Fundamental Concepts of Topological Insulators

Abstract

The notion of topological insulators was first introduced to explain the concept of Quantum Hall Effect. The Quantum Hall State (QHS) does not disrupt symmetries but showed fundamental properties (like quantized Hall conductivity, the number of conducting edge-mode) that are not affected by smooth changes in different material parameters and are not subject to change if the system goes through the quantum phase-transition. A topological insulator (TI) just like an ordinary insulator has a large energy gap that is separating the highest-filled electronic band from the lowest empty-band. However, a topological insulator's surface must have gapless electronic states which are protected by the time-reversal symmetry (TRS). Like QHS, having distinctive gapless chiral edge-states on the surface or the edge-states of the topological insulators (TIs) are topologically shielded and reveal conducting states having properties that are unlike any other known 1D and 2D electronic systems. Strong spin-orbit interactions under the conservation of time-reversal symmetry (TRS) are the driving force behind these substances. Moreover, Topological insulators (TIs) were revealed experimentally for the first time in 2007 by the consideration of the condensed-matter physics community which become fully focused on a novel category of materials. The 3D topological insulator's new qualities could result in some fascinating applications because they are very common semiconductors and their topological properties can withstand high temperatures. Hence, Topological insulators (TIs) are those materials that are electrically inert in bulk but can carry out electricity due to their topologically protected electronic edge-state as well as surface states.