We report infrared studies of the Landau level (LL) transitions in single layer graphene. Our specimens are density tunable and show in situ half-integer quantum Hall plateaus. Infrared transmission is measured in magnetic fields up to B=18 T at selected LL fillings. Resonances between hole LLs and electron LLs, as well as resonances between hole and electron LLs, are resolved. Their transition energies are proportional to sqrt[B], and the deduced band velocity is (-)c approximately equal to 1.1 x 10(6) m/s. The lack of precise scaling between different LL transitions indicates considerable contributions of many-particle effects to the infrared transition energies.

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B=18 T, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow square root[B] for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.

We report a study of the cyclotron resonance (CR) transitions to and from the unusual n=0 Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the n=0 level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the n=0 level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.

We have studied far infrared transmission spectra of α ′ -NaV2O5 between 3 and 200 cm −1 in polarizations of incident light parallel to a, b, and c crystallographic axes in magnetic fields up to 33 T. The temperature dependence of the transmission spectra was studied close to and below the phase transition temperature Tc = 34 K. The triplet origin of an excitation at 65.4 cm −1 (8.13 meV) is revealed by splitting in the magnetic field. The g-factors for the triplet state are ga = 1.96 ± 0.02, g b = 1.975 ± 0.004 and gc = 1.90 ± 0.03. The magnitude of the spin gap at low temperatures is found to be magnetic field independent at least up to 33 T. All other infrared-active transitions appearing below Tc are ascribed to zone-folded phonons. Two different dynamic DzyaloshinskiiMoriya (DM) mechanisms have been discovered that contribute to the oscillator strength of the otherwise forbidden singlet to triplet transition. First, the strongest singlet to triplet transition is an electric dipole transition where the polarization of the incident light's electric field is parallel to the ladder rungs (E1 a). This electric dipole active transition is allowed by the dynamic DM interaction created by a high frequency optical a-axis phonon. Second, in the incident light polarization perpendicular to the ladder planes (E1 c) an enhancement of the singlet to triplet transition is observed when the applied magnetic field shifts the singlet to triplet resonance frequency to match the 68 cm −1 c-axis phonon energy. The origin of the second mechanism is the dynamic DM interaction created by the 68 cm −1 c-axis optical phonon. The strength of the dynamic DM is calculated for both mechanisms using the presented theory.