Contents
What is a Chern insulator?
A Chern insulator is 2-dimensional insulator with broken time-reversal symmetry. (If you have for example a 2-dimensional insulator with time-reversal symmetry it can exhibit a Quantum Spin Hall phase). The topological invariant of such a system is called the Chern number and this gives the number of edge states.
What is band topology?
Band structure topology was found to become non-trivial in materials with large spin–orbit coupling if the conduction and valence bands are inverted, as explained and shown in Box 1. At these points, the energy disperses linearly with momentum, and the spin and momentum are locked to each other.
How can we identify a topological insulator?
A topological insulator is a material that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material.
Which is correct for a Chern insulator in 2D?
In the same time, ρ x x = σ x x = 0 (which may seems counterintuitive, but noticing the tensor nature of ρ and σ ). The quantization of σ x y is very accurate, it is the second best way to measure the fine structure constant, and it is inert to interactions and impurities. For a charge neutral particle in 2D: with H 0 = p ^ 2 2 m.
How to calculate the Dirac cone in Chern insulator?
From the dispersions also the analysis we can see that Dirac cone appears at k x, k y = 0, Δ = − 2; k x, k y = 0, ± π, Δ = 0; k x, k y = ± π, ± π, Δ = 2 .
Which is the symmetry gauge for Chern insulator?
We can also use symmetry gauge : A x = − B y 2, A y = B x 2, though it is more cumbersome, the physics is quite insightful. More on symmetry gauge, see [1]. Electrons at the edge can move along the edge in one direction, this edge states gives quantized Hall conductivity.
When do you use one Eigen base for Chern insulator?
In principle, for the whole Bloch sphere, we must at least use two different bases which are well defined. If for the whole band, we have h z < 0 or h z > 0 A, then, we can use one set of eigen base, which gives us zero Chern number.