Tunable edge states and their robustness towards disorder

Abstract

The interest in the properties of edge states in Chern insulators and in Z2 topological insulators has increased rapidly in recent years. We present calculations on how to influence the transport properties of chiral and helical edge states by modifying the edges in the Haldane and in the KaneMele model. The Fermi velocity of the chiral edge states becomes direction dependent as does the spin-dependent Fermi velocity of the helical edge states. Additionally, we explicitly investigate the robustness of edge states against local disorder. The edge states can be reconstructed in the Brillouin zone in the presence of disorder. The influence of the width and of the length of the system is studied as well as the dependence of the edge states on the strength of the disorder.

Two-spin entanglement induced by scattering of backscattering-free chiral electrons in a Chern insulator

“…It comes as no surprise since we expected the chiral edge states to be robust against the impurity scattering due to the topological protection (this was also shown by numerical computations in Ref. [9]). The interesting thing in Eq.…”

“…These states are robust to any kind of disorder and impurity because there are no states possible for backscattering. This is what we expect from topological protection and has been investigated numerically [9]. We are now going to achieve it analytically in the remainder of this section.…”

“…4 shows the band structure of the Haldane model for a ribbon of width N z = 80 which is obtained numerically. This seems to be sufficiently wide to suppress the backscattering of edge modes [9,24]. It is obvious that close to the zero energy, two edge bands composed of edge states cross the Fermi energy.…”

Tunable Signal Velocity in the Integer Quantum Hall Effect of Tailored Graphene

“…We are aware of three-dimensional topological insulators used as thermoelectric elements 6,7 . Recently, it has been proposed that the Fermi velocity of electrons in edge states of two-dimensional Chern insulators on lattices can be tuned by the design of the edges and by changing the potential of the outermost sites of a strip of the lattice 8,9 . It was conjectured that such systems enable one to tune the signal velocity of a charge signal propagating along the edges by controlling external parameters such as gate voltages.…”

Topological phases of higher Chern numbers in Kitaev–Heisenberg ferromagnet with further-neighbor interactions

“…Another TMI phase with C=±1 is obtained later in magnon dispersion of two-band honeycomb ferromagnet with DM interaction 13,14 . For the antiferromagnetic (AFM) case, Heisenberg Shastry-Sutherland model with DM interaction exhibits two distinct TMI phases with specific values of C=−2, 0, 2 and C=−1, 0, 1, obtained for three bosonic triplon dispersion bands under longitudinal and cross magnetic fields, respectively 15,16 .…”