Based on the scanned probe microscopes, the local current properties in a nanodevice can be clearly exposed. However, it is still a big challenge to experimentally observe the atomic scale varying current pattern. A numerical-aided method is therefore very important for getting the local current information in a microsystem. In this study, we show the nonequilibrium Green’s function method to calculate the transport properties of two-terminal devices. For applying this method to larger systems, a recursive procedure is present in detail. The correctness of this method is confirmed by calculating the transport properties of a clean 2DEG. The conductance steps in such a sample match the corresponding band structure very well. Then, we calculate the current patterns in quantum point contact under a saddle-point potential. Several current jets can be clearly spotted which correspond to transport channels in quantum point contact. Meanwhile, the interference streaks are spotted near the edges of the device due to the reflection of electrons at the edges.

We study the effect of edge methylene on transport properties in graphene nanoribbons (GNRs) using the recursive green's function method. The concentration of methylene (w) is defined as the substituted probability of edge dangling bonds. Due to the antiresonance of quasilocalized states, some conductance dips are found when single absorption (w = 0.005 in this work) sits on the edge. Localization analyses of wave functions also confirm this. With w increasing, the conductance is suppressed significantly and transport gap develops near E = 0.0 eV. Conductance suppression is induced by antiresonances between edge scattering centers. Meanwhile, these scattering centers prevent the formation of edge extended states which play an important role in the electronic transport at low energy and consequently the transport gaps develop. We found that a stable gap can be obtained at w = 0.3 and it becomes small as the width of the GNRs increases. An interesting oscillation at transport gaps for armchair edge GNRs is observed and it relates to the geometric symmetry of sample. The physical mechanisms behind the novel phenomenon are still unclear.

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We study theoretically the giant magnetoresistance (GMR) effect of 2-dimensional electron system (2DES) by the transfer matrix method. To produce the inhomogeneous magnetic field, two magnetic strips are pre-deposited on the surface of 2DES. In our work, we fix the magnetization M in one magnetic strip and adjust the tilting angle θ of magnetization in the other. The result shows that the electronic transmission and conductance vary significantly for different θ. The minimum conductance can be obtained at θ = π which corresponds to the magnetization anti-parallel alignment. The magnetoresistance ratio (MRR) calculation also indicates we would get the maximum in that case. Furthermore, we consider the magnetization M dependence of MRR in this work. When M increases, MRR peaks get higher and broader and more numbers of peaks can be observed. These results offer an alternative to get a tunable GMR device which can be controlled by adjusting the magnetization M and the magnetized angle θ.