The structural and vibrational properties of bismuth selenide (Bi 2 Se 3 ) have been studied by means of x-ray diffraction and Raman scattering measurements up to 20 and 30 GPa, respectively. The measurements have been complemented with ab initio total-energy and lattice dynamics calculations. Our experimental results evidence a phase transition from the low-pressure rhombohedral (R-3m) phase (α-Bi 2 Se 3 ) with sixfold coordination for Bi to a monoclinic C2/m structure (β-Bi 2 Se 3 ) with sevenfold coordination for Bi above 10 GPa. The equation of state and the pressure dependence of the lattice parameters and volume of α and β phases of Bi 2 Se 3 are reported. Furthermore, the presence of a pressure-induced electronic topological phase transition in α-Bi 2 Se 3 is discussed. Raman measurements evidence that Bi 2 Se 3 undergoes two additional phase transitions around 20 and 28 GPa, likely toward a monoclinic C2/c and a disordered body-centered cubic structure with 8-fold and 9-or 10-fold coordination, respectively. These two high-pressure structures are the same as those recently found at high pressures in Bi 2 Te 3 and Sb 2 Te 3 . On pressure release, Bi 2 Se 3 reverts to the original rhombohedral phase after considerable hysteresis. Symmetries, frequencies, and pressure coefficients of the Raman and infrared modes in the different phases are reported and discussed.

We report an experimental and theoretical lattice dynamics study of antimony telluride (Sb 2 Te 3 ) up to 26 GPa together with a theoretical study of its structural stability under pressure. Raman-active modes of the low-pressure rhombohedral (R-3m) phase were observed up to 7.7 GPa. Changes of the frequencies and linewidths were observed around 3.5 GPa where an electronic topological transition was previously found. Raman mode changes evidence phase transitions at 7.7, 14.5, and 25 GPa. The frequencies and pressure coefficients of the new phases above 7.7 and 14.5 GPa agree with those calculated for the monoclinic C2/m and C2/c structures recently observed at high pressures in Bi 2 Te 3 , and also for the C2/m phase in the case of Bi 2 Se 3 and Sb 2 Te 3 . Above 25 GPa no Raman-active modes are observed in Sb 2 Te 3 similarly to the case of Bi 2 Te 3 and Bi 2 Se 3 . Therefore, it is possible that the structure of Sb 2 Te 3 above 25 GPa is the same disordered bcc phase already found in Bi 2 Te 3 by x-ray diffraction studies. Upon pressure release, Sb 2 Te 3 reverts back to the original rhombohedral phase after considerable hysteresis. Raman-and IR-mode symmetries, frequencies and pressure coefficients in the different phases are reported and discussed.

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 Diractype Hamiltonian for massive particles with only two parameters: 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.PACS numbers: 71.70. Di, 76.40.+b, Inspiring analogies to relativistic systems have largely helped to elucidate the electronic properties of twodimensional graphene [1,2], surface states of topological insulators (TIs) [3][4][5][6], novel three-dimensional (3D) semimetals [7][8][9] as well as certain narrow gap semiconductors [10]. Here, we report on magneto-optical studies of bulk Bi 2 Se 3 , which imply the approximate applicability of the Dirac Hamiltonian for massive relativistic particles to approach the band structure of this popular representative of the TI family.The dispersion relations of genuine massive Dirac fermions in quantum electrodynamics are defined by two parameters: the energy gap 2∆ between particles and antiparticles and velocity parameter v D . At low energies, i.e., in the non-relativistic limit, these dispersions become parabolic and characterized by the same effective mass m D = ∆/v 2 D (rest Dirac mass). Such dispersions resemble the cartoon sketch of a direct gap semiconductor, which may be conventionally described using Schrödinger equation, completed by extra Pauli terms in order to include the spin degree of freedom. In contrast, no additional terms are needed when Dirac equation is employed, since it inherently accounts for spin-related effects. For instance, when the magnetic field B is applied, Dirac equation describes both cyclotron (E c ) as well as spin (E s ) splitting of the electronic states and implies that these two splitting energies are the same and linear with B in the non-relativistic approximation:For free electrons, this condition is equivalent to the effective g factor of 2 in E s = gµ B B (Bohr magneton µ B = e /2m 0 ) [11].In this Letter, we demonstrate experimentally that the conduction and valence bands of Bi 2 Se 3 are both, with a good precision, parabolic (perpendicular to the c-axis) and characterized by approximately the same effective mass. This crucial observation implies a great simplification of the multi-parameter Dirac Hamiltonian [5,12] commonly used to describe the bands of this material.The resulting simplified Dirac Hamiltonian differs from that of the genuine quantum electrodynamics system only by relevant (additional) diagonal dispersive terms, and importantly, it remains to be defined by two parameters only: by the bandgap energy 2∆ an...

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Spectrum of -Bi 2 Te 3 at 13.3 GPa and the corresponding fit of Voigt profiles corresponding to the Raman-active modes of the C2/m structure.