Von Klitzing Discovers the Quantized Hall Effect Summary

  • Last updated on November 10, 2022

Klaus von Klitzing’s discovery of the quantized Hall effect allowed scientists to make extremely accurate measurements of certain fundamental constants of nature.

Summary of Event

With the explosive growth in microelectronics technology, semiconductors Semiconductors became some of the most studied of materials. The understanding of the basic microscopic phenomena in these crystals has advanced to the point where semiconductors are manufactured and manipulated on a molecular level. The properties of silicon, Silicon for example, are perhaps the best understood among solids. The measurement of these properties often reflects the complicated nature of the microscopic structure of these materials as well as the specifications of the particular sample. Given such detailed knowledge, the discovery of a novel fundamental phenomenon in semiconductors was startling. Quantized Hall effect Physics;quantized Hall effect Hall effect [kw]Von Klitzing Discovers the Quantized Hall Effect (Feb. 5, 1980) [kw]Discovers the Quantized Hall Effect, Von Klitzing (Feb. 5, 1980) [kw]Quantized Hall Effect, Von Klitzing Discovers the (Feb. 5, 1980) Quantized Hall effect Physics;quantized Hall effect Hall effect [g]Europe;Feb. 5, 1980: Von Klitzing Discovers the Quantized Hall Effect[04060] [g]France;Feb. 5, 1980: Von Klitzing Discovers the Quantized Hall Effect[04060] [c]Science and technology;Feb. 5, 1980: Von Klitzing Discovers the Quantized Hall Effect[04060] [c]Physics;Feb. 5, 1980: Von Klitzing Discovers the Quantized Hall Effect[04060] Hall, Edwin Herbert Klitzing, Klaus von Laughlin, Robert Betts

The measurement of the quantized Hall effect depends only on fundamental constants of nature and not on sample irregularities or impurities. The properties of a solid are especially dependent on a host of internal and environmental parameters, such as the geometry, temperature, purity of the sample, and the history of its preparation. It was surprising to find a manifestation of quantum mechanical behavior in macroscopic samples that is so distinct and precise.

The Hall effect is a class of phenomena that occur when a material carrying current is subject to a magnetic field perpendicular to the direction of the current. As first observed in 1879 by the American physicist Edwin Herbert Hall, an electric voltage results in a direction perpendicular to both the current and the magnetic field. The ratio of this voltage to the current is the Hall resistance. In comparison, the normal electrical resistance is the ratio of the voltage in the direction of the current to the current. In the “classic” Hall effect, which occurs for a wide range of temperatures, the Hall resistance increases linearly with the strength of the magnetic field. The constant of proportionality depends on the individual characteristics of the sample and is a measure of the density of electrons that carry current.

The classic Hall effect is well described by what is called an “electron gas,” where the motions of the conducting electrons of the solid are considered to be independent from one another and the electrons can freely wander within the crystal matrix. The case of the quantized Hall effect, however, requires a two-dimensional electron gas, where the electrons are confined to a plane of conduction. This is realized at the interface between a semiconductor and an insulator, where an electric field draws the semiconductor’s electrons toward the two-dimensional interface. Temperatures of a few Kelvins are needed to keep the electrons stuck to the surface.

Klaus von Klitzing, winner of the 1985 Nobel Prize in Physics.

(The Nobel Foundation)

It was demonstrated in 1966 that electrons confined to motion in such a plane, typically 10 nanometers thick, result in new quantum mechanical Quantum mechanics;quantized Hall effect effects. The motion of the electrons is quantized, that is, their energies assume one of several evenly spaced discrete values. The number of electrons that can assume a particular energy, called a Landau level, Landau level is proportional to the strength of the magnetic field. Increasing the field strength also increases the spacing between the Landau levels. At low temperatures, the electrons try to minimize their energy; therefore, the Landau levels are filled sequentially by energy. The highest filled energy is called the Fermi level. Fermi level Raising the magnetic field effectively lowers the Fermi level, because more electrons can then be accommodated per Landau level. Alternatively, the Fermi level can be altered simply through a change in the number of electrons.

Certain general aspects of the quantized Hall effect were, in fact, predicted in 1975 (five years prior to Klaus von Klitzing’s experiments) by the Japanese theorists Tsuneya Ando, Ando, Tsuneya Yukio Matsumoto, Matsumoto, Yukio and Yasutada Uemura Uemura, Yasutada of the University of Tokyo. They recognized that when every Landau level is either completely filled or completely empty, the electrical resistance should vanish. Under these conditions of “integral filling,” the Hall resistance would be a certain ratio of fundamental constants divided by the number of filled levels and would be independent of the geometry. Unfortunately, the theory was only approximate and would not have been considered reliable for the actual experimental situation. The crucially important aspects of the extreme precision and the robustness of the effect under varying conditions were unforeseen. Also, in experiments as early as 1977 performed by von Klitzing’s coworker Thomas Englert, Englert, Thomas slight plateaus in the Hall resistance were visible in some samples. These anomalous plateaus were considered unexplained by any published theories.

Von Klitzing’s research through the 1970’s included studies of silicon devices in high magnetic fields and under conditions of mechanical stress. In 1980, von Klitzing decided to investigate the anomalies in the Hall resistance. The high-quality samples he used were “metal oxide semiconductor field-effect transistors,” Metal oxide semiconductor field-effect transistors or MOSFETs, constructed by his collaborators Gerhardt Dorda Dorda, Gerhardt of the Siemens Research Laboratory in Munich and Michael Pepper Pepper, Michael of the University of Cambridge. A layer of insulating oxide is sandwiched between a metal strip, which provides a voltage potential, and the silicon, which supports the two-dimensional electron gas at its surface. The samples were typically about 0.4 millimeter long and .05 millimeter wide. By increasing the voltage on the metal electrode, more electrons could be drawn to the surface of the semiconductor, thereby raising the Fermi level.

Von Klitzing took his experiment to the High Field Magnetic Laboratory of the Max Planck Institute Max Planck Institute in Grenoble, France, to make measurements using the lab’s 20-tesla magnet, the magnetic field strength of which is roughly one million times stronger than Earth’s at ground level. Von Klitzing found for practically every sample that the Hall resistances were equal to the same fundamental ratio divided by integers to within a few percent, extending over well-developed plateaus in the variation of the Fermi level. The subsequent high-precision results published were measured using the more stable 15-tesla magnet at the University of Würzburg. The accuracy improved to five parts per million, with the primary source of inaccuracy being the instability of the resistance standard. The ratio of the resistance at different plateaus, for example, was the ratio of integers to one part in thirty million. During the plateau regions, the electrical resistance fell very nearly to zero, ten times lower than any nonsuperconducting metal. Moreover, the resistivity continues to decrease as the temperature approaches absolute zero.

The surprising features of the quantized Hall effect sent theoreticians into a flurry of activity. Impurities had been conventionally thought of as either trapping or deflecting electrons off their paths, giving rise to electrical resistance and causing variation in measurements from sample to sample. The seeming lack of involvement of impurities or defects was particularly enigmatic. In 1981, preliminary calculations by University of Maryland theorist Richard E. Prange Prange, Richard E. suggested that although an electron can be trapped in a “localized state” around a defect in the crystal, under the condition that the Landau levels are integrally filled, the current lost to the trapped electron is exactly compensated by an increase in the velocity of electrons near the defect. The electrons move like a fluid, where flow speeds up around a barrier so that the total transported volume remains the same.

Theoreticians came to realize more generally that not only do impurities not cause resistance but ironically they also are responsible for the plateaus in the Hall resistance as the magnetic field or the Fermi level is varied. The localized states act as a reservoir between Landau levels. As the Fermi level rises past complete filling of the conducting states of a given Landau level, only localized states are left to be filled up. The conducting electrons are effectively unaffected, giving rise to the constancy of the current as the Fermi level is varied.

Significance

The measurement accuracy of the fundamental ratio found in the quantized Hall resistance subsequently improved to one part in 108, and resulted in several immediate benefits. After a series of tests in independent laboratories was completed by the end of 1986, the quantized Hall effect was adopted as the international standard for resistance. The fine-structure constant, which is related to the fundamental Hall ratio by the speed of light, is a measure of the coupling of elementary particles to the electromagnetic field. Complementing high-energy accelerator experiments, the improved determination of the fine-structure constant provides a stringent test for theories of the fundamental electromagnetic interactions.

Soon after the integral quantized Hall effect was explained, a new “fractional” quantized Hall effect was discovered in 1982 by Dan C. Tsui, Tsui, Dan C. Horst L. Störmer, Störmer, Horst L. and Arthur Charles Gossard Gossard, Arthur Charles of Bell Laboratories. The type of sample they used for creating the two-dimensional electron gas, called a heterojunction, was made by a process called molecular beam epitaxy, Molecular beam epitaxy where a layer of gallium arsenide positively doped with aluminum is grown onto a substrate layer of pure gallium arsenide. The gallium arsenide electrons are attracted toward the positively doped semiconductor and thus build up into a layer at the interface. The new device was a more perfect crystal and had better conduction properties, which were crucial for a successful observation of the fractional quantized Hall effect. In the fall of 1981, Tsui and his colleagues brought their sample to the Francis Bitter Magnet Laboratory at MIT, where they used the 28-tesla magnet. They were searching at high fields and temperatures less than 1 Kelvin for an “electron crystal,” where the electronic orbitals become arranged into a lattice. Instead, they found the same kind of plateaus and drops in the resistance observed in the integral quantized Hall effect, but occurring when only one-third or two-thirds of a Landau level is filled. Since this research was conducted, many other fractions have appeared.

Theoretical investigations indicated that the observations could not be explained by an electron solid and demanded a radical description of the electronic behavior. In 1983, Robert Betts Laughlin gave a remarkable explanation in terms of a “quantum electronic liquid,” in which the motions of the electrons are strongly affected by each other. The electronic liquid is incompressible: Rather than causing the density to increase, squeezing on the liquid causes a condensation of exotic fractional charges. These fractional charges play the role that electrons do in the integral Hall effect and so cause the plateaus at fractional values.

The impact on the field of physics reaches far beyond the accuracy of the measurement of the Hall resistance. Although the effect itself was not expected to be commercially significant, the MOSFET is essentially identical to components that may be important in the following generation of computers. Additionally, similarities emerged between the physical mechanisms of the fractional quantized Hall effect and those of high-temperature superconductors. Superconductivity Common features include a two-dimensional structure, low resistivity, and the collective motion of a macroscopic number of particles. The primary significance of the quantized Hall effects lies in revolutionizing and deepening an understanding of electronic properties of solids in high magnetic fields. For his work in this area, von Klitzing won the 1985 Nobel Prize in Physics. Nobel Prize in Physics;Klaus von Klitzing[Klitzing] Quantized Hall effect Physics;quantized Hall effect Hall effect

Further Reading
  • citation-type="booksimple"

    xlink:type="simple">Halperin, Bertrand I. “The 1985 Nobel Prize in Physics.” Science 231 (February 21, 1986): 820-822. Introduces the concepts of the quantized Hall effect at a basic level and provides some historical background. Halperin, professor of physics at Harvard, has contributed theoretical insights to the understanding of the quantized Hall effect.
  • citation-type="booksimple"

    xlink:type="simple">_______. “The Quantized Hall Effect: This Variation on a Classical Phenomenon Makes It Possible, Even in an Irregular Sample, to Measure Fundamental Constants with an Accuracy Rivaling That of the Most Precise Measurements Yet Made.” Scientific American 254 (April, 1986): 52-60. Provides an explanation of the quantized Hall effect in terms of simple classical ideas, without resorting to quantum mechanics. Includes diagrams and an illustration of the device.
  • citation-type="booksimple"

    xlink:type="simple">Klitzing, Klaus von. “The Quantized Hall Effect.” Reviews of Modern Physics 58 (July, 1986): 519-631. This lecture, presented at the Nobel ceremonies, is intended for the nonspecialist scientist. Some of the material is advanced, but interested nonspecialists will find the historical remarks and discussion about establishing resistance standards informative. Includes an extensive section with data characteristic of the quantized Hall effect and a technical bibliography.
  • citation-type="booksimple"

    xlink:type="simple">MacDonald, Allan H., ed. Quantum Hall Effect: A Perspective. Boston: Kluwer, 1989. Compilation of significant research articles in the history of the Hall effect includes the readable article “The Discovery of the Quantum Hall Effect” first published in Metrologia in 1986 by von Klitzing’s graduate adviser, G. Landwehr. Landwehr’s personal, anecdotal account of von Klitzing’s work gives an insider’s details, such as why von Klitzing’s results were originally rejected for publication.
  • citation-type="booksimple"

    xlink:type="simple">Schwarzschild, Bertram. “Von Klitzing Wins Nobel Physics Prize for Quantum Hall Effect.” Physics Today 38 (December, 1985): 17-20. Presents a chronological account of the developments surrounding the discovery of the quantized Hall effect. Includes bibliography.
  • citation-type="booksimple"

    xlink:type="simple">Yoshioka, D. The Quantum Hall Effect. Berlin: Springer-Verlag, 2002. Highly technical text aimed at graduate students in physics devotes its first chapter to the discovery of the quantum Hall effect. Includes exercises, diagrams, and index.

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