Quantization of the Magnetoresistance and Origin of the Empirical Resistivity Rule Horst Stormer - Aron Pinczuk, Columb

1. B A 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 world’s 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)

2. 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.