surface science lecture
TRANSCRIPT
![Page 1: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/1.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface Science Lecture
Band Structure: Bulk and Surface
David Vanderbilt Rutgers University
![Page 2: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/2.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
3D Crystals: Bloch’s theorem
Hamiltonian eigenstates:
Crystal Hamiltonian:
![Page 3: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/3.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bulk bandstructure
Occupation
![Page 4: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/4.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bloch’s Theorem
Brillouin zone
![Page 5: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/5.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bulk bandstructure of diamond (C)
fcc Brillouin
zone
![Page 6: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/6.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Real space and reciprocal space
Brillouin zone
Unit cell
![Page 7: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/7.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Beware alternate notations
Previous a1, a2, a3 now a, b, c
Previous A1, A2, A3 now A, B, C
![Page 8: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/8.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Periodicity in reciprocal space
k’
k
BZ is unit cell in reciprocal space
![Page 9: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/9.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Summary: 3D crystals
![Page 10: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/10.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface periodicity
![Page 11: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/11.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface Brillouin zone
![Page 12: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/12.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bulk Bloch state of wavevector k
k⊥: 1D wavenumber
k||: 2D wavevector
![Page 13: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/13.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bulk band-structure from surface viewpoint
![Page 14: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/14.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Projected bulk bands at surface
Example:
This is the conventional representation
![Page 15: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/15.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Tight binding, 1 band
A simple tight-binding model with one s state per site gives:
![Page 16: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/16.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Tight binding, 1 band
A simple tight-binding model with one s state per site gives:
Look down
![Page 17: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/17.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Tight binding, 1 band
![Page 18: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/18.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Tight binding, 1 band
![Page 19: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/19.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Tight binding, 1 band
![Page 20: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/20.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Add second band
![Page 21: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/21.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Cubic crystal: Redraw
![Page 22: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/22.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Sometimes you will see:
What are these solid and
dashed lines?
![Page 23: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/23.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface bandstructure of diamond (111)
![Page 24: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/24.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Bloch’s theorem for a surface
![Page 25: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/25.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface states and resonances
![Page 26: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/26.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
How do various states look at the surface?
Bulk state
Surface state
Resonance
Bulk Vacuum
Bulk Vacuum
Bulk Vacuum
![Page 27: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/27.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Experiments
Angle Resolved Photo-Emission Spectroscopy
Angle Resolved Inverse
Photo-Emission Spectroscopy
![Page 28: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/28.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Experiments
Angle Resolved Photo-Emission Spectroscopy
Angle Resolved Inverse
Photo-Emission Spectroscopy
occ.
empty
EF
occ.
empty
EF
![Page 29: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/29.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Experiments: Photoemission
![Page 30: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/30.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Experiments: Inverse Photoemission
A. Goldman, V. Dose and G. Borstel
![Page 31: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/31.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Recent: Topological insulators
![Page 32: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/32.jpg)
![Page 33: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/33.jpg)
Spin-Orbit Coupling
![Page 34: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/34.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
How do various states look at the surface?
Bulk state
Surface state
Resonance
Bulk Vacuum
Bulk Vacuum
Bulk Vacuum
![Page 35: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/35.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Typically, surface states exist if:
1. Character is similar to a bulk state, but shifted in energy by the surface perturbation
Bulk Vacuum
![Page 36: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/36.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
2. State of new character, e.g., a “broken bond” or “adsorbate state”, is created at the surface
Typically, surface states exist if:
Typically the state is near the middle of the gap and is very localized (e.g., within one or a few atom distances from the surface in real space)
Example: Si (111) 1x1:
![Page 37: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/37.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface bandstructure of diamond (111)
![Page 38: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/38.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Surface bandstructure of diamond (111)
![Page 39: Surface Science Lecture](https://reader035.vdocuments.us/reader035/viewer/2022071602/613d7387736caf36b75d7cb7/html5/thumbnails/39.jpg)
Vanderbilt Lecture, Surface Science, 3/4/2013
Summary
• Bulk bandstructure
– 3D Real space and reciprocal space
– Bloch’s theorem for 3D crystals
• Surface bandstructure
– 2D Real space and reciprocal space
– Projected bulk bandstructure
– Surface bands
– Resonances