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First principles calculation of ac conductance for Al-BDT-Al and Al-C n -Al systems
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Figures

Image of FIG. 1.

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FIG. 1.

The schematic structure of Al-C6-Al system. An atomic wire with six carbon atoms (gray) is sandwiched between two semi-infinite atomic Al electrodes (pink). The Al electrodes extended to ±∞ along (100) direction.

Image of FIG. 2.

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FIG. 2.

The LL component of emittance calculated by both the global formula and the local formula for the Al-Cn-Al system, n = 4, 5, ⋅⋅⋅, 9. The simulation box includes the carbon chain and 16 layers of buffering aluminum. In the figure, the ‘global emittance’ which means the emittance calculated by the global formula is plotted in blue, while the ‘local emittance,’ the emittance calculated by the local formula is plotted in green.

Image of FIG. 3.

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FIG. 3.

The schematic structure of Al-BDT-Al system. The leads are two semi-infinite atomic Al electrodes (pink) along (100) direction. In between is a benzenedithiol (BDT) including two sulfur atoms (yellow), four hydrogen atoms (white) and six carbon atoms (carbon). The 2D-structure BDT lies in the (110) plane of the aluminum.

Image of FIG. 4.

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FIG. 4.

The imaginary part of the LL component of the dynamic conductance Im[G LL (ω)] calculated by either the global or the local formula (red dots), comparing with −ωE LL (blue lines) from 0 to 50THz. The linear behavior of the imaginary part of the dynamic conductance even holds up to 50THz, and the slope is none other than the negative of its corresponding emittance.

Image of FIG. 5.

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FIG. 5.

The real part of the LL component of the dynamic conductance Re[G LL (ω)] (a.u.) calculated by either the global or the local formula. The frequency domain ranges from 0 to 50THz. Both of the curves show a binomial behavior, with a vanishing slope near zero frequency. varies faster than as the frequency increases.

Image of FIG. 6.

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FIG. 6.

The LL component of emittance calculated by both the global formula (blue dots) and the local formula (green triangles) for the Al-BDT-Al system, against the shifted Fermi level from -1eV to 1eV. The inset is the global total density of states as a function of the shift of the Fermi level, which behaves more similarly to the global result than to the local result.

Image of FIG. 7.

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FIG. 7.

The transmission function T LR for the Al-BDT-Al system calculated at different energy. There are five lines representing different numbers of buffer layers that are included in the scattering region, and these lines collapse to a single curve.

Image of FIG. 8.

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FIG. 8.

The LL component of emittance calculated by both the global formula (blue dots) and the local formula (green triangles) for the Al-BDT-Al system, against the number of buffer layers included in simulation box. It seems the one calculated by the global formula shows the generally linear behavior while the one calculated by the local formula shows the oscillatory behavior.

Image of FIG. 9.

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FIG. 9.

1D double-delta-potential-well system, the LL component of the ac emittance calculated against the length of the leads out of the potential well, with both sides having equal length, by the global formula (blue) and the local formula (red) respectively. The figure shows that the emittance calculated by either method has a generally linear with periodically oscillatory property. The period is represented by the circle dots.

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/content/aip/journal/adva/1/4/10.1063/1.3673566
2011-12-15
2014-04-18

Abstract

We perform first-principles calculation to investigate the dynamic conductance of atomic wires of the benzenedithiol (BDT) as well as carbon chains with different length in contact with two Al(100) electrodes (Al-C n -Al). Our calculation is based on the combination of the non-equilibrium Green's function and the density functional theory. For ac conductance, there are two theories that ensures the current conservation: (1). the global formula which is a phenomenological theory that partitions the total displacement current into each leads so that the current is conserved.(2). the local formula which is a microscopic theory that includes Coulomb interaction explicitly so that the current is conserved automatically. In this work, we use the local formula to calculate the dynamic conductance, especially the emittance. We give a detailed comparison and analysis for the results obtained from two theories. Our numerical results show that the global formula overestimates the emittance by two orders of magnitude. We also obtain an inequality showing that the emittance from global formula is greater than that from local formula for real atomic structures. For Al-C n -Al structures, the oscillatory behavior as the number of carbon chain N varies from even to odd remains unchanged when local formula is used. However, the prediction of local formula gives rise to opposite response when N is odd (inductive-like) as compared with that of global formula. Therefore, one should use the local formula for an accurate description of ac transport in nanoscale structures. In addition, the ‘size effect’ of the ac emittance is analyzed and can be understood by the kinetic inductance. Since numerical calculation using the global formula can be performed in orbital space while the local formula can only be used in real space, our numerical results indicate that the calculation using the local formula is extremely computational demanding.

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Scitation: First principles calculation of ac conductance for Al-BDT-Al and Al-Cn-Al systems
http://aip.metastore.ingenta.com/content/aip/journal/adva/1/4/10.1063/1.3673566
10.1063/1.3673566
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