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Ohmic conductance

Figure 7 shows the Ohmic conductance through two dots with a relatively strong inelastic tunnelling coefficient tex2html_wrap_inline1418. In order to analyse the structure of the peaks, assume that the total occupancy of each dot can only fluctuate by one electron. Moreover, assume that only a single level per dot (at the charge degeneracy points) contributes substantially to the transport. Then the global master equation is used to obtain an expression for the Ohmic conductance.
eqnarray368
When the two reservoirs are equally strongly coupled to the dots, i.e. tex2html_wrap_inline1420, then the above expression peaks at tex2html_wrap_inline1422. The peak conductance is given by (using tex2html_wrap_inline1388)
equation382
When the peak height is investigated as a function of the temperature, then it appears that it has a maximum at a value of tex2html_wrap_inline1426 which is given by the solution of the following transcendental equation.
equation390

The solution is plotted in figure 8. When the ratio of the inelastic tunnelling coefficient to the reservoir coupling tex2html_wrap_inline1428 is of order unity or larger, then the temperature at which a particular conductance peak reaches its maximum height is given by roughly half the energy difference tex2html_wrap_inline1430. This maximum height is larger as the energy difference tex2html_wrap_inline1396 gets smaller. This calculation is in good quantitative agreement with the temperature dependence of the conductance curves of figure 7. At higher temperatures the calculation becomes more inaccurate as several levels and more occupation numbers will start to contribute to the transport.

In figure 9 the conductance is shown for a double dot system which is identical to that of figure 7 with the exception that the inelastic tunnelling coefficient is two orders of magnitude smaller. From figure 8 one would expect the peaks to be maximised at a temperature tex2html_wrap_inline1434. The above description of the conductance peaks seems to apply to most of the peaks. However, it is clear that the peak which is situated at tex2html_wrap_inline1436 has an anomalous behaviour. The conductance at this point is much larger than expected. This is due to the fact that one of the lower levels in the first dot very nearly matches up with the dominant level in the second dot, thus strongly enhancing the inter-dot tunnelling rate.

This effect most strongly shows up when the inelastic tunnelling coefficient tex2html_wrap_inline1438 is small compared to the coupling tex2html_wrap_inline1440 to the reservoirs. This is simply due to the fact that the inter-dot tunnelling is the main current-limiting process and will therefore tend to dominate the physics. For large inelastic tunnelling coefficients the current will mainly be determined by the matching of the levels between dot and reservoir. This explains why the afore-mentioned effect is almost imperceptible in figure 7.


next up previous
Next: Current characteristics Up: Tunnelling through two dots Previous: Tunnelling through two dots

Angus MacKinnon - Aonghus Mac Fhionghuin Fri Nov 8 18:10:54 gmt 1996