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ARPES (Angle Resolved PhotoEmission Spectroscopy)

ARPES (Angle Resolved PhotoEmission Spectroscopy). Michael Browne 11/19/2007. What is ARPES?. An atomically flat sample is illuminated by a beam of monochromatic light. Due to the photoelectric effect, the sample emits electrons.

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ARPES (Angle Resolved PhotoEmission Spectroscopy)

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  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. Validation of Predictions : ARPES Measurement : Theoretical Calculation

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

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

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