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The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, and that does not require the application of a large magnetic field.
In 1988, it was proposed that there was a quantum Hall effect without Landau levels. [3] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents. [4]
Later sets of theoretical models for the 2D topological insulator (also known as the quantum spin Hall insulators) were proposed by Charles L. Kane and Eugene J. Mele in 2005, [15] and also by B. Andrei Bernevig and Shoucheng Zhang in 2006. [16]
Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 [1] and have been studied more intensely since early 2010. [2] [3] They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial ...
Note that Haldane phases of even-integer-spin chain do not have SPT order. A more well known example of SPT order is the topological insulator of non-interacting fermions, a SPT phase protected by U(1) and time reversal symmetry. On the other hand, fractional quantum Hall states are not SPT states. They are states with (intrinsic) topological ...
Zhang was one of the founders of the field of topological insulators. He made one of the first theoretical proposals of the quantum spin Hall effect. Soon after the initial theoretical proposal, his group theoretically predicted the first realistic quantum spin Hall material in HgTe quantum wells. [10]
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 ...
The massless fermions lead to various quantum Hall effects, magnetoelectric effects in topological materials, and ultra high carrier mobility. [10] [11] Dirac cones were observed in 2008-2009, using angle-resolved photoemission spectroscopy (ARPES) on the potassium-graphite intercalation compound KC 8 [12] and on several bismuth-based alloys ...