The scaling laws of edge vs. bulk interlayer conduction in mesoscale twisted graphitic interfaces

Abstract

The unusual electronic properties of edges in graphene-based systems originate from the pseudospinorial character of their electronic wavefunctions associated with their non-trivial topological structure. This is manifested by the appearance of pronounced zero-energy electronic states localized at the material zigzag edges that are expected to have a significant contribution to the interlayer transport in such systems. In this work, we utilize a unique experimental setup and electronic transport calculations to quantitatively distinguish between edge and bulk transport, showing that their relative contribution strongly depends on the angular stacking configuration and interlayer potential. Furthermore, we find that, despite of the strong localization of edge state around the circumference of the contact, edge transport in incommensurate interfaces can dominate up to contact diameters of the order of 2 μm, even in the presence of edge disorder. The intricate interplay between edge and bulk transport contributions revealed in the present study may have profound consequences on practical applications of nanoscale twisted graphene-based electronics.

Edge State Quantum Interference in Twisted Graphitic Interfaces

“…This circuit includes the constant serial resistances of the bulk graphite mesa structures, tip-sample contact, and spreading resistance of the graphite substrate, whereas the sliding interface is represented by two lateral shift dependent parallel resistors corresponding to the charge flow through the area and circumference of the sliding contact (see Section S2, Supporting Information). [22] Electronic Transport and Registry Index Calculations: To evaluate the interlayer electronic transport behavior of the graphitic interface, circular bilayer graphene junction models with a diameter of 10 nm and various twist angles and lateral shifts were constructed. It is noted that no chemical edge passivation was employed as the TB model does not account for 𝜎 orbitals, which are much lower in energy than 𝜋 orbitals.…”

“…The interfaces considered herein consist of single crystalline planar graphitic layers, as is evident by their observed superlubric characteristics. [6,10,22,31] Hence, the loss of interference signal beyond an overlap range of a few nanometers cannot be rationalized by the room temperature in-plane electronic mean free path, which can reach hundreds of nanometers in high quality graphitic structures. [33,34] Notably, a similar range of interference effects in graphitic interfaces was recently reported in a break-junction study manipulating bilayer graphene at room temperature, where the measured current periodicity of ≈6.9 Å was interpreted as a beating pattern of two lower periodicities (2.46 and 3.69 Å) that were theoretically predicted for an AB stacked graphene bilayer.…”

“…To demonstrate this, we use the transmittance probability curves, calculated to construct the transmittance-weighted Gaussians at various shift positions, to evaluate the Landauer vertical current through the bilayer flake (more details regarding the calculations are provided in Section S4, Supporting Information). [6,22,36] Figure 3a presents the interlayer current versus the relative lateral interlayer displacement of the 10°twisted bilayer system, calculated at a bias voltage of 0.8 V. This value is chosen to account for the entire low energy edge contribution to the transmittance probability (see insets of Figure 2 and Section S4, Supporting Information). To study the edge-to-edge transport properties, we focus on large lateral displacements that constitute the final 3 nanometers before full removal of the upper flake from its lower counterpart.…”

“…Graphitic systems with bare (or chemically passivated) zigzag edges exhibit strongly confined electronic edge states with a corresponding sharp zero-energy peak in their density of states (DOS). [16][17][18][19][20][21] Due to the unique nature of their wave function, these edge states manifest exotic properties, such as topologically protected subgap conductivity in bilayer graphene, [19,22] electric-field tunable magnetism, [17,23] and valley-dependent transport. [24,25] Such edges, however, may also pose challenges for practical applications, including edge leakage that is expected to limit the functionality of graphene-based logic devices, [22,26,27] and topologically protected metallic edge states that decrease the effectiveness of topological insulators.…”

“…[16][17][18][19][20][21] Due to the unique nature of their wave function, these edge states manifest exotic properties, such as topologically protected subgap conductivity in bilayer graphene, [19,22] electric-field tunable magnetism, [17,23] and valley-dependent transport. [24,25] Such edges, however, may also pose challenges for practical applications, including edge leakage that is expected to limit the functionality of graphene-based logic devices, [22,26,27] and topologically protected metallic edge states that decrease the effectiveness of topological insulators. [19,28] To overcome these challenges, a better understanding of the interplay between edge and bulk transport properties and of edge-based interlayer transport in confined bilayer interfaces is required.…”