The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductivity σ takes on the quantized values
where e is the elementary charge and h is Planck's constant. The prefactor ν is known as the "filling factor", and can take on either integer (ν = 1, 2, 3, .. ) or rational (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5 ...) values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see Landau quantization). The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions. It is also very well understood as an integer quantum Hall effect, not of electrons but of charge-flux composites known as composite fermions.
Read more about Quantum Hall Effect: Applications, History, Integer Quantum Hall Effect – Landau Levels, Mathematics
Famous quotes containing the words quantum, hall and/or effect:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“Having children can smooth the relationship, too. Mother and daughter are now equals. That is hard to imagine, even harder to accept, for among other things, it means realizing that your own mother felt this way, too—unsure of herself, weak in the knees, terrified about what in the world to do with you. It means accepting that she was tired, inept, sometimes stupid; that she, too, sat in the dark at 2:00 A.M. with a child shrieking across the hall and no clue to the child’s trouble.”
—Anna Quindlen (20th century)
“The law before us, my lords, seems to be the effect of that practice of which it is intended likewise to be the cause, and to be dictated by the liquor of which it so effectually promotes the use; for surely it never before was conceived by any man entrusted with the administration of public affairs, to raise taxes by the destruction of the people.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)