Detection of Edge Transport in Bernal Stacked Trilayer Graphene

In previous chapters, we have studied the electrical and thermal conductance of the topological edge modes of integer and fractional quantum Hall (QH) phases, which emerges by applying a large perpendicular magnetic field to the plane of the “graphene” layer. These edge modes’ topological protection makes them unique and prone to back-scattering. As a result, these quantum Hall edge modes become very important from the fundamental physics point of view and also become the host of exotic quasi-particles like Majorana fermion and para-fermion. However, in addition to these QH edge modes, edge modes also exist at zero magnetic fields at the boundary of several two-dimensional materials. These are also important for many possible applications and should be explored in detail. Many exciting phenomena, including electric-field-tunable magnetism and valley-dependent transport, have been predicted theoretically based on the characteristics of edge states in graphene layers. Although significant efforts have been made to understand the edge transport in single and bilayer graphene, a similar study is lacking in trilayer graphene, which has recently re-emerged as an exciting two-dimensional material, offering many interesting electronic phases. In this chapter, we report the detection of the edge states in bernal stacked trilayer graphene. We report the observation of the large non-local signal in dual-gated bernal stacked (ABA) trilayer graphene devices. The measured non-local signal is much larger than the classical ohmic contribution. We further did the scaling analysis of the non-local resistance and found that it scales linearly with the local resistance, suggesting the presence of edge-mediated non-local charge transport. The scaling exponent of unity was over the range of displacement fields and the temperature range. The experimental findings are attributed to the presence of the nontrivial valley Hall state, which emerges on applying the displacement fields predicted long back by Morimoto et al. (2013). In this phase, the energy gap at the Dirac points is filled by the chiral edge modes, which propagate in opposite directions between the two valleys.