Transcript ARPES
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. • 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 0.1 • Energy resolution of 2-10 MeV The Photoelectric Effect • Explained by Einstein (1905): Ekmax hf • More generally, Ek hf EB where E B is the binding energy of the electron. 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: 8 1 • k photon p photon / E photon / c 10 m • kelectron 1010 m 1 (See Table 2.1) The photon momentum is small and can be neglected! 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: I k , I 0 k , , A f A k , where I 0 k , , A depends on the photon. f is the Fermi-Dirac distribution. A k , is the one-particle spectral function. 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 Validation of Predictions Sr2 RuO4 : ARPES Measurement Theoretical Calculation 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. Further Advances • Laser ARPES: lower energy means sharper pictures (image of Bi2Sr2CaCu 2O8 in “nodal” direction) 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/Tal ks/ARPES_Intro.pdf • Slide 14, 15: http://arpes.phys.tohoku.ac.jp/contents/calendar-e.html • Slide 16: http://wwwssrl.slac.stanford.edu/research/highlights_archive/high-tc.html • Slide 18: http://spot.colorado.edu/~dessau/index.html