Abstract
There are two classes of topological invariants for topological phases of matter. The first is characterized by the elements of the group Z , which consists of all integers. For example, the integer quantum Hall effect is characterized by the integer n, i.e., the filling factor of electrons. The second class is characterized by the elements of the group \(\mathrm {Z}_{2}\), which consists of 0 and 1, or 1 and \(-1\) depending on convention. In a topological insulator with time reversal symmetry, 0 and 1 represent the existence of odd and even numbers of the surface states in three dimensions or even and odd numbered pairs of helical edge states in two dimensions, respectively.
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Shen, SQ. (2017). Topological Invariants. In: Topological Insulators. Springer Series in Solid-State Sciences, vol 187. Springer, Singapore. https://doi.org/10.1007/978-981-10-4606-3_4
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DOI: https://doi.org/10.1007/978-981-10-4606-3_4
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