# Wave function matching in Graphene nano ribbob?

• hiyok
Your Name]In summary, the conversation discusses a paper on zigzag Graphene nanoribbon and the use of wave function matching method to calculate electron transmission through a p-n interface. The concept of transmission prob. density, t(y), is introduced and clarified as a function of the probability of an electron passing through different points along the interface. The difference in transverse wave numbers on either side of the interface does not necessarily mean the wave function has to vanish on one side. The wave function matching method integrates over all possible transverse coordinates to accurately calculate the transmission probability.
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

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.

## 1. What is wave function matching in Graphene nano ribbons?

Wave function matching is a method used to study the electronic properties of Graphene nano ribbons. It involves matching the wave functions of the electrons in the ribbon to those of the surrounding materials, such as the substrate or other layers of Graphene.

## 2. How is wave function matching used in Graphene nano ribbons?

Wave function matching is used to understand the behavior of electrons in Graphene nano ribbons, which can have unique properties due to their one-dimensional structure. This method helps to predict the electronic properties of the ribbons and how they interact with other materials.

## 3. What are the challenges of performing wave function matching in Graphene nano ribbons?

One of the main challenges is accurately measuring the wave functions of the electrons in the ribbons. This requires precise experimental techniques and can be difficult due to the small size of the ribbons. Another challenge is understanding the effects of defects or impurities on the wave functions.

## 4. How does wave function matching contribute to the development of Graphene-based devices?

By understanding the electronic properties of Graphene nano ribbons through wave function matching, scientists can design and optimize devices that utilize these unique properties. This can lead to advancements in areas such as electronics, energy storage, and sensors.

## 5. Are there any limitations to using wave function matching in Graphene nano ribbons?

While wave function matching is a valuable tool, it is not the only method used to study Graphene nano ribbons. Other techniques, such as density functional theory, may be more suitable for certain research questions. Additionally, wave function matching may not be applicable to all types of Graphene nano ribbons, as their properties can vary depending on factors such as their size and edge shape.

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