1. ARPES (Angle Resolved PhotoEmission Spectroscopy) Michael Browne 11/19/2007

2. What is ARPES? An atomically flat sample is illuminated by a beam of monochromatic light. Due to the photoelectric effect, the sample emits electrons. The kinetic energy and direction of these electrons are measured by the apparatus. This data reflects the structure of the Fermi surface within the material.

3. What is ARPES?

4. The ARPES Apparatus at SSRL Photon energies of 12-30 eV Angular resolution of Energy resolution of 2-10 MeV

5. The Photoelectric Effect Explained by Einstein (1905): More generally, where is the binding energy of the electron.

6. Photoemission Spectra The work function is known/measurable. The photon energy is known. We can calculate the energy of the electron in the solid!

7. Theoretical Basis of ARPES Point #1: The flat surface of the sample has translational symmetry. Therefore, as electrons escape from the solid, linear momentum is conserved parallel to the surface.

8. Theoretical Basis of ARPES Point #2: (See Table 2.1) The photon momentum is small and can be neglected!

9. Theoretical Basis of ARPES Conclusion: ARPES is directly measuring the components of electron momentum that are parallel to the surface! How many electrons of a given momentum will ARPES measure?

10. Theoretical Basis of ARPES Theoretically, the measured intensity can be described as: where depends on the photon. is the Fermi-Dirac distribution. is the one-particle spectral function.

11. What is ARPES used for? ARPES is an almost ideal tool for imaging the Fermi surface of 1-D and 2-D solids. Since many of the high temperature superconductors are essentially 2-D materials, much of the work in this field is done using ARPES.

12. Momentum and Binding Energy

13. Direct k Space Imaging

14. Fermi Surface Images

15. Band Structure Images

16. : Theoretical Calculation Validation of Predictions : ARPES Measurement

17. Disadvantages of ARPES Must be done in an ultrahigh vacuum (otherwise electrons would collide) so cannot measure pressure effects. Cannot measure magnetic effects (a magnetic field would deflect electrons). Only measures surface effects in the top 10 Å or so.

18. Laser ARPES: lower energy means sharper pictures (image of in “nodal” direction) Further Advances

19. Credits Slide 1,13: http://www.coe.berkeley.edu/AST/srms/2007/Lec18.pdfhttp://www.coe.berkeley.edu/AST/srms/2007/Lec18.pdf Slide 3-5,12: http://www.physics.ubc.ca/~quantmat/ARPES/PRESENTATIONS/T alks/ARPES_Intro.pdf http://www.physics.ubc.ca/~quantmat/ARPES/PRESENTATIONS/T alks/ARPES_Intro.pdf Slide 14, 15: http://arpes.phys.tohoku.ac.jp/contents/calendar-e.htmlhttp://arpes.phys.tohoku.ac.jp/contents/calendar-e.html Slide 16: http://www- ssrl.slac.stanford.edu/research/highlights_archive/high-tc.htmlhttp://www- ssrl.slac.stanford.edu/research/highlights_archive/high-tc.html Slide 18: http://spot.colorado.edu/~dessau/index.htmlhttp://spot.colorado.edu/~dessau/index.html