Analytic and numeric computation of edge states and conductivity of a Kane-Mele nanoribbon

TL;DR

This paper analytically and numerically investigates the edge states and conductivity in Kane-Mele nanoribbons, demonstrating their topological protection and robustness under various spin-orbit coupling conditions.

Contribution

It provides explicit analytic expressions for edge states in Kane-Mele nanoribbons considering different spin-orbit couplings, enhancing understanding of their topological properties.

Findings

Edge states are topologically protected by P-T symmetry.

Robustness of edge states confirmed through analytic calculations.

Conductance spectra show stability of edge states under various conditions.

Abstract

We compute analytic expressions for the edge states in a zigzag Kane-Mele nanoribbon (KMNR) by solving the eigenvalue equations in presence of intrinsic and Rashba spin-orbit couplings. Owing to the P-T symmetry of the Hamiltonian the edge states are protected by topological invariance and hence are found to be robust. We have done a systematic study for each of the above cases, for example, a pristine graphene, graphene with an intrinsic spin-orbit coupling, graphene with a Rashba spin-orbit coupling, a Kane-Mele nanoribbon and supported our results on the robustness of the edge states by analytic computation of the electronic probability amplitudes, the local density of states (LDOS), band structures and the conductance spectra.