Datta’s ballistic transport formalism vs KWANT
Hi, I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as Ttot=T(E)M(E) Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression? Best, Ran �
Hi Ran,
I tried to compare KWANT’s results for transmission with Datta’s ballistic transport formalism where total transmission is written as
Ttot=T(E)M(E)
Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl. Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse direction. When I compared KWANT's results with Datta’s expression, for the system given in “quantum_wire_revisited.py”, I found different results (please see the attached figure where I tried to put every relevant thing in the calculation). Since the reflectance is zero for that system and so transmission is 1 for each mode, shouldn’t it give the same results with Datta’s transmission expression?
Nice question! Looking at your results it seems that the energies at which new modes open is shifted with respect to Datta's result. I believe that this is simply due to the fact that your discretization is not fine enough. Datta's result is valid in the continuum limit, whereas the Kwant simulation (in the case presented) uses a finitedifference discretization to render the problem discrete. If you decrease the 'a' parameter, you should see the discrepancy between the two result decrease. Happy Kwanting, Joe
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Joseph Weston

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