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The most promising applications of topological insulators are spintronic devices and dissipationless transistors for quantum computers based on the quantum Hall effect [14] and quantum anomalous Hall effect. [62] In addition, topological insulator materials have also found practical applications in advanced magnetoelectronic and optoelectronic ...
The topological insulators and superconductors are classified here in ten symmetry classes (A,AII,AI,BDI,D,DIII,AII,CII,C,CI) named after Altland–Zirnbauer classification, defined here by the properties of the system with respect to three operators: the time-reversal operator , charge conjugation and chiral symmetry . The symmetry classes are ...
Magnetic topological insulators have proven difficult to create experimentally. In 2023 it was estimated that a magnetic topological insulator might be developed in 15 years' time. [16] A compound made from manganese, bismuth, and tellurium (MnBi2Te4) has been predicted to be a magnetic topological insulator.
Topological order in solid state systems has been studied in condensed matter physics since the discovery of integer quantum Hall effect.But topological matter attracted considerable interest from the physics community after the proposals for possible observation of symmetry-protected topological phases (or the so-called topological insulators) in graphene, [3] and experimental observation of ...
Bismuth telluride is a well-studied topological insulator. Its physical properties have been shown to change at highly reduced thicknesses, when its conducting surface states are exposed and isolated. These thin samples are obtained through either epitaxy or mechanical exfoliation.
This can be another potential application of topological order in electronic devices. Similarly to topological order, topological insulators [48] [49] also have gapless boundary states. The boundary states of topological insulators play a key role in the detection and the application of topological insulators.
In a separate paper, Kane and Mele introduced a topological invariant which characterizes a state as trivial or non-trivial band insulator (regardless if the state exhibits or does not exhibit a quantum spin Hall effect). Further stability studies of the edge liquid through which conduction takes place in the quantum spin Hall state proved ...
The integers that appear in the Hall effect are examples of topological quantum numbers. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase . A striking model of much interest in this context is the Azbel–Harper–Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in ...