| We present a study of cyclotron resonance in graphene. Graphene is a novel two-dimensional system consisting of a single sheet of atoms arranged in a honeycomb lattice, and exhibits a unique, linear low-energy dispersion. Bilayer graphene, two sheets stacked together, is an equally interesting system displaying a second unique, but hyperbolic, dispersion. In this work, we study the quantized Landau levels of these systems in strong magnetic fields, via Fourier-transform infrared spectroscopy. We have fabricated large area single layer and bilayer graphene devices on infrared-transparent Si/SiO2 substrates, using standard electron beam lithography and thin-film liftoff techniques. At cryogenic temperatures and high magnetic fields, we measure the infrared transmission through these devices as a function of the back gate voltage, which changes the Fermi level and hence the carrier density. We analyze the normalized transmission traces, assigning the observed minima to the cyclotron resonance wherein carriers are excited between Landau levels.;In single layer graphene, we study Landau level transitions near the charge neutral Dirac point, and find a set of particle-hole symmetric transitions, both within the conduction and valence band, and between the bands. These experiments confirm the unusual B- and n -dependencies of the LL energies, where B is the magnetic field and n the LL index. The CR selection rule is determined to be Delta n = |nfinal| -- |n initial| = +/-1. The ratio of the observed interband and intraband transitions exceeds the expected value by 5%, and this excess is interpreted as an additional contribution to the transition energy from many-particle effects. We explore several higher LL transitions for both electron and hole doping of single layer graphene. The data are consistent with a renormalization of the carrier band velocity near the Dirac point, and suggest that impurity scattering strengthens at low energies. We also study the CR at the Dirac point, where the n = 0 LL is half-filled, and find the CR energy to shift upward relative to when the level is completely filled. The magnitude of this shift increases linearly with increasing B field. These results indicate a possible opening of a gap in the n = 0 LL.;The lowest four CR transitions for both electron and hole doping are studied in bilayer graphene. The transition energy dependence on magnetic field is found to depart from the values predicted by the lowest-order tight-binding theory, strongly suggesting that other band parameters, an electric field-induced gap at zero energy, and many-particle effects must be included in order to correctly model the observed CR energies.;We present experimental procedures and sample fabrication details, and describe the cryogenic dipper probes we built in order to conduct these experiments. Summaries of collaborative work on the zero-field infrared spectroscopy of single and bilayer graphene are given. |
