the first observation of QHE at room temperature (performed at B = 30-45 T) (Novoselov, 2007). More recently, sample mobility has been improved to 10-100 m2/Vs by either suspending graphene or using hexagonal boron nitride as the substrate, so that IQHE and FQHE have been observed using lower electron densities, at fields available in commercial magnets.

The knowledge and insights gained from the early quantum Hall measurements on graphene have been invaluable in elucidating the peculiar properties of that material, and high field studies of graphene continue to be indispensible today. The current outstanding questions include the nature of the QH states at f = 0, or zero charge density, which have diverging Hall and longitudinal resistance in both single-layer and bilayer graphene; quantum phase transitions among the symmetry-broken QH states; topologically nontrivial phases; presence of sky-rmions (spin textures); Wigner crystals (electron solid); and FQHE with unusual fractions or sequence due to the approximate SU(4) symmetry of the electron states in graphene (see Figure 2.14). These questions can be answered only with transport


FIGURE 2.14 Longitudinal resistance (left axis) and Hall resistance (right axis) of a graphene sample versus gate voltage, which changes the carrier density, measured at B = 35 tesla. Quantized Hall conductance values are indicated. SOURCE: Reprinted by permission from Macmillan Publishers Ltd.: Nature Physics. C.R. Dean, A.F. Young, P. Cadden-Zimansky, L. Wang, H. Ren, K. Watanabe, T. Taniguchi, P. Kim, J. Hone, and K.L. Shepard, 2011, Multicomponent fractional quantum Hall effect in graphene, Nature Physics 7:693-696. Copyright 2011.

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