https://www.psi.ir/physics_society_iran_1_homeIranian Journal of Physics Research1682-695720120200521Principles of topology in understanding and development of topological
states of matterPrinciples of topology in understanding and development of topological
states of matter122160610.47176/ijpr.20.1.11111FAMKargarianDepartment of physics, Sharif University of Technology, Tehran, IranJournal Article20200408By using concepts of topology in mathematics, quantum mechanics, and their synergetic development during the past few decades, condensed matter physicists have discovered new phases of matter and introduced general frameworks to classify them. The research includes a vast gamut from chemistry of atomic orbitals to material science, promising new applications in the growing technologies. This review article aims to provide a better understanding of these unprecedented electron systems and their underlying topological principles. The article consist of two parts. First, there is a historical review of using topological concepts in condensed matter systems. Then, in the second part, we elaborate on some basics of topology in quantum mechanics and the concept of topological invariants.By using concepts of topology in mathematics, quantum mechanics, and their synergetic development during the past few decades, condensed matter physicists have discovered new phases of matter and introduced general frameworks to classify them. The research includes a vast gamut from chemistry of atomic orbitals to material science, promising new applications in the growing technologies. This review article aims to provide a better understanding of these unprecedented electron systems and their underlying topological principles. The article consist of two parts. First, there is a historical review of using topological concepts in condensed matter systems. Then, in the second part, we elaborate on some basics of topology in quantum mechanics and the concept of topological invariants.http://ijpr.iut.ac.ir/article_1606_8191f922b76a1e10a95325960fbf49fc.pdf