Magnetic breakdown refers to the tunneling of electrons between distinct orbitals beyond a critical magnetic field. In the past, studies on magnetic breakdown have largely focused on the semiclassical regime, by detecting the interference difference frequencies (usually designated as β − α) in the Shubnikov-de Haas or de Haas-van Alphen oscillations. Recently, researchers derived quantization rules under magnetic breakdown through matching WKB functions across regions of strong quantum interference. A host of topological solids were found to inevitably undergo magnetic breakdown and exhibit a quasi-random spectrum.
In this thesis I report the observation of magnetic breakdown in square net layered charge-density-wave (CDW) topological material GdTe3 under hydrostatic pressure. The high mobilities of electrons in symmetry-protected pockets lead to sharp quantum oscillations in the magnetoresistance (MR) of GdTe3. The applied pressure causes FS reconstruction and the appearance of a second CDW. For a narrow pressure region from 16.8 kbar to 21.6 kbar, we observe Shubnikov-de Haas oscillations that appear chaotic and quasi-random. The FFT spectrum of the quantum oscillations in the chaotic region is found to be “continuous”.
In the rest of the thesis I explore three other topological chalcogenides: CeSbxTe2−x−δ, ZrTe5, and Pb1−xSnxSe/Pb1−xSnxTe. CeSbxTe2−x−δ exhibits Dirac fermions which are protected by non-symmorphic symmetries that can survive under CDW. Here we study the magnetic and transport properties in several CeSbxTe2−x−δ compounds. Researchers have been exploring whether ZrTe5 is a Weyl semimetal or a topological insulator. We find that the properties of ZrTe5 vary with the growing conditions. In one batch of ZrTe5 we observe negative MR and anomalous Hall effect which are signs of a Weyl semimetallic phase and in another we see 2D quantum oscillations and RT/MR behaviors under pressure that suggest a TI phase. In the last part of the thesis I report the thermoelectric properties and quantum phase transitions in topological crystalline insulators Pb1−xSnxSe/Pb1−xSnxTe.