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

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SUMMARY

The primary distinction between local density of states (LDOS) and density of states (DOS) lies in their spatial dependence. DOS represents a macroscopically averaged density, n(E), applicable in homogeneous materials, while LDOS is spatially dependent, denoted as n(E,x,y,z), crucial for non-homogeneous materials. LDOS is typically measured using Scanning Tunneling Microscopy (STM), where the tunnel current correlates with the LDOS beneath the STM tip. For further reading, refer to Michael Marder's "Condensed Matter Physics," Chapter 8.

PREREQUISITES
  • Understanding of density of states (DOS) in solid-state physics
  • Familiarity with local density of states (LDOS) concepts
  • Knowledge of Scanning Tunneling Microscopy (STM) techniques
  • Basic principles of non-homogeneous materials in condensed matter physics
NEXT STEPS
  • Study the mathematical formulation of local density of states (LDOS)
  • Explore the principles and applications of Scanning Tunneling Microscopy (STM)
  • Investigate the effects of non-homogeneity on electronic properties of materials
  • Read Michael Marder's "Condensed Matter Physics," focusing on Chapter 8
USEFUL FOR

Researchers, physicists, and students in condensed matter physics, particularly those interested in electronic properties of materials and advanced microscopy techniques.

snooper007
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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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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
 
Thank you Gokul43201!
 

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