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Ultracold atom research presents many avenues to study problems at the forefront of physics. Due to their unprecedented controllability, these systems are ideally suited to explore new exotic states of matter, which is one of the key driving elements of the condensed matter research. One such topic of considerable importance is topological insulators, materials that are insulating in the interior but conduct along the edges. Quantum Hall and its close cousin Quantum Spin Hall states belong to the family of these exotic states and are the subject of this chapter.
Cold atoms with laser-induced spin-orbit (SO) interactions provide promising platforms to explore novel quantum physics, in particular the exotic topological phases, beyond natural conditions of solids. The past several years have witnessed important
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems,
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key concepts of geome
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest leng
Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being d