weaker symmetries like crystal symmetries or valley conservation. In this paper, we quantitatively studied the robustness of subwavelength edge modes originating from two frequently used topological designs, namely metamaterial spin-Hall (SP) effect based on C6 symmetry, and metamaterial valley-Hall (VH) insulators based on valley preservation. For the first time, robustness is evaluated for position and frequency disorder and for all possible interface types, by performing ensemble average of the edge mode transmission through many random realizations of disorder. In contrast to our results in the previous study on the chiral metamaterial waveguide, the statistical study presented here demonstrates the importance of the specific interface on the robustness of these edge modes and the superior robustness of the VH edge stated in both position and frequency disorder, provided one works with a zigzag interface.

scholarly journals Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

2020 ◽  
Vol 23 (3) ◽  
Author(s):  
Eli Fonseca ◽  
Jacob Shapiro ◽  
Ahmed Sheta ◽  
Angela Wang ◽  
Kohtaro Yamakawa
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Fredholm Theory ◽  
Two Dimensional

scholarly journals The bulk-edge correspondence in three simple cases

2019 ◽  
Vol 32 (03) ◽  
pp. 2030003 ◽  
Author(s):  
Jacob Shapiro
Keyword(s):  
Time Reversal ◽  
Topological Insulators ◽  
Two Dimensions ◽  
Symmetry Classes ◽  
New Formula

We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle without the overhead of the more general proofs which are available. We also give a new formula for the [Formula: see text]-index of our time-reversal invariant systems inspired by Moore and Balents.

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