ARPES (Angle Resolved PhotoEmission Spectroscopy)

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ARPES (Angle Resolved PhotoEmission Spectroscopy)

• Michael Browne
• 11/19/2007

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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.

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What is ARPES?
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The ARPES Apparatus at SSRL

• Photon energies of 12-30 eV
• Angular resolution of
• Energy resolution of 2-10 MeV

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The Photoelectric Effect

• Explained by Einstein (1905)
• More generally,
• where is the binding
• energy of the electron.

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Photoemission Spectra

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

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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.

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Theoretical Basis of ARPES

• Point 2
• (See Table 2.1)
• The photon momentum is small and can be
  neglected!

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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?

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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.

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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.

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Momentum and Binding Energy
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Direct k Space Imaging
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Fermi Surface Images
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Band Structure Images
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Validation of Predictions
Theoretical Calculation

• ARPES Measurement

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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.

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Further Advances

• Laser ARPES lower energy means sharper pictures
• (image of
• in nodal
• direction)

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Credits

• Slide 1,13 http//www.coe.berkeley.edu/AST/srms/2
  007/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/conte
  nts/calendar-e.html
• Slide 16 http//www-ssrl.slac.stanford.edu/resear
  ch/highlights_archive/high-tc.html
• Slide 18 http//spot.colorado.edu/dessau/index.h
  tml