In 1879 Edwin Hall found that if a metal
strip were put in a magnetic field and an electric current went through the strip, then
there would be a voltage across the strip, as shown at the right with the + and - signs.
The appearance of the voltage is called the Hall effect, and voltage itself is called the
Hall voltage, VH. The Hall effect is used to determine the charge (+
or -) of the carriers of electric current and the speed with which they move through the
material. It is frequently used to study the semiconductors used in integrated circuits.
About one
hundred years later Hall effect experiments done in very cold materials (a few degrees
above absolute zero, i.e. around -272oC) in very strong magnetic fields (up to
30 T, or 600,000 times Earth's field) found a surprising effect. The experimenters studied
the Hall resistance, the ratio VH/I, and found that it didn't
increase linearly with magnetic field. Instead, it increased in steps, as shown at the
right. The size of the steps doesn't depend on the material or the temperature, but
depends only on a combination of fundamental physical constants, h/e2,
where e is the charge of the electron, and h is Planck's constant (the
ratio of energy to frequency of a photon). Any quantity that can have only certain
specified values is said to be quantized. In this case the resistance is quantized and the
effect is called the quantum Hall effect (qhe).
The quantum Hall effect is explained by noting that at these low temperatures, the electrons are trapped to move on a plane surface, in only two dimensions. The electrons act like a gas, but one that can move in only two dimensions. Further, the electrons can move in only certain circular paths. The sizes of these paths depends on the magnetic field. Klaus von Klitzing won the Nobel Prize in Physics in 1985 for his discovery of the quantum Hall effect.
The quantum Hall effect is important beyond pure physics. The value of h/e2, the "quantum" of resistance, about 25 000 ohms, is used as the standard of electrical resistance by all national standards laboratories, including the United States' National Institution of Standards and Technology (NIST).
In 1985 Horst
Stoermer (Bell Labs, now at Columbia University) and Daniel Tsui (Princeton Univesity)
pushed the experiments to even lower temperatures and higher magnetic fields (30 tesla in
the graph at the right as opposed to 7 in the graph above). They were surprised to find
new steps, both above and below the integer steps. In all cases the step size could be
written as (h/e2)f, where f is a fraction, a ratio
of two integers. That is, each step is a fraction of the quantum of resistance.
Therefore the effect they discovered is called the fractional quantum Hall effect (fqhe).
A year after the discovery, Robert Laughlin (Stanford University) published a theory that explained the effect. He proposed that in the high magnetic fields and low temperatures the electrons don't act as a gas like they do in normal metals. They have condensed to form a new type of quantum fluid. Because electrons have a great reluctance to condense, each must first capture and combine with a quantum unit of magnetic flux. The unique property of Laughlin's quantum fluid is that if one electron is added, the fluid is excited, creating "quasiparticles" that have a fraction of the charge of an electron. These are not normal particles, but just the coordinated motion of several electrons in the fluid.
Computer graphics
visualizing the Laughlin wave function for the 1/3 charged state. The green balls
represent electrons that are pinned momentarily in the two-dimensional plane. The blue
mountain represents the charge distribution of one "free" prototype electron
moving in the presence of the magnetic field and the potential of the other (green)
electrons. The black arrows are magnetic flux quanta captured by the electrons. This image
was generated by Tom Duff of Lucent Technologies.
A quantum fluid may see like an unlikely material. But at very low temperatures, liquid helium becomes a superfluid, able to escape through tiny holes and climb uphill. Pairs of electrons in superconductors are another kind of quantum fluid. Further, additional experiments with better materials by Stoermer and Tsui showed excellent agreement with the details of Laughlin's predictions. In the past two years direct evidence of fractionally-charged quasiparticles has been obtained by groups in New York, Israel, and France.
Material in this essay is based on articles published by the Nobel Foundation, the American Institute of Physics, and ABC News.
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