Goran Sljuka. Fractional Quantum Hall Effect. History of Hall Effect Hall Effect (Integer ) Quantum Hall Effect Fractional Hall Effect HEMT Topological Order. History. 1878 The Hall Effect discovered by Edwin Hall, grad student at John Hopkins University, Baltimore, Maryland
Fractional Quantum Hall Effect
1878 The Hall Effect discovered by Edwin Hall, grad student at John Hopkins University, Baltimore, Maryland
1930 Lev Davidovich Landau(Nobel Prize 1962) for discivery of Landau levels which explain the integer quantum Hall effect
In 1980 Klaus von Klitzing discovered Integer QHE (Nobel Prize)
1982 FQHE experimentally discovered by Daniel C. Tsui and Horst L.Stormer
1985 Robert B. Laughlin showed that the electrons in a powerful magnetic field can condense to form a kind of quantum fluid related to the quantum fluids that occur in superconductivity and in liquid helium.
Consequence of the forces that are exerted on moving charges by electric and magnetic fields
Used to distinguish weather semiconductor is n(negative Hall voltage)or p type(positive Hall voltage)
Measure majority carrier concentration and mobility
jx = vxNq RH=1/Nq
-plateau regions in the Hall resistivity where it remains constant as density is changed
- The the value of Hall resistivity in plateau region is given exactly by h/e2divided by a integer
-differences between two samples of different size
-differences between two materials
- differences between different plateau
are smaller than 10^-10times the quantized value
The zeros and plateaux in the two components of the resistivity tensor are intimately connected and both can be understood in terms of the Landau levels (LLs) formed in a magnetic field.
-The value of resistance only depends on the fundamental constants of physics:e the electric charge and h Plank's constant.
-It is accurate to 1 part in 100,000,000.
Ym(z1,z2,z3,.,zN) = (z1- z2)m (z1- z3)m (z2- z3)m . (zj- zk)m. (zN-1- zN)m
liquid - continuous translation symmetry crystal - discrete translation symmetry change in symmetry -symmetry breaking.
The Landau symmetry-breaking description of a system
principal quantum number
azimuthal quantum number
magnetic quantum number
spin quantum number
ground state degeneracy,
The topological order is new since it is not related to symmetries
quantum order with a finite energy gap