SLIDE 1
Quantum Hall Quantum Hall effect effect
Hall bar geometry classical Hall effect
flux quantum flux per electron
flux quanta per electron
Quantum Hall effect effect Quantum Hall integer integer Hall bar - - PowerPoint PPT Presentation
Quantum Hall effect effect Quantum Hall integer integer Hall bar - - PowerPoint PPT Presentation
Quantum Hall effect effect Quantum Hall integer integer Hall bar geometry classical quantum classical Hall effect flux quantum 1 = flux quanta per electron flux per electron Quantum Hall effect effect Quantum Hall integer integer
SLIDE 2
SLIDE 3
Quantum Hall Quantum Hall effect effect
integer integer Landau levels: symmetric gauge
ground state radius (peak):
integer flux quantum enclosed quasiclassical cyclotron orbit
SLIDE 4
Quantum Hall Quantum Hall effect effect
integer integer Landau levels & circular potential
exactly solvable lifting the degeneracy
wave function peak position
SLIDE 5
Quantum Hall Quantum Hall effect effect
integer integer Landau levels & circular potential
quasiclassical limit
(weak potential) x y trajectories equipotential lines
random potential landscape closed and extended trajectories
SLIDE 6
Quantum Hall Quantum Hall effect effect
integer integer
Potential landscape islands lakes percolating coastlines coastlines as equipotential lines (contour lines)
SLIDE 7
Quantum Hall Quantum Hall effect effect
integer integer
Laughlins argument
L
B
x y
V
I
- uniform magnetic field B through
Corbino disk
- change of Aharonov-Bohm phase
through
- Aharonov-Bohm phase acts on extended
trajectories around the Corbino ring extended state (pure case) rm rm-1 shift by one ''trajectory''
fixed current
single-valued wave function integer
conserved flux enclosed by trajectory
SLIDE 8
Quantum Hall Quantum Hall effect effect
integer integer
Laughlins argument
L
B
x y
V
I
rm rm-1 shift by one ''trajectory'' net shift of 1 el from outer to inner edge potential energy
fixed current
electromagnetic energy
per filled Landau level
energy argument
moving electron against electric potential (V) inductive energy
- f current loop
no energy change for
gauge invariance
SLIDE 9
Quantum Hall Quantum Hall effect effect
integer integer
localized versus extended states
degeneracy
clean
disorder Landau levels
(without spin)
extended localized
T
potential landscape lifts degeneracy
SLIDE 10
Quantum Hall Quantum Hall effect effect
fractional fractional
integer QHE fractional QHE
Störmer, Tsui and Gossard (1982) von Klitzing, Dorda and Pepper (1980)
SLIDE 11
Properties Properties of metals
- f metals
elementary excitations properties of metal
well described by ''free electrons" Jellium-model (lattice not essential) strong renormalization of external perturbations: dynamical dielectric function
continuum electron-hole excitations plasmon collective mode