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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?
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.
