Interlayer Conductance in the Armchair Nanotube - Zigzag Graphene Ribbon Parallel Contact: Theoretical Proposal of Detection of Wavefunction Growing from the Edge to the Center in the Graphene Ribbon

Abstract

Sublattices A and B are opposite in the decay direction of the edge state of the zigzag graphene ribbon (ZGR). Detecting exponential growth from the zigzag edges to the ZGR center remains challenging. The tight-binding model calculations in this letter reveal that interlayer conductance manifests this growth in parallel contact with the armchair nanotube.The transfer integrals of oblique interlayer bonds are comparable to those of vertical interlayer bonds. However, the phase of the ZGR wave function strongly suppresses the contribution of oblique bonds, allowing the selective detection of the growing component.Since their discovery, 1) carbon nanotubes (NT) have attracted significant attention owing to their electronic and mechanical properties, accompanied by high aspect ratios. 2, 3) These characteristics are suitable as tips of atomic force microscopy, [4][5][6] Kelvin force microscopy, 7,8) electrical probes, 9,10) and scanning tunneling microscopy (STM); [11][12][13] the nanometer-sized radius guarantees a high spatial resolution. Using the chiral index (n 1 , n 2 ), the NTs were metallic when n 1 − n 2 was a multiple of three (mod(n 1 − n 2 , 3)=0) and semiconducting otherwise (mod(n 1 − n 2 , 3)=1,2). 2, 3) Progress continues in single-chirality separation. [14][15][16] An important target of the NT tip measurement is the edge states of the zigzag graphene ribbon (ZGR), 17) which has been evaluated from various aspects: spin Seebeck effects, 18) magnetism, [19][20][21][22] spin transport, 23,24) valleytronics, [25][26][27][28] and zero-conductance dips. 29,30) STM signals of the edge states appear at the zigzag edge [31][32][33][34][35] but are absent at the armchair edge. 36,37) In a standard STM setup, the NT tip is perpendicular to the ZGR surface, whereas the NT π orbitals are orthogonal to those of the ZGR. Contrarily, theoretical calculations show that the π-orbital mixing governs the I-V characteristics 38,39) and charge distribution 40) in the parallel contacted graphene-NT junctions. Experimental studies on this parallel setup have been reported regarding the conductance [41][42][43] and charge transfer. 44) We can slide an NT 1/13