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The spin-orbit coupling field, an atomic magnetic field inside a Kramer'ssystem, or discrete symmetries can create a topological torus in the BrillouinZone and provide protected edge or surface states, which can containrelativistic fermions, namely, Dirac and Weyl Fermions. The topology-protectedhelical edge or surface states and the bulk electronic energy band definedifferent quantum or topological phases of matters, offering an excellentprospect for some unique device applications. Device applications of thequantum materials rely primarily on understanding the topological properties,their mutual conversion processes under different external stimuli, and thephysical system for achieving the phase conversion. There have been tremendousefforts in finding new topological materials with exotic topological phases.However, the application of the topological properties in devices is stilllimited due to the slow progress in developing the physical structures forcontrolling the topological phase conversions. Such control systems oftenrequire extreme tuning conditions or the fabrication of complex multi-layeredtopological structures. This review article highlights the details of thetopological phases, their conversion processes, along with their potentialphysical systems, and the prospective application fields. A general overview ofthe critical factors for topological phases and the materials properties arefurther discussed to provide the necessary background for the followingsections.

Topological Quantum Matter to Topological Phase Conversion: Fundamentals, Materials, Physical Systems for Phase Conversions, and Device Applications