Hi,

Firstly, thanks for creating Kwant - it's so nice to use physics code written by people who understand software-engineering as well as physics :)

I've got a few questions about units and density-of-states in Kwant, please respond if you know anything about any of them; don't feel the need to respond to them all at once.

I'm trying to add self-consistent electrostatics to my Kwant system (using FiPy as a finite-element/volume Poisson-solver). Obviously, I need to calculate the electron-carrier-density of the system by integrating over the Fermi-Dirac occupation, then feed that (via real-space basis functions) to my Poisson solver. I'm not quite sure how to handle the density of states in the context of Kwant:

I assume that just summing over the LDOS (integrating over all space) will give the density of states as a function of energy, D(E). Plotting it seems to produce reasonable bands, but I'm not quite sure about the units, or how it scales with system size. In the system I'm modelling (low-temperature p-donors in silicon), every lattice site adds an electron to the system (the temperatures are low enough that the silicon is frozen-out as a conductor and can just be treated as a background dielectric constant). I should be able to integrate over the density-of-states until the total equals the (known) number of electrons, but the density of states obtained by summing over the LDOS calculated by Kwant does not scale properly with the number of sites in the system; larger systems always need higher Fermi energies, which isn't physical at all.

What am I missing here? Are the units of the LDOS Kwant calculates somehow normalised? How can I get a density-of-states which scales appropriately with the total number of electrons/sites in my system?

The lead unit-cell of my system will need to be solved self-consistently too; how can I calculate the local density of states (and thus, via Fermi-Dirac, the electron-density) of a lead?

Am I correct in assuming that the LDOS produced by Kwant is equivalent to summing over the state-density-weighted scattering-wavefunctions from the modes in all leads (and thus that integrating it over the occupied-energies will produce a sensible total electron-density)?

Finally, and slightly unrelated, do my chosen energy-units need to be accounted-for anywhere in Kwant's Schroedinger-solutions? I'm writing my Hamiltonian terms in meV; will bands, LDOS etc. all naturally scale to make this choice transparent? Similarly, doesÂ effective electron-mass need to be accounted for at all?

Thanks so much for your help,

Daniel R-P