We report on magneto-optical studies of Bi2Se3, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parame
ters: the fundamental bandgap and the band velocity. In a magnetic field, this model implies a unique property - spin splitting equal to twice the cyclotron energy: Es = 2Ec. This explains the extensive magneto-transport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The Es = 2Ec match differentiates the massive Dirac electrons in bulk Bi2Se3 from those in quantum electrodynamics, for which Es = Ec always holds.
Solid state physics and quantum electrodynamics with its ultra-relativistic (massless) particles meet, to their mutual beneit, in the electronic properties of one-dimensional carbon nanotubes as well as two-dimensional graphene or surfaces of topolog
ical insulators. However, clear experimental evidence for electronic states with conical dispersion relations in all three dimensions, conceivable in certain bulk materials, is still missing. In the present work, we fabricate and study a zinc-blend crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition. Three-dimensional massless electrons with a velocity of about 10$^6$ m/s are observed in this material, as testifed by: (i) the dynamical conductivity which increases linearly with the photon frequency, (ii) in a magnetic field $B$, by a $sqrt{B}$ dependence of dipole-active inter-Landau-level resonances and (iii) the spin splitting of Landau levels, which follows a $sqrt{B}$ dependence, typical of ultra-relativistic particles but not really seen in any other electronic system so far.
HgTe/HgCdTe quantum wells with the inverted band structure have been probed using far infrared magneto-spectroscopy. Realistic calculations of Landau level diagrams have been performed to identify the observed transitions. Investigations have been gr
eatly focused on the magnetic field dependence of the peculiar pair of zero-mode Landau levels which characteristically split from the upper conduction and bottom valence bands, and merge under the applied magnetic field. The observed avoided crossing of these levels is tentatively attributed to the bulk inversion asymmetry of zinc blend compounds.
We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to B = 34 T. Two series of absorption lines whose energy scales as sqrtB and B are present in the spectra and identified as contributions of massless ho
les at the H point and massive electrons in the vicinity of the K point, respectively. We find that the optical response of the K point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective inter-layer coupling 2gamma_1, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the c-axis. The K point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.
Multi-layer epitaxial graphene (MEG) is investigated using far infrared (FIR) transmission experiments in the different limits of low magnetic fields and high temperatures. The cyclotron-resonance like absorption is observed at low temperature in mag
netic fields below 50 mT, allowing thus to probe the nearest vicinity of the Dirac point and to estimate the conductivity in nearly undoped graphene. The carrier mobility is found to exceed 250,000 cm$^2$/(V.s). In the limit of high temperatures, the well-defined Landau level (LL) quantization is observed up to room temperature at magnetic fields below 1 T, a phenomenon unique in solid state systems. A negligible increase in the width of the cyclotron resonance lines with increasing temperature indicates that no important scattering mechanism is thermally activated, supporting recent expectations of high room-temperature mobilities in graphene.
Magneto-transmission of a thin layer of bulk graphite is compared with spectra taken on multilayer epitaxial graphene prepared by thermal decomposition of a SiC crystal. We focus on the spectral features evolving as sqrt{B}, which are evidence for th
e presence of Dirac fermions in both materials. Whereas the results on multi-layer epitaxial graphene can be interpreted within the model of 2D Dirac fermions, the data obtained on bulk graphite can only be explained taking into account the 3D nature of graphite, e.g. by using the standard Slonczewski-Weiss-McClure model.
Far infrared magneto-transmission spectroscopy has been used to probe relativistic fermions in highly oriented pyrolytic and natural graphite. Nearly identical transmission spectra of those two materials are obtained, giving the signature of Dirac fe
rmions via absorption lines with an energy that scales as sqrt{B}. The Fermi velocity is evaluated to be c*=1.02x10^6 m/s and the pseudogap at the H point is estimated to be below 10 meV.
We report on far infrared magneto-transmission measurements on a thin graphite sample prepared by exfoliation of highly oriented pyrolytic graphite. In magnetic field, absorption lines exhibiting a blue-shift proportional to sqrtB are observed. This
is a fingerprint for massless Dirac holes at the H point in bulk graphite. The Fermi velocity is found to be c*=1.02x10^6 m/s and the pseudogap at the H point is estimated to be below 10 meV. Although the holes behave to a first approximation as a strictly 2D gas of Dirac fermions, the full 3D band structure has to be taken into account to explain all the observed spectral features.
