Synchrotron-based electronic
structure measurements
Ben Ruck
The MacDiarmid Institute for Advanced Materials and
Nanotechnology
Victoria University of Wellington
What is “electronic structure”?
• The set of electron energy levels of an atom, molecule, solid, liquid…
• Determines almost all properties of a material, including:
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–
–
–
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Structure
Electrical conductivity
Chemical reactivity
Colour
Hardness
Calculating electronic structure
• Always the same goal: solve Schrodinger’s
equation!!!
Calculating electronic structure
• Always the same goal: solve Schrodinger’s
equation!!!
• Many approximations are used:
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–
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–
Hartree-Fock theory
Density functional theory (many approaches to this)
Dynamic mean field theory
Model Hamiltonians (Anderson model, Kondo
Hamiltonian, Heisenberg model…)
Independent electron approximation
• To calculate wave function of one electron you need to
know where all the others are – chicken and the egg
problem!!!
• Usually assume that each electron moves in the average
field of all of the others, so you can treat them one at a
time. Approximations:
–
–
–
–
Ignore all other electrons!!!
Self-consistent field approximation
Local density approximation to DFT
etc
• Good news: electrons avoid each other, so often their
interaction energy is less than you might think, so the
approximations work better than you might imagine
Electronic structure
Molecules vs solids
One atom
Two atoms
Many atoms
Antibonding
Linear combinations of bonding orbitals
Bonding
How good are the theories?
• Job for experiment!!!
Spectroscopy
• Electron absorbs a photon and jumps to a new energy level:
E2-E1=hf
• Vary the photon frequency to map out the available energy
levels
• Simple approximation: new level is just one of the empty
levels from your calculation of the ground state
• More realistic: when one electron makes a transition, all of
the other electrons respond to the fact that the initial
electron is now in a new state. Exciting one electron affects
them all!!!
Optical spectroscopy
• For a given photon energy there may be many
possible transitions
– Only require an occupied initial state and an empty
final state separated by the photon energy
• Measure a joint density of states
Forbidden
k
X-ray absorption (XANES, NEXAFS,
XAS)
• Same as optical absorption, but the initial state of the
electron is a core state – very well defined energy
• Absorption spectrum measures density of final states – easy
to compare to theory
X-ray absorption example
• Example: oxygen K-edge in ZnO
• Initial electron is in O 1s orbital
• Final state must have symmetry of a p-orbital on the same
oxygen site
Zinc oxide
unoccupied states
(XAS/XANES)
theory
X-ray absorption example 2
• M-edge of Eu in EuN
• Initial electron is in Eu 3d orbital
• Final state depends on how the 9 remaining 3d electrons organise
themselves – two main peaks (M4 and M5)
• Structure of the peaks is a fingerprint of charge state of Eu ion
X-ray emission
• X-ray absorption creates a core hole
• Core hole is filled by decay of another electron
– Auger
– X-ray emission (rare, but no background)
• Measure energy of emitted photons, and hence find density
of occupied electron energy levels
Zinc oxide: absorption and emission
occupied states
(XES)
unoccupied states
(XAS/XANES)
O p-states
Zn d-states
theory
X-ray photoelectron spectroscopy
(XPS)
• Photons of sufficient energy eject electrons
from materials – photoelectric effect
• Kinetic energy of emitted electron is
measured, and hence binding energy of
electron is obtained:
– Eb = Eph - (Ek + f)
• Energy of electrons is a fingerprint of the
atoms that they came from, and their
environment
X-ray photoelectron spectroscopy
(XPS)
Angle-resolved photoemission
spectroscopy (ARPES)
• In solids, valence electrons are not localised. Their molecular
orbitals extend throughout the crystal in so-called Bloch
wavefunctions.
• ARPES can measure the full band structure of the occupied
states.
ARPES
• Must measure both energy and direction (momentum) of
outgoing photoelectrons, and use conservation of energy and
momentum to infer initial state of electron
ARPES uses: Graphene
Dirac point of graphene
ARPES uses: Topological insulators
Topological insulator: Bi2Se3, from Yulin Chen at Stanford
ARPES uses: High temperature
superconductors
This kink is thought to be due
to the “pairing boson” that
gives rise to high-temperature
superconductivity
Bi2Sr2CaCu2O8-d