This graduate-level textbook is the first pedagogical synthesis
of the field of topological insulators and superconductors, one of
the most exciting areas of research in condensed matter physics.
Presenting the latest developments, while providing all the
calculations necessary for a self-contained and complete
description of the discipline, it is ideal for graduate students
and researchers preparing to work in this area, and it will be an
essential reference both within and outside the classroom.
The book begins with simple concepts such as Berry phases,
Dirac fermions, Hall conductance and its link to topology, and the
Hofstadter problem of lattice electrons in a magnetic field. It
moves on to explain topological phases of matter such as Chern
insulators, two- and three-dimensional topological insulators, and
Majorana p-wave wires. Additionally, the book covers zero modes on
vortices in topological superconductors, time-reversal topological
superconductors, and topological responses/field theory and
topological indices. The book also analyzes recent topics in
condensed matter theory and concludes by surveying active subfields
of research such as insulators with point-group symmetries and the
stability of topological semimetals. Problems at the end of each
chapter offer opportunities to test knowledge and engage with
frontier research issues. "Topological Insulators and Topological
Superconductors" will provide graduate students and researchers
with the physical understanding and mathematical tools needed to
embark on research in this rapidly evolving field.
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