and/or optical measurements in dc and pulsed high magnetic fields with varying field angles and temperature.
A rather unique direction of graphene research is strain-based engineering of its electrical properties, which takes advantage of the “softer” side of graphene. Being both an excellent electrical conductor and an elastic membrane that can sustain more than 25 percent strain, graphene’s electrical properties can be strongly affected by strain and morphology. Moreover, inhomogeneous strains in graphene affect the electronic motion in a similar way to an applied magnetic field. In fact, electrons in highly strained graphene have been observed to experience pseudomagnetic fields greater than 300 T (Levy et al., 2010). Thus, one can tailor graphene’s electronic properties via careful design of strains. Interplay of such enormous pseudomagnetic field with the real magnetic field will be an exciting frontier and a step toward strain-based graphene electronics.
A closely related allotrope of graphene is carbon nanotubes (Smalley et al., 2001), which can be visualized as seamless cylinders of graphene, with diameters ~1 nm for single-walled carbon nantoubes and up to hundreds of nanometers for multiwalled carbon nanotubes. Depending on the orientation of the cylinder axis relative to the atomic honeycomb lattice, a carbon nanotube can be either a one-dimensional metal or semiconductor. High magnetic fields have been employed to probe the spin-orbit interactions, to close band gaps in semiconducting nanotubes, and to induce spin polarization and Aharonov-Bohm quantum interference effects. These high field studies are expected to continue to yield important information on fundamental interactions in 1D wires.
One of the most interesting semimetal materials is bismuth, which has an unusual band structure consisting of one hole and three electron pockets. The electrons are massless, similar to graphene, except that here the degenerate Dirac point occurs slightly below the Fermi energy of the pure material. The density of electrons and holes in bismuth is exceptionally low. Consequently, the so-called “quantum limit,” where all the charge carriers are confined to the lowest Landau level, can be achieved at relatively modest magnetic field ~ 10 T, above which electrical properties were expected to be featureless. Surprisingly, recent experiments at magnetic fields up to 31 T reveal striking oscillations and sharp rises in measurements of the Nernst effect, resistivity, and magnetization, as well as signatures for first-order phase transition induced by magnetic fields (Behnia et al., 2007; Li et al., 2008). Theoretical investigation (Alicea and Balents, 2009) suggests that the