# Atoms to topological electronic materials: A bedtime story for beginners

## TL;DR

This review provides a comprehensive overview of the theoretical foundations and experimental discoveries of various topological electronic states in condensed matter, highlighting recent advances and different material classes.

## Contribution

It offers a unified overview of topological phases, including insulators, semimetals, and crystalline insulators, with insights into recent experimental progress and theoretical understanding.

## Key findings

- Discussion of the transition from 2D QSH to 3D topological insulators
- Overview of topological semimetals like Dirac and Weyl semimetals
- Introduction to topological crystalline insulators and magnetic effects

## Abstract

In this review, We discussed the theoretical foundation and experimental discovery of different topological electronic states of material in condensed matter. At first, we briefly reviewed the conventional electronic states, which have been realized in band theory of solid. Next, the simplest non-trivial insulating phase (Integer Quantum Hall State) and the concept of topological order in condensed matter electronic system have been introduced. In the following sections, we discussed Quantum Spin Hall (QSH) State in two dimensions (2D), and reviewed the theoretical and experimental developments from 2D QSH state to 3D topological insulators (TI). Subsequently, we gave a brief overview on theoretical and experimental understanding on recently discovered topological Dirac semimetals, Weyl semimetals, three-, six- , and eight-fold degenerate semimetals, and Nodal line semimetals. Then, topological crystalline insulator, which can not be considered as a descendent of Quantum Spin Hall or Integer Quantum Hall insulator, has been introduced. Finally, we discussed the presence of magnetism in some topological materials and its consequence on electronic band structure.