Is the transmission/conductance matrix at zero temperature calculated at E = 0?
Hi All, I have a general question about kwant package. In the kwant paper (https://downloads.kwant-project.org/doc/kwant-paper.pdf), I presume the conductance matrix given in Eq. (10) is for zero temperature calculation. I also presume that the conductance matrix G should be dependent on energy E, i.e., G(E). I am wondering if the output from the transmission matrix t(E) (used to calculate G(E)) of kwant is calculated at E = 0, i.e., what we have is actually t(E=0) and G(E=0). Although this looks like that the Fermi level is fixed at E = 0, the actual Fermi level (e.g., relative to charge neutral point) can be changed via the onsite potential. Please correct me if I have the wrong understanding. Thanks! -- Jiuning Hu
Jiuning Hu wrote:
I am wondering if the output from the transmission matrix t(E) (used to calculate G(E)) of kwant is calculated at E = 0, i.e., what we have is actually t(E=0) and G(E=0). Although this looks like that the Fermi level is fixed at E = 0, the actual Fermi level (e.g., relative to charge neutral point) can be changed via the onsite potential.
This has been discussed before, try searching for “temperature” in the history of this mailing list [1]. You then should be able to find relevant threads like [2] or [3]. In a nutshell, Kwant’s transmission() gives the conductance at zero temperature in the regime where the left and right chemical potentials differ only infinitesimally. From this, it is possible to calculate an (approximate) finite-temperature, finite-voltage conductance through numerical integration. This is explained in the literature, for example in S. Datta’s book that we mention in the tutorial [4]. [1] https://kwant-project.org/community [2] https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00208.html [3] https://www.mail-archive.com/kwant-discuss@kwant-project.org/msg00909.html [4] https://kwant-project.org/doc/1/tutorial/introduction#quantum-transport
participants (2)
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Christoph Groth
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Jiuning Hu