# Study of edge states and conductivity in spin-orbit coupled bilayer graphene

## TL;DR

This paper systematically investigates the conductance and edge states in spin-orbit coupled bilayer graphene nanoribbons, revealing how various spin-orbit interactions influence topological phases and spintronic potential.

## Contribution

It analytically derives edge state conditions and explores the effects of spin-orbit couplings on quantum spin Hall phases in bilayer graphene.

## Key findings

- Even-numbered ribbons have a finite energy gap at Dirac points.
- Spin-orbit couplings can destroy the quantum spin Hall phase.
- Bilayer graphene shows enhanced spintronic properties over monolayer.

## Abstract

We present an elaborate and systematic study of the conductance properties of a zigzag bilayer graphene nanoribbon modeled by a Kane-Mele (KM) Hamiltonian. The interplay of the Rashba and the intrinsic spin-orbit couplings with the edge states, electronic band structures, charge and spin transport are explored in details. We have analytically derived the conditions for the edge states for a bilayer KM nanoribbon and show how these modes decay for lattice sites inside the bulk. It is particularly interesting to note that for a finite-size ribbon an even number of zigzag ribbon hosts a finite energy gap at the Dirac points, while the odd ones do not. This asymmetry is present both in presence and absence of a bias voltage that may exist between the layers. The interlayer Rashba spin-orbit coupling, along with the intralayer intrinsic spin-orbit and intralayer Rashba spin-orbit couplings seem to destroy the quantum spin Hall (QSH) phase where the QSH phase is identified by the presence of a conductance plateau (of magnitude 4e/h) in the vicinity of zero Fermi energy. The plateau is sensitive to the values of the spin-orbit coupling parameters. Further, the spin polarized conductance data reveal that a bilayer KM ribbon is found to be more efficient for spintronic applications compared to a monolayer graphene. Finally, a quick check with experiments is done via computing the effective mass of electrons.