Integer Quantum hall effect
Formula
topological quantum numbers: the first
Chern numbers(no similar topology-
based theory exists for FQHE.)
Berry's phase
Azbel-Harper-Hofstadter model whose
quantum phase diagram is the
Hofstadter butterfly
Fractal and self-similarity
Fractal and self-similarity (*ref)
Fractional quantum hall effect
a filling factor
principal series
*ref
Quantum spin hall effect
*ref
1985 Nobel Prize in Physics.
1975
•predicted by Ando, Matsumoto, and Uemura
1977 •Observed inversion layer of MOSFETs
1980
•exactly quantized with samples developed by Michael Pepper
1998 Nobel Prize in Physics
experimentally discovered in 1982
The 5/2 (even denominator) FQHE, discovered in 1987
1995, the fractional charge of Laughlin quasiparticles was measured directly
not well-understood yet
• IQHE
• Klaus von Klitzing
• FQHE
• Robert B. Laughlin
• Horst Ludwig Störmer
• Daniel C. Tsui
• QSHE
• Kane and Mele
28 June 1943
Clarendon
Laboratory in Oxford
von Klitzing constant,
$Rk = h/e^2$
November 1, 1950
Stanford
doubting the
existence of black
holes
provide a many
body wave function:
Laughlin wave
function
April 6, 1949
Columbia University
working at Bell Labs
at the time of the
experiment
modulation doping
February 28, 1939
Princeton University
Experimental physics
and Electrical
engineering
Composite fermions
FQHE= IQHE of composite fermions
Hierarchy states
condensing quasiparticles into their own Laughlin states
Fractional exchange statistics of quasiparticles
anyons with fractional statistical angle
Laughlin states and fractionally-charged quasiparticles
excitations have fractional charge
Computer graphics visualizing the Laughlin wave function for the nu=1/3 FQHE state (*ref)
Various facets of composite fermion physics
Kane-Mele model Bernevig and Zhang
spin up electron exhibits a chiral integer quantum Hall Effect while the spin down electron exhibits an anti-chiral integer quantum Hall effect.
due to spin-orbit coupling, a magnetic field pointing upwards for spin-up
electrons and a magnetic field pointing downwards for spin-down electrons
theorysimulation
a topological invariant: characterizes a state as trivial or non-trivial band insulator (regardless if the state exhibits or not
exhibits a quantum spin Hall effect)
analytically and numerically proved: the non-trivial state(TI) is robust to interactions and extra spin-orbit coupling terms that mix spin-up and spin-down electrons.
symmetries
difference
TI AND QSHE ARE different symmetry protected topological states: do not need TR symmetry to protect
QSHE
TI: symmetry protected topological order protected by charge conservation symmetry
and time reversal symmetry
QSHE: symmetry protected topological
state protected by charge conservation
symmetry and spin- conservation symmetry
http://en.wikipedia.org/wiki/Nobel_Prize_
in_Physics
http://en.wikipedia.org/wiki/Quantum_H
all_effect
http://en.wikipedia.org/wiki/Quantum_s
pin_Hall_effect
http://en.wikipedia.org/wiki/Fractional_q
uantum_Hall_effect
a new kind of order in zero-temperature
phase of matter
corresponds to pattern of long-range
quantum entanglement
beyond the Landau symmetry-breaking
description
