  The spin-orbit coupling field, an atomic magnetic field inside a Kramer's
system, or discrete symmetries can create a topological torus in the Brillouin
Zone and provide protected edge or surface states, which can contain
relativistic fermions, namely, Dirac and Weyl Fermions. The topology-protected
helical edge or surface states and the bulk electronic energy band define
different quantum or topological phases of matters, offering an excellent
prospect for some unique device applications. Device applications of the
quantum materials rely primarily on understanding the topological properties,
their mutual conversion processes under different external stimuli, and the
physical system for achieving the phase conversion. There have been tremendous
efforts in finding new topological materials with exotic topological phases.
However, the application of the topological properties in devices is still
limited due to the slow progress in developing the physical structures for
controlling the topological phase conversions. Such control systems often
require extreme tuning conditions or the fabrication of complex multi-layered
topological structures. This review article highlights the details of the
topological phases, their conversion processes, along with their potential
physical systems, and the prospective application fields. A general overview of
the critical factors for topological phases and the materials properties are
further discussed to provide the necessary background for the following
sections.
