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.
Compressively strained epitaxial (001) EuTiO3 thin films of tetragonal symmetry have been deposited on (001) (LaAlO3)_0.29-(SrAl_{1/2}Ta_{1/2}O3)_0.71 (LSAT) substrates by reactive molecular-beam epitaxy. Enhancement of the Neel temperature by 1 K wi
th 0.9% compressive strain was revealed. The polar phonons ofthe films have been investigated as a function of temperature and magnetic field by means of infrared reflectance spectroscopy. All three infrared active phonons show strongly stiffened frequencies compared to bulk EuTiO3 in accordance with first principles calculations. The phonon frequencies exhibit gradual softening on cooling leading to an increase in static permittivity. A new polar phonon with frequency near the TO1 soft mode was detected below 150 K. The new mode coupled with the TO1 mode was assigned as the optical phonon from the Brillouin zone edge, which is activated in infrared spectra due to an antiferrodistortive phase transition and due to simultaneous presence of polar and/or magnetic nanoclusters. In the antiferromagnetic phase we have observed a remarkable softening of the lowest-frequency polar phonon under an applied magnetic field, which qualitatively agrees with first principles calculations. This demonstrates the strong spin-phonon coupling in EuTiO3, which is responsible for the pronounced dependence of its static permittivity on magnetic field in the antiferromagnetic phase.
Cyclotron resonance has been measured in far-infrared transmission of GaAs/Al$_x$Ga$_{1-x}$As heterostructures with an etched hexagonal lateral superlattice. Non-linear dependence of the resonance position on magnetic field was observed as well as it
s splitting into several modes. Our explanation, based on a perturbative calculation, describes the observed phenomena as a weak effect of the lateral potential on the two-dimensional electron gas. Using this approach, we found a correlation between parameters of the lateral patterning and the created effective potential and obtain thus insights on how the electronic miniband structure has been tuned. The miniband dispersion was calculated using a simplified model and allowed us to formulate four basic criteria that have to be satisfied to reach graphene-like physics in such systems.
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.
Magnetotransport of natural graphite and highly oriented pyrolytic graphite (HOPG) has been measured at mK temperatures. Quantum oscillations for both electron and hole carriers are observed with orbital angular momentum quantum number up to $Napprox
90$. A remarkable agreement is obtained when comparing the data and the predictions of the Slonczewski--Weiss--McClure tight binding model for massive fermions. No evidence for Dirac fermions is observed in the transport data which is dominated by the crossing of the Landau bands at the Fermi level, corresponding to $dE/dk_z=0$, which occurs away from the $H$ point where Dirac fermions are expected.
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.
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 have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However,
at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.
