Gauge argument for accurate quantization of the Hall conductance
A theory of the Ordinary Quantum Hall Effect which identifies the quantum measured in these experiments as the electron charge is reviewed. This concept is important for understanding why the effect is so accurate, and also for understanding why fractionally charged quasiparticles need be invoked to explain the Fractional Quantum Hall Effect. The vehicle for making this identification is a thought experiment which is described in detail. Von Klitzing's original data are reproduced. A current I is forced to flow between the source and drain of a MOSFET subjected to a magnetic field of strength H /sub O/ normal to its surface. Both the voltage drop in the direction of current flow and the Hall voltage observed at low temperature are plotted against Fermi level (gate voltage). Over a range of Fermi levels one sees the voltage drop in the direction of current flow going to zero and the Hall voltage plateauing to a constant current flow going to zero and the Hall voltage plateauing to a constant value. Von Klitzing originally reported that this value obeyed the equation I/V/sub H/ = n e/sup 2//h to one part in a million. More recent measurements by the US Bureau of Standards in collaboration with Bell Laboratories have decreased the error to 10-/sup 7/. Thus the facts we wish to explain are the following: (1) the system exhibits a zero resistance state; (2) it does this over a range of carrier densities; (3) the Hall conductance is constant over this range; and (4) the constant value of the Hall conductance obeys von Klitzing's equation. The elementary quantum mechanics of this system is described, and the explanation of the effect in terms of quantization of the charge density is given. (WHK)
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 6801529
- Report Number(s):
- UCRL-90789; CONF-840284-2; ON: DE84012611
- Resource Relation:
- 3. international winterschool on new developments in solid state physics, Salzubrg, Austria, 26 Feb 1984
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantum Hall effect in quantum electrodynamics
A unified realization of electrical quantities from the quantum International System of Units
Related Subjects
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CHARGE DENSITY
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
ENERGY LEVELS
FERMI LEVEL
FIELD EFFECT TRANSISTORS
HALL EFFECT
MOS TRANSISTORS
MOSFET
PHYSICAL PROPERTIES
QUANTIZATION
QUASI PARTICLES
SEMICONDUCTOR DEVICES
TRANSISTORS
VOLTAGE DROP