Clarifying question about surface states

[mt42]

Recently, I was giving a presentation for my research group related to ARPES to improve my understanding. I mentioned that the probing depth of ARPES is a few angstroms, meaning we can only look at surface states, and I was sort of giving a real space picture. In other words, ARPES can only probe electrons that are near the physical surface of the material because "deeper" electrons are scattered.

After someone asked a question about measuring surface states and bulk states, my PI stopped us and said that this is not quite accurate; ARPES is actually probing the surface of the Brillouin zone (e.g. surface relates to momentum space, not real space). My PI actually became a bit confused himself because he said that the BZ surface is related to the real surface, or at least they should be, but it really didn't make sense to me and he couldn't paint a coherent picture for me. I also just finished year one of grad school and haven't taken any formal solid state course, so I am self-learning about the BZ and I couldn't ask him any proper follow-up questions.

How do I relate these momentum surface states to physical surfaces, if there is such a relation? Perhaps someone can point me to references if this is not such a straightforward question. This is a pretty fundamental question for my research, which will be related to ARPES and topological materials, so I greatly appreciate your help!

 

[Fred Wright]

I recommend that you get a copy of Charles Kittel's "Introduction to Solid State Physics" and work through chapters 1-9. Ashcroft and Mermin "Solid State Physics" is also good but Kittel was preferred as an introductory text when I was in graduate school.

 

[crashcat]

Surface electrons will have a different E-k structure than bulk electrons. It depends on the material, but electrons can look like "bulk" electrons just a few lattice lengths down, could be deeper though. ARPES can probe surface electrons by using low energy photons, which don't penetrate as deep, and can probe bulk electrons by using high energy light (x-rays).

The "surface" of the BZ is a different concept than the "surface" of the material.

If you're going to self-study solid state, you might get more mileage by starting with Omar's Elementary Solid State Physics. It doesn't have the depth of Kittel, and you'll probably want to get Kittel as well, but Omar is way more approachable as a first course if you've never taken solid state or semiconductor physics. Kittel is the standard though.

 

[mt42]

I recommend that you get a copy of Charles Kittel's "Introduction to Solid State Physics" and work through chapters 1-9. Ashcroft and Mermin "Solid State Physics" is also good but Kittel was preferred as an introductory text when I was in graduate school.

Thanks. I read some Kittel last year but will try to revisit. Currently reading "Quantum Theory of Materials" by Kaxiras per recommendation from my PI.

Surface electrons will have a different E-k structure than bulk electrons. It depends on the material, but electrons can look like "bulk" electrons just a few lattice lengths down, could be deeper though. ARPES can probe surface electrons by using low energy photons, which don't penetrate as deep, and can probe bulk electrons by using high energy light (x-rays).

The "surface" of the BZ is a different concept than the "surface" of the material.

If you're going to self-study solid state, you might get more mileage by starting with Omar's Elementary Solid State Physics. It doesn't have the depth of Kittel, and you'll probably want to get Kittel as well, but Omar is way more approachable as a first course if you've never taken solid state or semiconductor physics. Kittel is the standard though.

Thanks for your response. So when you say surface electrons in the first paragraphs, are you referring to physical surface or BZ surface? When you mention electrons a few lattice lengths down, I picture electrons physically embedded below the surface, but not sure if this is accurate.

I haven't read Omar so I will be sure to take a look!

 

[crashcat]

Thanks for your response. So when you say surface electrons in the first paragraphs, are you referring to physical surface or BZ surface? When you mention electrons a few lattice lengths down, I picture electrons physically embedded below the surface, but not sure if this is accurate.

I meant physical surface, and electrons physically beneath the surface.