Questions about conductance of nanowire

[chp]

Recently I have performed calculations for conductance of Au nanowire ( see the following script and output ), however, the obtained value (1.368 G0) is much smaller than other experimental and theoretical results ( about 3 G0 ). This situation is more notable in other thicker nanowires. I have tried to adjust some parameters such as basis set size, mesh cut-off, exchange-correlation function, and k-points, no obvious change has been observed. What is the matter ?

I appreciate any reply.  Thanks a lot !

[Nordland]

There is a related post on the subject that might give you inspiration:
Current Calculations in wires

From the transmission spectrum it appears that something is not correct in the calculation, and I think that if we nail what that problem is, then you will get better agreement.

[serhan]

Hi,

Some points that have taken my interest are:

1. Mesh cutoff is 150 Ry. It may be small. You can try increasing.
2. You may not need Monkhorst Pack of (8,8,x), since it is a 1-D wire. You can utilize (1,1,x) I think. When you increase mesh cutoff, you'll need to save some time from other parts of the code 
3. Is there a reason to select temperature as 1000 K?
4. Most importantly, is this a 1-D nanowire? A tube, or sth else? Sorry, but the coordinates does not seem to be as a 1-D wire. Where have you generated these coordinate, in VNL? Or did you optimize the geometry?

Cheers,
Serhan

[Anders Blom]

As Serhan says, it is perfectly sufficient to use 1x1xN k-points (there is no dispersion in X and Y, so adding k-points there will just make the calculation run slower, nothing else). Same thing goes for the transmission spectrum, you only need 1x1 point. This will save you a lot of time

1000 K might be a nice idea to get it to converge, you can then try to initialize the calculation from the converged result, using a lower temperature to "anneal" the results.

Geometry looks ok at first glance (in VNL!). It's a triangular wire.

The transmission spectrum is very feature-rich, I would have expected a bit smoother curve at least around the Fermi level.

However, the main problem most likely lies in the choice of contour integration parameters. The integral lower bound, 200 Ry, is way, way, way too large. It will not give accurate results. 1000 points on the contour will, well, be slooooooooooooooooow (although you probably need it for 200 Ry lower bound!).

If 5-7 Ry and 50-70 points are not sufficient to reach convergence, look into other techniques for improving the convergence (we'll help you!).

With all the changes above, your script should run 10-100 times faster!

Also see the new gold nanowire tutorial at http://quantumwise.com/publications/tutorials/!

[nori]

Dear chp,

The electric structure you got is apparently unphysical because there are excessively 33 electrons in central region and the transmission is not ballistic.

I calculated SCF and the transmission with some different parameters you had and the reasonable result was obtained.
Please check attached.

[Anders Blom]

Nice work Nori.

I also noticed the large q, and I'm quite convinced the reason was the contour integral parameters, where you have used more suitable values.

For a perfect 1D system like this you would always expect "ballistic" transport as you note, i.e. plateaus of integer transmission. Any deviation from that picture indicates something is not optimal in the calculation (e.g. bad parameters or too short electrodes or too little screening).

[Nordland]

I think that there is a need for adding more layers in the electrodes in order to get a perfect transmission spectrum, however the transmission spectrum is good enough at the fermi and hence the conductance at zero bias the correct one. As I read nori transmission spectrum It would lead to a perfect 3 G0 conductance....

[chp]

Thanks everyone !

Indeed, the problem lies in the choice of contour integration parameters. In my initial calculations for the Au nanowire, the default value (i.e., circle_points = 30, integral_lower_bound = 3*Rydberg) results in charge missing, which converge to an incorrect state with no electrons in the central region. 

As I change to the above parameters (circle_points = 1000, integral_lower_bound = 200*Rydberg), the test calculations for 1D Au line give a correct result. But it does not work correctly for the triangular wire.     What is the reason? How can we obtain siutable contour integration prarmeters with efficiency and reasonableness for a special system?

I also perform some test calculations for conductance of a thicker Au nanowire with nori’s parameters. In general, the reasonable result can be obtained. However, when I increase the length of the central region, the obtained conductance show a little difference (i.e., 5.92 G0 vs 5.87 G0 with longer central region, see the attached log file for details). Since the 1D model represents the same nanowire, I want to know what causes this difference and how we can improve it.

[Anders Blom]

The value 200 Ry for the lower bound just makes the circle too large, and you end up integrating a lot of small values with a lot of points on a very long contour. If you have very many points (and you do...) it should give the same, but I think you just lose too much accuracy in the process.

Unfortunately there is no simple way to know a priori which contour parameters to use. If the defaults do not work, you need to increase the value a bit, and try again, etc. But if you still cannot converge at 5-7 Ry, with 50 points, then the problem in reality lies somewhere else. For instance, k-point sampling and temperature are usually very important to control. And, not least important, you must ensure that the electrodes are not too short; see the discussion in this post and the ones following below it.

I think the electrodes are the reason you are getting deviating values for different electrode lengths.