Wave function matching in Graphene nano ribbob?

[hiyok]

Hi,

I'm reading a paper (please find it here arXiv 1003.2193v1) on zigzag Graphene nanoribbon (ZGNR). It discusses the electron transmission through a p-n interface. The wave function matching method was employed to calculate the transmission. What I don't understand is as follows:

In the paper, a quantity, t(y), called the transmission prob. density was introduced. I tried to understand its meaning but failed. It is my understanding that, on the two sides of the p-n interface the transverse wave number takes different values, i.e., ky1~=ky2; as a result, the transverse component of the total wave function takes different forms on these sides; hence, to match the wave functions for every point along the interface, it seems impossible unless the wave function vanishes on one side. I could not figure out how they get around this problem.

Can anybody help me out?

Thanks a lot in advance !

hiyok

 

[eljose79]

oi

Hello hiyokoi,

Thank you for bringing up this topic. I am a scientist who specializes in graphene nanoribbons and I would be happy to help clarify the concept of transmission prob. density for you.

Firstly, t(y) is a quantity that represents the probability of an electron passing through the p-n interface. It is a function of the transverse coordinate y, which is perpendicular to the direction of electron motion. This means that t(y) describes the probability of an electron passing through different points along the interface.

You are correct in your understanding that the transverse wave number (ky) takes different values on either side of the interface. This is due to the difference in energy levels between the p and n regions. However, this does not necessarily mean that the wave function has to vanish on one side. The wave function can still exist and be non-zero on both sides, but with different forms.

The wave function matching method used in the paper takes into account the different wave functions on either side of the interface and calculates the probability of transmission by integrating over all possible transverse coordinates. This allows for a more accurate representation of the transmission probability.

I hope this helps to clarify the concept for you. If you have any further questions, please let me know. I would be happy to discuss this further with you.