Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching

We have discovered that in gated bilayer graphene, gap states with topological origin may be present despite of having stacking boundaries, which introduces atom-size defects that cause mixing between sublattices. Furthermore, the number of gap states depends on the sign of the gate voltage applied, a fact of interest for the design of future electronic devices.

These results are obtained in a long-term cooperation of researchers between Poland and Spain, which is focusing

on graphene nanostructures. Recent experiments [L. Ju et al., Nature, 2015, 520, 650] confirm the existence of topologically protected gapless states at domain wallsin gated graphene with Bernal stacking. We are considering the study of topologically protected gapless states for different types of possible domain walls bet we en bilayer graphene with the AB and BA stackings.

We begin investigating the case when one of the graphene layers deforms defectless as a corrugation [M. Pelc et. al., Phys. Rev. B,

2015, 92, 085433]. We found gapless states that are topologically protected and have valley-polarization, so that they give rise to conductance along the domain walls. Besides we identify other localized states in the corrugation originating from electron confinement. The interplay between these two ty

pes of states is small enough, so that topological states are still closing the gap. Notice that current theoretical models predict the appearance of topologically protected states at domain walls, which preserve the sublattice order.

In this work we show that the appearance of gapless states in stacking domain walls can be much more common in bilayer graphene.

They are also shown in unexpected geometries, for instance, at grain boundaries with atomic-scale topological defects. We focus on bilayer graphene in which one of the layers contains a line of octagon—double-pentagon defects. We demonstrate that even with pentagonal defects mixing graphene sublattices, gap states are preserved. We however observe that both topological and defect-originated states strongly hybridize, in a game mainly determined

by the gate voltage polarization. Thus, unlike previous predictions, the number of gap states changes by inverting the gate voltage sign, which is originating an asymmetric conductance along the grain boundary under gate reversal. We expect that this effect, linked to defect states, should be detectable in transport measurements and could be exploited in electrical switches.

Bilayer graphene having a boundary with a change of stacking from AB to BA built by a defect line in the top layer. (a) Structural model. Atoms are coloured in cyan and blue following the A and B sublattices, respectively. The nodes in grey color are mixing the two sublattices. Local density of states as a function of energy and wavevector along the defect line, for gate voltages either (c) positive V=0.3 eV or (d) negative V=-0.3 eV. Note that due to gate voltage polarization, the number of gap states is assymetric.