Quantization of the Magnetoresistance and

1
Quantization of the Magnetoresistance and Origin
of the Empirical Resistivity Rule Horst Stormer -
Aron Pinczuk, Columbia University, DMR-0352738
The integer (IQHE) and fractional quantum Hall
effects (FQHE) have been discovered some 20
years ago. The IQHE has become the worlds
resistance standard. The FQHE told us about
fractional electron charge. The measurements
determine two resistances the Hall resistance,
which is quantized in plateaus and the
magnetoresistance, which vanishes in the region
of quantized Hall plateaus. In recent
experiments on FQHE at ultra-low temperatures of
6mK the magneto resistance also showed quantized
plateaus. Their origin could be traced back to a
slight electron density gradient across the
sample of about 1/cm. This discovery actually
explains the origin of a previous, empirical
resistivity rule between Hall resistance and
magneto resistance.
Quantization of magneto resistance at 6mK as a
consequence of a small density gradient in a
two-dimensional electron system
Physical Review Letters, 95, 066808 (2005)
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Quantization of the Magneto Resistance and
Origin of the Empirical Resistivity Rule Horst
Stormer - Aron Pinczuk, Columbia University,
DMR-0352738

• Education
• This is a collaborative program which leverages
  the expertise from Columbia U., Princeton U., the
  National High Magnetic Field Lab, U. Florida, and
  Bell Labs while training students and postdocs on
  complex instrumentation and in forefront science.

• Societal Impact
• The quantum Hall effect is important to
  metrology. Understanding the mechanisms
  underlying the quantization and its accuracy is
  relevant to electronic technologies. FQHE states
  at this magnetic field regime offer the
  possibility to perform a new type of quantum
  computations.