2D Electrons in Out-of-Plane Magnetic Field: DOS & Collision Broadening

In summary, the conversation discusses the derivation of the density of states (DOS) for 2D electrons in an out of plane magnetic field, with a focus on collision broadening and the resulting oscillatory nature of the DOS. The suggested method involves adding a component to the vector potential and including the Zeeman energy term. In the limit of an ideal 2D electron gas, the parallel field primarily affects the spin split nature of the DOS. While the speaker does not have a specific link, they suggest looking in any book that covers the Quantum Hall effect for more information.
  • #1
jpr0
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Does anyone have a link for the derivation of the density of states for 2D electrons in an out of plane magnetic field, which also details collision broadening leading to the oscillatory density of states?
 
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  • #2
jpr0 said:
Does anyone have a link for the derivation of the density of states for 2D electrons in an out of plane magnetic field, which also details collision broadening leading to the oscillatory density of states?
I don't have a link, but I can suggest how to do it.

If you've seen the derivation for the DOS of a 2D electrons in a perpendicular field *(say, in the Landau gauge), all you need to do is add a component to the vector potential (giving rise to an in-plane component for the field) and solve the SE again with the two extra terms that emerge. Also, you will want to make sure you include the Zeeman energy term.

In the limit where the width of the confining potential, V(z), is small compared to the classical cyclotron radius (i.e, an ideal 2D electron gas), the parallel field will only noticeably affect the spin split nature of the DOS.

*EDIT : Oops! I thought you were asking about an in-plane (parallel) field. I just realized you were asking about the DOS from an out-of-plane (perpendcular) field. I don't have a link for that either, but you will find this in any book that deals with the Quantum Hall effect.

PS: You will find a partial discussion here: https://www.physicsforums.com/showthread.php?t=133409
 
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  • #3


There are several resources available that provide derivations of the density of states for 2D electrons in an out-of-plane magnetic field and discuss the effects of collision broadening on the oscillatory density of states. One such resource is the book "Introduction to Solid State Physics" by Charles Kittel, which provides a detailed derivation of the density of states in the presence of a magnetic field and discusses the effects of scattering on the oscillatory behavior.

Another resource is the paper "Quantum Oscillations in Two-Dimensional Electron Systems in an Out-of-Plane Magnetic Field" by J. M. Ziman and P. A. Lee, which provides a comprehensive analysis of the density of states and its dependence on magnetic field strength and scattering mechanisms.

It is important to note that the density of states in 2D systems is highly sensitive to the presence of a magnetic field, and collision broadening can significantly affect the oscillatory behavior. Therefore, it is crucial to understand the underlying physics and mathematical derivations in order to accurately interpret experimental results.

In summary, there are various resources available for the derivation of the density of states for 2D electrons in an out-of-plane magnetic field and the effects of collision broadening on the oscillatory behavior. It is recommended to consult multiple sources and thoroughly understand the underlying principles in order to properly interpret and analyze experimental data.
 

1. What is the significance of studying 2D electrons in an out-of-plane magnetic field?

Studying 2D electrons in an out-of-plane magnetic field has important implications for understanding the electronic properties of materials, particularly in the field of condensed matter physics. This research can provide insights into the behavior of electrons in low-dimensional systems, such as graphene, and can also have practical applications in developing new electronic devices and technologies.

2. How does the density of states (DOS) change in the presence of an out-of-plane magnetic field?

The DOS, or the number of available energy states in a material, is affected by the presence of an out-of-plane magnetic field. In this system, the DOS becomes highly anisotropic, meaning it depends on the direction of the magnetic field. This can lead to interesting phenomena, such as the Hofstadter butterfly, where the DOS exhibits a fractal structure.

3. What is collision broadening and how does it affect the electronic properties of 2D electrons in an out-of-plane magnetic field?

Collision broadening refers to the broadening of energy levels in a material due to scattering events between electrons. In the presence of an out-of-plane magnetic field, the electrons experience a Lorentz force that can cause them to collide with impurities or defects in the material, leading to collision broadening. This can change the electronic properties of the system, such as the conductivity and mobility of the electrons.

4. How do experimental techniques measure the DOS and collision broadening in 2D electron systems?

There are several experimental techniques used to measure the DOS and collision broadening in 2D electron systems. These include scanning tunneling microscopy, angle-resolved photoemission spectroscopy, and transport measurements such as magnetoresistance and Hall effect measurements. These techniques allow researchers to study the electronic properties of 2D electrons in real time and under various conditions.

5. What are the potential applications of understanding the DOS and collision broadening in 2D electron systems?

Understanding the DOS and collision broadening in 2D electron systems has potential applications in the development of new electronic devices and technologies. This research can also provide insights into the behavior of electrons in other low-dimensional systems, which could lead to advancements in fields such as quantum computing and spintronics. Additionally, this knowledge can help in the design and optimization of materials for specific electronic applications.

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