Topologically Ordered Zigzag Nanoribbon

This is the first graduate level textbook of topologically ordered phases with emphasis on graphene zigzag nanoribbons. It also explains common properties of several other topologically ordered phases as well as the e/2 fractional charge quantization and spin-charge separation of an electron.

Contents:

• Preface

• Basics:

  • Introduction
  • Geometric Berry Phase and Chern Number
  • Basic Topological Properties
  • Polyacetylene
  • Anomalous Velocity, Polarization, Zak Phase, and Chern Number
  • Hartree-Fock Method: Self-consistent Field Method
  • Bosonization

• Topologically Ordered Phases:

  • Superconductivity
  • p-Wave Superconductors and Majorana Zero Modes
  • Integer Quantum Hall Effect
  • Fractional Quantum Hall Effect
  • Edge Excitations of Quantum Hall States*
  • Toric Code for Pedestrians

• Topologically Ordered Zigzag Nanoribbons:

  • Graphene
  • Quantum Anomalous Hall Effect
  • Non-interacting Graphene Nanoribbons: Zero-Energy Soliton States of Zigzag Edges
  • Interacting Graphene Nanoribbon and Mott Insulator
  • Topologically Ordered Interacting Disordered Ribbon: Mott-Anderson insulator and Soliton Fractional Charge
  • Anyons and Spin-Charge Separation in Zigzag Ribbon
  • Topological Order and Entanglement Spectrum of Zigzag Ribbon
  • Matrix Product States and Disordered Anyon Phase*

• Appendices:

  • Envelope Wave Functions
  • Matrix Diagonalization

Readership: Graduate level students and researchers interested in topologically ordered phases with emphasis on graphene zigzag nanoribbons.
Key Features:

• Explains a new topologically ordered phase of graphene zigzag nanoribbons
• Explains common properties of several other topologically ordered phases
• Explains e/2 fractional charge quantization and spin-charge separation of an electron