Magneto-transport in topological nanostructures due to novel spin states and trajectories

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In 1980, the quantum Hall (QH) effect was observed in a two-dimensional electron gas subject to an external magnetic field. The QH state was the first example of an electronic structure exhibiting a topological invariant: its behavior depends only on the system’s topological structure and is thus immune to scattering events from impurities and geometric perturbations. A quarter of a century later, the two-dimensional (2D) topological insulator (TI) was discovered as a realization of the quantum spin Hall effect, which is driven by a strong spin-orbit coupling rather than an external magnetic field, and is topologically protected by time-reversal symmetry. TIs are interesting materials for use in future electronic and spintronic technologies. The discovery of the 2D TI triggered the search for other topological materials, including the TI (i.e. three-dimensional TI), and Weyl and Dirac semimetals.When such a topological material is subject to an applied magnetic field, the QH and topological states join and can even hybridize to form new magnetic states, like for instance unusual spin-momentum-locked magnetic trajectories in phase space. Such states and trajectories gather great interest since they exhibit exotic magnetic and spin transport properties. In addition to new magnetic states, the magnetoresistance (MR) measured in topological nanostructures is generally non-saturating; the MR slope increasing with the field can be either linear, quadratic, or square root, depending on the class of the topological material and the geometry.In this project we will study new magnetic states and trajectories by taking into account effects of both the electronic-state topology and the nanostructure geometry. We propose and search for: (1) rich forms of magnetic trajectories exhibiting different spin-orbital dynamics in a TI nanostructure, and (2) a new magnetic state, namely, the resonant Weyl orbit, in a topological-semimetal slab. We aim at understanding the exotic MR and the spin transport in topological nanostructures in both quantum and classical transport regimes by integrating the contributions of these magnetic states and trajectories. The investigations will provide versatile platforms for designing advanced spintronics and magneto-electronics based on topological materials.