Resonant Inelastic X-ray Scattering (RIXS)
 is an X-ray in, X-ray out technique that enables one to study the 
dispersion of excitations in solids. In this thesis, we investigated how
 various elementary excitations of transition metal oxides show up in 
RIXS spectra.

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Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

Electrons and Phonons

Author(s): Streubel, R; Fischer, P; Kronast, F; Kravchuk, VP; Sheka, DD; Gaididei, Y; Schmidt, OG; Makarov, D | Abstract: Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

Magnetism in curved geometries

The Wigner-function (WF) approach to quantum electron transport in semiconductors is reviewed in this paper. The main definitions and properties related to the WF are presented, with a discussion of the various forms of the dynamical equations that govern its evolution. Monte Carlo solutions of such equations are also discussed. Interactions of electrons with applied fields, potential profiles, and phonons are analysed in detail. Finally, several physical applications are presented. Each topic has been developed from basic principles for the benefit of interested readers who are not experts in the particular subjects discussed in this paper.

https://iopscience.iop.org/article/10.1088/0034-4885/67/7/R01/pdf

The Wigner-function approach to non-equilibrium electron transport

We report on observation of coherent electron transport in suspended high-quality InAs nanowire-based devices. The InAs nanowires were grown by low-temperature gold-assisted vapor-liquid-solid molecular-beam-epitaxy. The high quality of the nanowires was achieved by removing the typically found stacking faults and reducing possibility of Au incorporation. Minimizing substrate-induced scattering in the device was achieved by suspending the nanowires over predefined grooves. Coherent transport involving more than a single one-dimensional mode transport was observed in the experiment and manifested by Fabry-Perot conductance oscillations. The length of the Fabry-Perot interferometer, deduced from the period of the conductance oscillations, was found to be close to the physical length of the device. The high oscillations visibility imply nearly ballistic electron transport through the nanowire.

Multimode Fabry-Perot conductance oscillations in suspended stacking-faults-free InAs nanowires.

We derive the Schrodinger equation for a spinless charged particle constrained to move on a curved surface in the presence of an electric and magnetic field. The particle is confined on the surface using a thin-layer procedure, which gives rise to the well-known geometric potential. The electric and magnetic fields are included via the four potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, we derive an analytic form of the Hamiltonian for spherical, cylindrical, and toroidal surfaces.

Schrödinger equation for a particle on a curved surface in an electric and magnetic field.

We study the electronic states of core multishell semiconductor nanowires, including the effect of strong magnetic fields. We show that the multishell overgrowth of a free-standing nanowire, together with the prismatic symmetry of the substrate, may induce quantum confinement of carriers in a set of quasi-1D quantum channels corresponding to the nanowire edges. Localization and interchannel tunnel coupling are controlled by the curvature at the edges and the diameter of the underlying nanowire. We also show that a magnetic field may induce either Aharonov-Bohm oscillations of the energy levels in the axial configuration, or a dimensional transition of the quantum states from quasi-1D to Landau levels for fields normal to the axis. Explicit predictions are given for nanostructures based on GaAs, InAs, and InGaN with different symmetries.

Magnetic states in prismatic core multishell nanowires.

We study the electronic states of core multi-shell semiconductor nanowires, including the effect of strong magnetic fields. We show that the multi-shell overgrowth of a free-standing nanowire, together with the prismatic symmetry of the substrate, may induce quantum confinement of carriers in a set of quasi-1D quantum channels corresponding to the nanowire edges. Localization and inter-channel tunnel coupling are controlled by the curvature at the edges and the diameter of the underlying nanowire. We also show that a magnetic field may induce either Aharonov-Bohm oscillations of the energy levels in the axial configuration, or a dimensional transition of the quantum states from quasi-1D to Landau levels for fields normal to the axis. Explicit predictions are given for nanostructures based on GaAs, InAs, and InGaN with different symmetries.

Magnetic states in prismatic core multishell nanowires

We compute the single-particle states of a two-dimensional (2D) electron gas confined to the surface of a cylinder immersed in a magnetic field. The envelope-function equation is solved exactly for both a homogeneous and a periodically modulated magnetic field perpendicular to the cylinder axis. The nature and energy dispersion of the quantum states reflects the interplay between different length scales, namely, the cylinder diameter, the magnetic length, and, possibly, the wavelength of the field modulation. We show that a transverse homogeneous magnetic field drives carrier states from a quasi-2D (cylindrical) regime to a quasi-one-dimensional regime where carriers form channels along the cylinder surface. Furthermore, a magnetic field which is periodically modulated along the cylinder axis may confine the carriers to tunnel-coupled stripes, rings, and dots on the cylinder surface depending on the ratio between the field periodicity and the cylinder radius. Results in different regimes are traced to either incipient Landau-level formation or Aharonov-Bohm behavior.

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Cylindrical two-dimensional electron gas in a transverse magnetic field

The effective potential originated by the nonplanar geometry of a two-dimensional electron gas (2DEG) modifies its coherent transport properties. To date no direct evidence of such purely geometric potential has been revealed. Here we expose its effects by computing the transmission characteristics of a semiconductor cylindrical 2DEG forming a Y junction. For some cylinder radii, we find that the activation thresholds of the transmission channels in the two drain leads are exchanged, with this effect being robust against the geometrical details of the three-terminal junction.

Giulio Ferrari

Papers

Schrödinger equation for a particle on a curved surface in an electric and magnetic field.

Magnetic states in prismatic core multishell nanowires.

Magnetic states in prismatic core multishell nanowires

Cylindrical two-dimensional electron gas in a transverse magnetic field

Surface carrier transport in Y nanojunctions: Signatures of the geometric potential