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The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance R xy exhibits steps that take on the quantized values
The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene in 2005 by Geim's group and by Philip Kim and Yuanbo Zhang. This effect provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions and proof of the Dirac fermion nature of electrons.
This is a result of the Atiyah–Singer index theorem index theorem and causes the "+1/2" term in the Hall conductivity for neutral graphene. [4] [47] In bilayer graphene, the quantum Hall effect is also observed but with only one of the two anomalies. The Hall conductivity in bilayer graphene is given by:
Each Landau level is degenerate because of the second quantum number , which can take the values =, where is an integer. The allowed values of N {\displaystyle N} are further restricted by the condition that the center of force of the oscillator, x 0 {\displaystyle x_{0}} , must physically lie within the system, 0 ≤ x 0 < L x {\displaystyle 0 ...
In 2014 researchers described the emergence of complex electronic states in bilayer graphene, notably the fractional quantum Hall effect and showed that this could be tuned by an electric field. [13] [14] [15] In 2017 the observation of an even-denominator fractional quantum Hall state was reported in bilayer graphene. [16]
The effect was reported by Geim's group and by Kim and Zhang, whose papers [13] [15] appeared in Nature in 2005. Before these experiments other researchers had looked for the quantum Hall effect [27] and Dirac fermions [28] in bulk graphite. Geim and Novoselov received awards for their pioneering research on graphene, notably the 2010 Nobel ...
At high temperatures, the quantum Hall effect could be measured. IBM built 'processors' using 100 GHz transistors on 2-inch (51 mm) graphene sheets. [55] In June 2011, IBM researchers announced the first graphene-based wafer-scale integrated circuit, a broadband radio mixer. [56] The circuit handled frequencies up to 10 GHz.
The quantum Hall effect in epitaxial graphene can serve as a practical standard for electrical resistance. The potential of epitaxial graphene on SiC for quantum metrology has been shown since 2010, displaying quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene. [25]