A first principles scanning tunneling potentiometry study of an opaque graphene grain boundary in the ballistic transport regime

Abstract

We report on a theoretical interpretation of scanning tunneling potentiometry (STP), formulated within the Keldysh non-equilibrium Green's function description of quantum transport. By treating the probe tip as an electron point source/sink, it is shown that this approach provides an intuitive bridge between existing theoretical interpretations of scanning tunneling microscopy and STP. We illustrate this through ballistic transport simulations of the potential drop across an opaque graphene grain boundary, where atomistic features are predicted that might be imaged through high resolution STP measurements. The relationship between the electrochemical potential profile measured and the electrostatic potential drop across such a nanoscale defect is also explored in this model system.

Spatial extent of a Landauer residual-resistivity dipole in graphene quantified by scanning tunnelling potentiometry

“…This Landauer residual-resistivity dipole 12 is caused by the reduced transmission probability of the electrons past a defect. Consequently, the electrochemical potential (ECP) changes locally leading to the observed voltage drop 1,[13][14][15][16] . In the case of one-dimensional defects in a two-dimensional conductor, an interesting parallel can be drawn to electron transport through single molecules 9 , which has been theoretically studied in great detail in the past.…”

“…Up to now highly spatially resolved information of a transition region of the electrochemical potential in the presence of a localized barrier was accessible only by theoretical treatments 1,9,10,[12][13][14][15][16] . Dissecting experimentally, the spatial evolution of the ECP with Angstrom resolution at low temperature opens a new way to non-thermal equilibrium, molecular and coherent quantum transport phenomena.…”

Local temperatures out of equilibrium

“…Referring to the principle of a scanning tunneling potentiometry, a theoretical approach based on the ZCC has been proposed to image the local electrochemical potential distribution of a two-dimensional network [12,[459][460][461]: one weakly couples a voltage probe to a two-dimensional network shown in Figure 42(b), and shifts the µ p (r) at every site such that the current I p (r) between the probe and a site r in the network vanishes. By keeping I p (r) = 0, the local electrochemical potential µ * (r) is determined to be identical µ p (r).…”

“…A strong electron-phonon interaction leads to the electronic dephasing, and the charge transport in the network is in the classical regime when g → ∞ [459]. Therefore, one can tune the network's charge transport properties from the quantum to classical regime by increasing g. The current I p (r) [461], and the current I r,r between the sites r and r of the network [462,463] are both computed using the NEGF formalism. The spatial distributions of µ * (r) and I r,r are shown in Figure 42(c-f) under different g. It has been found that the Ohm's law relates µ * (r) to I r,r , I r,r = σ(r, r )[µ * (r) − µ * (r )], with σ(r, r ) being the electric conductivity between two neighboring sites [84].…”

Electronic Transport Properties of 1D‐Defects in Graphene and Other 2D‐Systems

“…Moreover, STP has received interest from theory in recent years. More recent approaches consider graphene‐specific geometries and defects and extend general treatments that were started over two decades ago …”