Topological Insulators and Topological Superconductors

כריכה קדמית
Princeton University Press, 2013 - 247 עמודים

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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תוכן

1 Introduction
1
2 Berry Phase
6
3 Hall Conductance and Chern Numbers
15
4 TimeReversal Symmetry
33
5 Magnetic Field on the Square Lattice
41
The BulkEdge Correspondence
60
7 Graphene
70
8 Simple Models for the Chern Insulator
91
12 TimeReversal Topological Insulators with Inversion Symmetry
158
13 Quantum Hall Effect and Chern Insulators in Higher Dimensions
164
14 Dimensional Reduction of 4D Chern Insulators to 3D TimeReversal Insulators
177
15 Experimental Consequences of the Z2 Topological Invariant
186
16 Topological Superconductors in One and Two Dimensions
193
17 TimeReversalInvariant Topological Superconductors by Taylor L Hughes
214
18 Superconductivity and Magnetism in Proximity to Topological Insulator Surfaces
226
References
241

9 TimeReversalInvariant Topological Insulators
109
10 Z2 Invariants
123
11 Crossings in Different Dimensions
147

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מידע על המחבר (2013)

B. Andrei Bernevig is the Eugene and Mary Wigner Assistant Professor of Theoretical Physics at Princeton University. Taylor L. Hughes is an assistant professor in the condensed matter theory group at the University of Illinois, Urbana-Champaign.

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