Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

Abstract

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one- and two-dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the Pseudo quantum electrodynamics (PQED). The well known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.

arXiv commentBraz. J. Phys. (2017)

References in corpus (16)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Black phosphorus field-effect transistors
• Quantum Spin Hall Effect in Graphene
• Unpaired Majorana fermions in quantum wires
• Suspended Graphene: a bridge to the Dirac point
• Epitaxial Growth of a Silicene Sheet
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• On the minimal conductivity of graphene
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• The Influence of the Full Vertex and Vacuum Polarization on the Fermion Propagator in QED3
• Quantum Electrodynamics of Particles on a Plane and the Chern-Simons Theory
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index

Cited by in corpus (4)

• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics
• Dynamical Mass Generation in Pseudo Quantum Electrodynamics with Four-Fermion Interactions
• The two-gap BCS model in the large-$N$ approximation within a field-theory approach