ARPES (Angle Resolved ARPES (Angle Resolved PhotoEmission Spectroscopy)PhotoEmission Spectroscopy)

Michael BrowneMichael Browne

11/19/200711/19/2007

What is ARPES?

• An atomically flat sample is illuminated by a beam of monochromatic light.

• Due to the photoelectric effect, the sample emits electrons.

• 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.

What is ARPES?

The ARPES Apparatus at

SSRL

• Photon energies of 12-30 eV

• Angular resolution of

• Energy resolution of 2-10 MeV

0.1

The Photoelectric Effect• Explained by Einstein (1905):

• More generally,

where is the binding

energy of the electron.

maxkE hf

BEk BE hf E

Photoemission Spectra

• The work function is known/measurable.

• The photon energy is known.

• We can calculate the energy of the electron in the solid!

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.

Theoretical Basis of ARPES

Point #2:

•

• (See Table 2.1)

The photon momentum is small and can be neglected!

8 1/ / 10 mphoton photon photonk p E c

10 110 melectronk

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?

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.

0 , ,I Ak 0, , , ,I I f A k k A k

f ,A k

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.

Momentum and Binding Energy

Direct k Space Imaging

Fermi Surface Images

Band Structure Images

: Theoretical Calculation

Validation of Predictions

: ARPES Measurement2 4Sr RuO

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.

• Laser ARPES: lower energy means sharper pictures

(image of

in “nodal”

direction)

Further Advances

2 2 2 8Bi Sr CaCu O

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