Figure 4 : Resistor network analysis of the void defects.

From: Electrical resistance of individual defects at a topological insulator surface

Figure 4

(a) Schematic of a current carrying two-dimensional conductor. The conductor can be approximated by dividing it into virtual parts (squares) where each square corresponds to the inverse of the defect density in size and has one defect (orange circle) residing in it. (b) Simplified resistor network model of one virtual part of the conductor indicated in a. An incoming current j is initially transmitted by the three parallel resistors left from the defect. However, at the position of the defect the current has to flow via smaller number of parallel resistors (two) before it can flow again via three resistors after it passed the defect. The resulting potential distribution shows a higher local voltage drop ΔV located at the position of the defect. The result is a voltage offset ΔVdefect compared with the voltage drop across a defect-free conductor, which results in a voltage drop corresponding to the dotted line. (c) Full resistor network model of a void in a conductor. Size: 200 × 200 pixel, with each pixel corresponding to a nodal point of the resistor network. (d) Background-subtracted potential distribution resulting from c upon current flow. (e) Section of the transport dipole along the solid black line in d. The position of the void is indicated by the shaded area. The persistent voltage drop ΔVdefect after the current passed the defect is indicated by the dashed lines. (f) Sections perpendicular to the current along the lines labelled as 1, 2 and 3 in d and with the corresponding line styles. The amplitude of the lateral potential distribution decays with increasing distance to the defect. The constant black dashed line corresponds to the average value of each section and equals to ΔVdefect/2.