Efficient quantum transport simulation for bulk graphene heterojunctions

The quantum transport formalism based on tight-binding models is known to be powerful in dealing with a wide range of open physical systems subject to external driving forces but is, at the same time, limited by the memory requirement's increasing with the number of atomic sites in the scattering region. Here we demonstrate how to achieve an accurate simulation of quantum transport feasible for experimentally sized bulk graphene heterojunctions at a strongly reduced computational cost. Without free tuning parameters, we show excellent agreement with a recent experiment on Klein backscattering [A. F. Young and P. Kim, Nature Phys. 5, 222 (2009)].

Figure 1

(a) Schematic of double-gated graphene. (b) Carrier density profile $n\left(x\right)$ (top) and its corresponding local Fermi level $E_F\left(x\right)$ (middle). The extracted potential profile $V\left(x\right)$ (bottom) is given by the difference between the global Fermi level $E_F^0$ and $E_F\left(x\right)$; see text. (c) Reproduced densities $n\left(x\right)$ provided in the Supplementary Material for Ref. 15, with $V_{\text{bg}}=50$ V and $V_{\text{tg}}=-8.9,-7.9,\cdots ,0.1,1.1$ V (curves from bottom to top), and the extracted corresponding $V\left(x\right)$ (curves from top to bottom).

Figure 2

(a) Comparison of the top-gate voltage dependence of the measured conductance $G_{\text{YK}}$[27] and the computed single-mode conductance $g$ at $V_{\text{bg}}=40$ V and $V_{\text{bg}}=60$ V. (b) Conductance map of $G(V_{\text{tg}},V_{\text{bg}})$.

Figure 3

(a) Oscillating part of the computed conductance $G_{\text{osc}}(n_2,B_z)$ (see text for definition) as a function of the carrier density of the locally gated region $n_2\equiv n$ $(x=0)$ and the external magnetic field $B_z$. (b) Comparison of computed $G_{\text{osc}}$ curves [solid (black) curves] at various magnetic field strengths with the experimental data from Ref. 15 [dotted gray (blue) curves].