Contours for the integral of linewidth function. The upper contour (solid line, denoted as ) and lower contour (dotted line, denoted as ) are used for different signs of τ − t. The filled circles (on y axis) and hollow circles represent the Padè poles (μα = 0) and Lorentzian poles, respectively. The arrows indicate the contour integral directions.
(Left) Transient currents for single level system with different W values; (Right) Transient currents for the same system reported in Ref. 34.
Left: Lorentzian fitting curves (dotted line for 4 Lorentzian fitting and dashed line for 9 Lorentzian fitting) and the accurate curve (solid line) for the dimensionless linewidth function (); Right: transmission spectrum of 4-site chain TB system calculated with the 4-Lorentzian fitted self-energy (dotted line) and 9-Lorentzian fitted self-energy (solid line).
Time-dependent current for a 4-site 1D system with two linewidth fitting schemes: 4-Lorentzian (dashed line) and 9-Lorentzian (solid line) fitting. The inset is the magnified figure. The coupling constant: in the leads and device, t 0 = 2 eV; between leads and device h = 0.9t 0. Temperature is 300 K, bias voltage is 0.01 V, 10 Padè points are used.
I-V curve (left), DOS spectrum (middle), and the transient current (right) for a 2-atom device with good contact (upper row) and poor contact (lower row). The bias voltage is 2 V, the coupling constants t in leads and device are 2 eV; and t from leads to device is 1.8 eV (good contact) or 0.4 eV (poor contact).
The linewidth functions with the lead Green's functions obtained from the accurate iteration method (a) or from the Lorentzian fitting (b) scheme. (Λ12 and Λ21correspond the same curves.) The system is a 4-site TB model with the next nearest neighbor interactions. The parameters: t = 2 eV; h2 = 0.4 eV. (c) The transient current of the system under a step bias voltage (2 V) symmetrically applied on two leads at time = 0. The dotted line is the mirror (opposite sign) of the dashed line (right current).
CPU time dependence on the simulation time (left) and site number N (right). In the left figure, the system is a 1D TB chain with 20 sites, 4 Lorentzians and 10 Padè points. And in the right figure, the simulation time is fixed at 0.1 fs, and the time step is 0.002 fs for these two cases.
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