Abstract: Low-dimensional topological insulators are the frontier of condensed matter physics in semiconductor power devices and solid materials. Physicists combine the theory of condensed matter physics and topology to analyse and explore the solid state structure and properties of electron spin in low-dimensional mercury telluride (HgTe). The quantum spin Hall effect and the topological quantum doublet are two significant physical theories of low-dimensional topological insulators,which play a fundamental role in predicting and discovering the material configuration and energy band structure of topological insulators. A strong field physics is used to prove them experimently. In conclusion,the low-dimensional topological insulators are the frontier theory and material application of condensed matter physics,which is incorporated with the theory of mathematical topology and thus represent the aesthetics of condensed matter.

Key words: condensed matter physics, topological insulators, quantum Hall effect, electron spin, semiconductor devices