Conductance between Two Scanning-Tunneling-Microscopy Probes in Carbon Nanotubes

Abstract

The conductance image between two probes of scanning tunneling microscopy (STM) is calculated in an armchair carbon nanotube within a tight-binding model and a realistic model for STM probes. A Kekulé-type pattern usually appears due to interference of states at K and K 0 points except in special cases.

Interface Landau levels in graphene monolayer-bilayer junctions

“…When the wave amplitudes at the K and K ′ points coexist in a single eigenstate, LDOS has a Kekulé pattern due to the interference between the factors e iK•R and e iK ′ •R . 55 In the present case, this is expected to appear in the armchair boundary which mixes the K and K ′ valleys, while absent in ZZ1 or ZZ2, where every eigenstate is a single-valley state. We also define the spatially averaged LDOS for site A as…”

Kekulé pattern on conductance images between two STM probes

“…We have demonstrated in armchair nanotubes that the Kekulé pattern disappears for special cases and original periodicity recovered in the conductance images, due to the lack of interference between K and K' states [10]. In the special case, the electron is injected into a single traveling state at one of Fermi points, if a wave is injected from three carbon atoms in the specific ratio shown in our previous work for arbitrary chirality, because the injected wavefunction is orthogonal to that of traveling waves at the other Fermi point.…”

“…1(c). This model hopping integral with parameters λ = 0.085 nm, α −1 ≈ 0.13 nm, and Δ = 0.5 nm has been introduced in previous works [8,10]. The STM tip is modeled by a chain of s-like atoms with nearest neighbor hopping integral −t and the Fermi energy being fixed at the center of the one-dimensional band.…”

“…Electron transmission has been studied between two STM tips as leads which contact the nanotube via single carbon atoms [9]. Recently, we have shown a Kekulé type pattern in two-probe STM images in armchair carbon nanotubes due to interference of states at K and K' point except in special cases [10]. In this paper, we calculate the conductance in a zigzag nanotube and discuss the robustness of the Kekulé pattern for arbitrary chirality.…”

Graphene edges; localized edge state and electron wave interference

“…To understand the three-fold symmetrical fine structure observed in the honeycomb superlattice, it is necessary to calculate the spatial distribution of the current between the graphene and the STM tip [13,22]. The calculated current distribution is shown in Fig.7(d).…”