accuracy of current

[nazi]

Dear experts,

The calculated current in my system under an applied bias voltage is in order of 1E-16.

I am sure about different convergence parameters like cutoff energy and k-points.

As the exact order of current is important for me, can I trust such a small current value?

I really appreciate your response in advance.

Best regards,
Nazi

[Petr Khomyakov]

I think it also depends on the units of the current you have not specified, as well as on the particular system of study.

[nazi]

Dear Petr,

Thank you for your response. The unit of the current is Amper, my system is 2D phosphorene.

Thank you.

[Petr Khomyakov]

Also, what is the bias voltage value corresponding to this current? In fact, if you did IV calculations for pristine, perfect phosphorene, the non-zero bias calculations do not make much sense because there are no scatters in the central region.  The only physically relevant quantity in this case is the Transmission Spectrum at zero bias voltage and related conductance of the perfect system that can be computed from the transmission spectrum in the linear response regime.

[nazi]

The bias voltage is ~ 1V.

My transmission spectrum under bias and in equilibrium (zero bias) is completely different.
Also in the transport book of Datta it comes that linear response is valid just when the bias voltage is smaller than the thermal energy and band broadening. These conditions were not satisfied in nanostructures. Am I right?

[Petr Khomyakov]

The transmission spectrum should be different for zero and non-zero bias voltage cases, but my point is that non-zero bias calculations for a perfect, ballistic system do not have much physical sense, because for a given bias voltage, the potential profile across the central region depends on the central region length, which is totally arbitrary for the system with no defects, interfaces or whatever scatters. This issue is discussed in the book by Datta.   

[nazi]

Dear Petr,
I am a little confused 

the potential profile across the central region depends on the central region length,
Yes, the resistance and conductance depend on the length, what is wrong with this?

Also as the system is 2D, the transport regime is not ballistic in the terms of quantized conductance and transmission spectrum.

[Petr Khomyakov]

- I would advise reading the Datta's book about applying bias voltage in the ballistic regime.

- It is ballistic if the system has no scatters. It does not matter 3D, 2D or even 1D. The transport properties are then described with Sharvin conductance (resistance), which is the conductance of a perfect material, given by the number of conducting channels at the Fermi energy of the system.

[nazi]

Dear Petr,

Thank you very much for your guides. Just one question to be sure that I got your meaning correctly.

The calculated currents using the transmission in zero bias and finite bias are different. You believe that for such a system the calculated current using the linear response (zero bias) is correct and the other one does not make sense. Am I right?

Additionally, if  I turn to my first question, if we sure about the cutoff parameters, can we trust the small current values in the order of 1E-16A?

[Petr Khomyakov]

The calculated currents using the transmission in zero bias and finite bias are different. You believe that for such a system the calculated current using the linear response (zero bias) is correct and the other one does not make sense. Am I right?

Additionally, if  I turn to my first question, if we sure about the cutoff parameters, can we trust the small current values in the order of 1E-16A?

At zero bias, there is no current. Only conductance (i.e., the derivative of the current wrt bias voltage, dI/dV) is to be calculated for the zero bias case, and it does not require explicit calculation of the current. 

Regarding the 2nd question, you have, in general, to check convergence of whatever physical quantity with respect to the computational settings, e.g., cutoff parameters. If converged, you should not see much of a change when making the settings stricter. But as I said your bias calculations do not make sense.