# Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index

@article{Sticlet2012GeometricalEO, title={Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index}, author={Doru Sticlet and Fr'ed'eric Pi'echon and J N Fuchs and Pavel Kalugin and Pascal Simon}, journal={Physical Review B}, year={2012}, volume={85} }

Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index. This tool allows in principle to conceive 2-bands Hamiltonians with arbitrary Chern numbers. We apply our methodology to gradually construct a quantum anomalous Hall insulator (Chern insulator) which can be tuned through five topological phases indexed by the…

## 59 Citations

Topological quantum transitions in a two-band Chern insulator with n = 2

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2015

A characteristic topological phase transition from n = 2 to n = 0, which is in sharp contrast to the plateau-plateau transition in the integer quantum Hall effect, is observed.

Topological quantum phase transitions of Chern insulators in disk geometry

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2018

A machine learning algorithm is used as an effective way to automatically identify various topological phases and phase diagrams for the Haldane model in disk geometry.

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

- Physics
- 2017

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…

The Valley-Degeneracy-Breaking Induced Arbitrary-Chern Number Insulator on Square Lattice and the Quantum Hall Effect

- Physics
- 2015

The arbitrary-Chern number (ACN) insulator describes the system with Chern number C that may be modulated beyond 0 and ±1. In this work, we take the two-orbit square lattice as an example to study…

INVARIANTS OF TOPOLOGICAL INSULATORS AS GEOMETRIC OBSTRUCTIONS

- Mathematics
- 2021

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i. e. the time-reversal operator squares to −1. We investigate the existence of periodic and…

Generating and detecting topological phases with higher Chern number

- PhysicsPhysical Review A
- 2021

Topological phases with broken time-reversal symmetry and Chern number |C|>=2 are of fundamental interest, but it remains unclear how to engineer the desired topological Hamiltonian within the…

Topological and geometrical aspects of band theory

- PhysicsJournal of Physics: Materials
- 2021

This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of…

Z_2 invariants of topological insulators as geometric obstructions

- Mathematics
- 2014

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and…

Dynamical detection of topological charges

- PhysicsPhysical Review A
- 2019

We propose a generic scheme to characterize topological phases via detecting topological charges by quench dynamics. A topological charge is defined as the chirality of a monopole at Dirac or Weyl…

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