What is the difference between local density of states and density of state?

In summary, the essential difference between local density of states and density of state is that the former is spatially dependent while the latter is macroscopically averaged. This means that the LDOS can vary within a material, while the DOS represents an overall average. The LDOS is often measured using an STM, where the tunnel current reflects the LDOS just beneath the tip. Additional information can be found in Michael Marder's book "Condensed Matter Physics", Chapter 8.
  • #1
snooper007
33
1
what is the essentail difference between local density of states and density of state?

It is very difficult to figure it out
 
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  • #2
In a non-homogeneous material, there is no reason for the DOS to be spatially invariant. For instance, in a finite crystal, it is unwise to expect the DOS in the bulk to equal the DOS at the surface. So, instead of a macroscopically averaged density, n(E), we use a spatially dependent density n(E,x,y,z).

The LDOS is typically probed by an STM, where the tunnel current is a function of the LDOS just beneath the tip.

See also, Michael Marder, "Condensed Matter Physics", Ch. 8
 
  • #3
Thank you Gokul43201!
 

What is the essential difference between local density of states and density of state?

The local density of states (LDOS) refers to the density of electronic states at a specific point in space, while the density of states (DOS) refers to the overall density of electronic states in a material. In other words, LDOS gives information about the electronic states at a specific location, while DOS gives information about the electronic states throughout the entire material.

How are local density of states and density of state measured?

Both LDOS and DOS can be measured using various experimental techniques, such as scanning tunneling microscopy (STM) or photoemission spectroscopy. These techniques allow scientists to map out the energy levels and spatial distribution of electronic states in a material.

What factors influence the local density of states and density of state?

The local density of states and density of states are influenced by several factors, including the electronic band structure of the material, the atomic and molecular structure, and external factors such as temperature and pressure.

How do local density of states and density of state relate to each other?

The local density of states and density of states are closely related, as they both provide information about the electronic states in a material. The LDOS can be integrated over all energy levels to obtain the DOS, and the DOS can be used to calculate the LDOS at a specific energy level.

What are the applications of local density of states and density of state?

The local density of states and density of states are important for understanding the electronic properties of materials, which is crucial in various fields such as materials science, condensed matter physics, and nanotechnology. They can also provide insight into the behavior of electrons in different environments and how they interact with each other. This information is essential for developing new materials and improving existing technologies.

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