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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:
Over the years precisions of parts-per-trillion in the Hall resistance quantization and giant quantum Hall plateaus have been demonstrated. Developments in the encapsulation and doping of epitaxial graphene have led to the commercialization of epitaxial graphene quantum resistance standards. [353]
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.
The name of Dirac cone comes from the Dirac equation that can describe relativistic particles in quantum mechanics, proposed by Paul Dirac. Isotropic Dirac cones in graphene were first predicted by P. R. Wallace in 1947 [ 6 ] and experimentally observed by the Nobel Prize laureates Andre Geim and Konstantin Novoselov in 2005.
The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied.
The two-dimensional electron system in graphene can be tuned to either a 2DEG or 2DHG (2-D hole gas) by gating or chemical doping. This has been a topic of current research due to the versatile (some existing but mostly envisaged) applications of graphene. [2] A separate class of heterostructures that can host 2DEGs are oxides.
Graphene reacts to the infrared spectrum at room temperature, albeit with sensitivity 100 to 1000 times too low for practical applications. However, two graphene layers separated by an insulator allowed an electric field produced by holes left by photo-freed electrons in one layer to affect a current running through the other layer.
The quantum Hall transition will therefore not be in the Fermi-liquid universality class, but in the 'F-invariant' universality class that has a different value for the critical exponent. [5] The semi-classical percolation picture of the quantum Hall transition is therefore outdated (although still widely used) and we need to understand the ...