Is Dynamical matrix and Hamiltonian Derivative Independent of Spatial region

[weixiang]

Hi,
I am calculating the InelasticTransmissionSpectrum for a defective GNR device which requires DynamicalMatrix and HamiltonianDerivative calculated first.
I am wondering if the  Dynamical matrix and Hamiltonian Derivative calculation are independent of the spatial region? i.e. For the same device configuration with different Gate voltage on the metallic region, do I need to calculate the  Dynamical matrix and Hamiltonian Derivative differently?   Or I can use the  Dynamical matrix and Hamiltonian Derivative calculated at one gate voltage for all other gate voltage.
I am studying the transfer characteristics of the device, so I need to calculate the inelastic current of the device at different gate voltage.

Thank you!

[Petr Khomyakov]

Please take a look at this tutorial, https://docs.quantumatk.com/tutorials/inelastic_current_in_si_pn_junction/inelastic_current_in_si_pn_junction.html. There are different options in doing these calculations, e.g., "Using the bulk dynamical matrix and Hamiltonian derivatives" as discussed in the tutorial. 

[weixiang]

Thank you for the reply!
I have read about this tutorial case study. The use of bulk dynamical matrix and bulk Hamiltonian derivatives does help for reducing the calculation time. But it only valid for a homogenous device configuration as I understand.
 The device that I am studying have defects in the scattering region, i.e. it is not homogenous along the c direction. Therefore I will need to calculate the dynamical matrix and Hamiltonian derivatives for the whole device instead of its bulk configuration, in order for calculating the inelasticTransmissionSpectrum.
Therefore my question is, if I want to calculate the inelasticTransmissionSpectrum at different gate voltages (suppose I have a transistor device), do I need to calculate the dynamical matrix and Hamiltonian derivatives at these gate voltages as prior for  the corresponding inelasticTransmissionSpectrum calculation?  Or calculating them at one gate voltage is enough and can be used for all other gate voltages?

i.e. Are dynamical matrix and Hamiltonian derivatives independent of gate voltage?

Based on my understanding of them from the ATK manual, I feel like they are. And I did some toy case study which confirmed my guess.
Can you provide some opinion about this?

Thanks!

[Daniele Stradi]

Hi,

that depends on whether you want to include the effect of the gate or not:

1) if you don't want to include the effect of the gate on the inelastic current, using the phonons and dHdR calcuated at V_GS = 0 V is sufficient.

2) if you want to include the effect of the gate in the calculated inelastic transmission spectrum, then you will have to recalculate the phonons and dHdR for each value of V_GS.

Both approaches are valid, as long as you know which effects are taken into account and which are not in your calculation.

Best,
Daniele

[weixiang]

Thanks for the reply!
I don't understand that is it possible to choose to include or not include the gate effect?
My understanding is since the gate is there, its effect will be accounted for in the calculation. If we do not want to include the gate effect, then we have to delete the gate from the device, but that is not what we want.
In my test cases. I calculated an inelasticTransmissionSpectrum using the dHdR of different value of gate voltage V_G, 0V and 1.5V. They gave me the exactly same result.
I just wonder if it doesn't matter what value of V_G a dHdR is calculated at.