@article{ISI:000378888500003,
 abstract = {Following the centuries old concept of the quantization of flux through
a Gaussian curvature (Euler characteristic) and its successive dispersal
into various condensed matter properties such as quantum Hall effect,
and topological invariants, we can establish a simple and fairly
universal understanding of various modern topological insulators (TIs).
Formation of a periodic lattice (which is a non-trivial Gaussian
curvature) of `cyclotron orbits' with applied magnetic field, or `chiral
orbits' with fictitious `momentum space magnetic field' (Berry
curvature) guarantees its flux quantization, and thus integer quantum
Hall (IQH), and quantum spin-Hall (QSH) insulators, respectively, occur.
The bulk-boundary correspondence associated with all classes of TIs
dictates that some sort of pumping or polarization of a `quantity' at
the boundary must be associated with the flux quantization or
topological invariant in the bulk. Unlike charge or spin accumulations
at the edge for IQH and QSH states, the time-reversal (TR) invariant
Z(2) TI class pumps a mathematical quantity called `TR polarization' to
the surface. This requires that the valence electron's wavefunction
(say, psi(up arrow)(k)) switches to its TR conjugate (psi(dagger)(down
arrow)(-k)) odd number of times in half of the Brillouin zone. These two
universal features can be considered as `targets' to design and predict
various TIs. For example, we demonstrate that when two adjacent atomic
chains or layers are assembled with opposite spin-orbit coupling (SOC),
serving as the TR partner to each other, the system naturally becomes a
Z(2) TI. This review delivers a holistic overview on various concepts,
computational schemes, and engineering principles of TIs.},
 author = {Das, Tanmoy},
 eissn = {0019-4964},
 issn = {0970-4140},
 journal = {JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE},
 month = {APR-JUN},
 number = {2},
 pages = {77-105},
 times-cited = {1},
 title = {A Pedagogic Review on Designing Model Topological Insulators},
 unique-id = {ISI:000378888500003},
 volume = {96},
 year = {2016}
}