# Are there tools to calculate the electrical conductivity of large (>1000 atom) nanostructures?

Are there any free to use tools which can be used to calculate the electrical conductivity of nanostructured materials. The systems that I am interested in consist of several thousand atoms, and running DFT calculations is not an option due to the lack of computational resources.

Are there any tools or theoretical methods which I can use to calculate the electrical conductivity of these 2D and 1D materials?

• Can you be more specific what kind of methods are you looking for? MC, QMC and finite element analysis labels seems unrelevant to your question.
– Greg
Jan 3, 2022 at 15:22
• @Greg I have seen articles where MC, QMC and finite element analysis have been used to estimate electrical conductivity in nanowires and carbon nanotube composites. My specific requirement is to reduce the computational power required to estimate the electrical conductivity of these structures since it is not achievable using DFT methods (based on available resources).
– PBH
Jan 4, 2022 at 1:08
• I doubt you would have resources for a QMC calulation when you do not have for DFT, therefore it is misleading.
– Greg
Jan 4, 2022 at 2:00
• Any idea of a less resource intensive method?
– PBH
Jan 4, 2022 at 2:17
• @PBH You could ask a question about the RAM usage on the main site and might get a bigger audience that way. Jan 11, 2022 at 0:23

There are a lot of detailed considerations when computing electronic transport, but in general the answer is "yes", provided you can calculate (or estimate) a model Hamiltonian. For example, a DFT calculation may be used to compute the parameters for a model tight-binding Hamiltonian (e.g. using a local basis set, or Wannier90) which can then be used for much larger transport calculations.

Many studies use the (linearised) Boltzmann Transport Equations (BTE), for example as implemented in BoltzTraP2 or BoltzWann. A more sophisticated approach is to solve the quantum transport problem directly from the tight-binding Hamiltonian, for example the Quantum Kite software of my colleague Aires Ferreira and coworkers.

Although a few thousand atoms would usually require a small computer cluster for DFT (depending on the basis set), the tight-binding Hamiltonian can be solved much more quickly. A common limiting factor is computer RAM, and you may need to invest in more RAM to perform large calculations.

These methods typically give you the electrical conductivity per unit of time; the actual conductivity will depend on how long it takes for conduction electrons to relax back down to the (non-conducting) valence state, which is called the "relaxation time". The main factor affecting this is usually the electron-phonon interaction, but calculating that is computationally intensive. The common method is to use DFT, but this will not be practical for your situation; even if you did have the computational resources for a DFT calculation, an $$N$$-atom system has $$3N$$ phonons, and you need one DFT calculation for each phonon!

It may be possible to estimate the relaxation time, for example by calculating it for a prototypical bulk system (which has far fewer atoms), or by using acoustic deformation potential theory. Even if you do not know the relaxation time, you can still investigate differences in conductivity per unit time, and if you assume that the relaxation time is similar across the various structures then this trend should be reflected in the actual conductivity.

Yes. Take a look at SIESTA: the "Spanish Initiative for Electronic Simulations with Thousands of Atoms". Love that name.

It is much more efficient than the plane-wave DFT codes for this type of calculation, since it considers wavefunctions using a tight-binding basis and exploits matrix sparsity.

I have not used it, but another student in my group has. It still took a while to converge the wavefunctions and atomic positions for a massive supercell, but it is worth a cursory glance. Especially if you are simply inputting the atomic positions, converging the wavefunctions, and running very simple landauer transport.

Depending on your supercell/atomic complexity, you might alternatively be able to construct a simple tight-binding model and build up green's functions and electrodes to model transport. Take a look at Supriyo Datta's course on nanohub.

Out of curiosity, what is the system you are trying to consider? I understand if you don't want to answer.

• I am looking at nanoparticle based structures such as the ones studied here.
– PBH
Sep 24, 2022 at 7:07
• Okay. So in general yes, though this might be kind of hard. SIESTA / transiesta might be the way to go for some simple test systems, but you should see how those scale. You should also ask if you want to consider an infinite chain of nanoparticles, or a finite chain of nanoparticles with solid electrodes at either end. The latter would be more doable with a home-built NEGF transport code or Kwant if you are okay with a simple model. How realistic do you want this? transiesta can model IV curves and temperature, though it would be inherently computationally intensive. Sep 28, 2022 at 22:19