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Summary of Topological insulators
Topological insulators (TI) are materials that behave as insulators in their interiors or bulks while permitting the movement of charges (metallic) on their surface. Inside these materials, as conventional insulators, the energy band structures are shown large energy gap, as shown as Fig. 1 (a) red and blue bands, and Fermi level is falling between conduction and valence bands. At room temperature, T is about 300 K, the gap is so wide that electrons energy level cannot leap from Fermi level to conduction levels. However, this situation only happens for the topological insulator’s interior. For surface parts, their band structures are much different and behaves as metallic non-gap band structure, described by the green line in Fig. 1 (a). Meanwhile, the surface bandstructure is linear, ~ and has Z2 symmetry. Topological insulators Graphene
Due to topological insulator’s linear structure, it is many similarities to grapheme, a real two-dimension material whose bandstructure is also shown linear relationship at low energy. Especially, the grapheme armchair bandsrtructure is extremely similar to topological insulators, but the only different is the energy gap is at semi-conductor range. Although the their bandstructures are similar to each other, their electrical motions shows different. In armchair grapheme ribbons, electrons move at centre part while for topological insulators, electrons only transport on surface, which is easily recall the phenomena of Hall effects.
In several years ago, integral quantum Hall effect and fractional quantum Hall effect were discovered and explained in theory, which are the important quantum phenomena we could observe quantum phenomena in normal. For quantum Hall effect, boundary is a crucial factor for creating quantum Hall effect. In conventional quantum Hall effect, the electrons move along the surface, shown in Fig. 2 (a). However, for quantum spin Hall effect, the electrons have
Topological insulators (TI) are materials that behave as insulators in their interiors or bulks while permitting the movement of charges (metallic) on their surface. Inside these materials, as conventional insulators, the energy band structures are shown large energy gap, as shown as Fig. 1 (a) red and blue bands, and Fermi level is falling between conduction and valence bands. At room temperature, T is about 300 K, the gap is so wide that electrons energy level cannot leap from Fermi level to conduction levels. However, this situation only happens for the topological insulator’s interior. For surface parts, their band structures are much different and behaves as metallic non-gap band structure, described by the green line in Fig. 1 (a). Meanwhile, the surface bandstructure is linear, ~ and has Z2 symmetry. Topological insulators Graphene
Due to topological insulator’s linear structure, it is many similarities to grapheme, a real two-dimension material whose bandstructure is also shown linear relationship at low energy. Especially, the grapheme armchair bandsrtructure is extremely similar to topological insulators, but the only different is the energy gap is at semi-conductor range. Although the their bandstructures are similar to each other, their electrical motions shows different. In armchair grapheme ribbons, electrons move at centre part while for topological insulators, electrons only transport on surface, which is easily recall the phenomena of Hall effects.
In several years ago, integral quantum Hall effect and fractional quantum Hall effect were discovered and explained in theory, which are the important quantum phenomena we could observe quantum phenomena in normal. For quantum Hall effect, boundary is a crucial factor for creating quantum Hall effect. In conventional quantum Hall effect, the electrons move along the surface, shown in Fig. 2 (a). However, for quantum spin Hall effect, the electrons have