Topological Quantum Matter (eBook)

A Field Theoretical Perspective

Thomas Klein Kvorning (Autor)

eBook Download: PDF

2018 | 1st ed. 2018
X, 81 Seiten
Springer International Publishing (Verlag)
978-3-319-96764-6 (ISBN)

Infos

This book offers a theoretical description of topological matter in terms of effective field theories, and in particular topological field theories, focusing on two main topics: topological superconductors and topological insulators.

Even though there is vast literature on these subjects, the book fills an important gap by providing a concise introduction to both topological order and symmetry-protected phases using a modern mathematical language, and developing the theoretical concepts by highlighting the physics and the physical properties of the systems. Further, it discusses in detail the topological interactions for topologically ordered matter, and the response to smooth external fields for symmetry protected matter.

The book also covers more specialized topics that cannot be found elsewhere. Specifically, the response of superconductors to geometry, including the newly discovered geo-Meissner effect; and a correction to the usual Meissner effect, only present in the topologically interesting chiral superconductors.

 

Inhalt

Supervisor’s Foreword 6
Acknowledgements 8
Contents 10
1 Introduction 12
1.1 Entanglement 13
1.2 Topological Interactions 14
1.3 Topological Response 16
1.4 Outline 20
1.5 Notations and Conventions for Topological Matter 20
References 22
2 Anyons and Topological Order 23
2.1 Bosons, Fermions and Abelian Anyons 23
2.1.1 A Single Particle on An Annulus 24
2.1.2 Indistinguishable Particles and the Braid Group 26
2.1.3 Mediating Topological Interactions with a Gauge Boson 30
2.2 Topological Order in Two Dimensions 32
2.2.1 Torus Degeneracy 37
2.3 Abelian Chern-Simons Theory 39
References 42
3 Response Theory and Symmetry Protected Topological Phases 44
3.1 The Quantization of the Hall Conductance 45
3.2 U(1) Response Theory 49
3.2.1 Functional Bosonization 52
3.3 The Wen-Zee Term and Chiral Superconductors 55
3.3.1 Chiral Superconductors 56
References 58
4 Topological Geometric Response and Topological Order of Super Conductors 60
4.1 A Superconducting Bosonic Model 61
4.2 Adding Fermions to Get Topological Order 64
4.2.1 The Chiral p-Wave SC 65
4.3 Non-Abelian Statistics in the Adiabatic Limit 70
4.4 The Majorino Conundrum 74
References 76
A Conventions and Notation Concerning Differential Forms and U(1) Connections 77
A.1 Differential Forms 77
A.2 Normalization 78
Appendix B Definitions 79
Appendix C Vector Bundles and Chern Numbers in Quantum Mechanics 85
C.1 The Berry Connection 85
C.2 The Berry Field Strength 86
C.3 Chern Numbers and Chern-Simons Invariants 88
Reference 89

Produkt-Details

• Erscheint lt. Verlag: 12.8.2018
• Reihe/Serie: Springer Theses
• Reihe/Serie: Springer Theses
• Zusatzinfo: X, 81 p. 24 illus., 6 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Schlagworte: Anyon physics • Chiral Superconductors • quantum field theory • Symmetry Protected Topological Order • The Geo-Meissner Effect • Topological Field Theory • Topological Matter • Topological Order
• ISBN-10: 3-319-96764-9 / 3319967649
• ISBN-13: 978-3-319-96764-6 / 9783319967646