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Infrared magneto-spectroscopy of relativistic-like electrons in three-dimensional solids

Abstract : The use of the Dirac/Weyl equation leads to a conceptual simplification in a description of the band structure in solids at low energy scales. In particular, electron-hole excitations can be regarded as an analogue to the relativistic case with several expected phenomena to be observed in the condensed systems such as a suppressed back-scattering, linear optical conductivity or the manifestation of the Fermi arcs and particle's chirality. Moreover, the semimetallic phase also symbolizes a boundary between the trivial and topological insulators and thus play a crucial role for the material classification. The size of the gap qualitatively affects the type of the energy dispersion by a continuous crossover from the linear to parabolic bands. This fact can be easily understood as a classical or ultra-relativistic limit of the motion of a free massive particle.Infrared Fourier transform spectroscopy is a unique technique for studying optical excitations in a wide range of energies and it represents in combination with the high magnetic field a powerful tool for probing electronic structure and overcomes the main obstacle of the gapless systems that is a strong doping due to the structural disorder.The first part of the work is devoted to cadmium arsenide, where we elaborate an approach to qualitatively distinguish between the Dirac and Kane systems that was used to prove on the basis of the observed magneto-optical response the realization of the nearly gapless Kane model with a striking similarity to HgCdTe, contradicting the existence of purely Dirac cones. The magneto-reflectivity revealed a strong splitting of the plasma edge that turns into the cyclotron resonance characteristic by a squareroot-of-B dependence in the high magnetic field with a particular behaviour in the quantum limit independent on the initial Fermi level. In contrast, the magneto-transmission revealed interband Landau level transitions that could be only interpreted as a flat-to-cone type in order to preserve a full consistency of the model. The Dirac cones predicted by theory are feasible to coexist within the Kane model in the form of a substructure described by the Bodnar model that approximates the complex crystal structure by a simple antifluorite cell, which allows to use the conventional k.p-theory.In the second part, we focus on bismuth selenide entitled as an archetypal 3D topological insulator. We study a peculiar condition fulfilled for the BHZ-hamiltonian that brings intriguing properties such as an unusual relation of the spin gap and cyclotron resonance, the specific pinning between fancharts of Landau subsets or the compensated g-factors of the conduction and valence bands. The photoluminescence measurements showed a direct-gap emission, that gives a new insight to the widely accepted structure from ARPES data, where the declared camel-back structure of the valence band needs to be explained within the surface confinement and the Dirac point of the surface state should be repositioned with respect to the bulk bands. The magneto-optical response can be fully explained in a classical picture of the Pauli paramagnetism as a purely occupational effect. Such behaviour is evinced in the transmission as a gradual splitting of the interband absorption edge with a successive saturation due to the partial or total spin polarization of electrons. The related dichroism drives also a strong linear Faraday rotation described by a simple model of the Verdet constant that depends only on the Fermi level.
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  • HAL Id : tel-01795505, version 1

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Michael Hakl. Infrared magneto-spectroscopy of relativistic-like electrons in three-dimensional solids. Materials Science [cond-mat.mtrl-sci]. Université Grenoble Alpes, 2017. English. ⟨NNT : 2017GREAY085⟩. ⟨tel-01795505⟩

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