Flux-periodic oscillations in proximitized core-shell nanowires.

Flux-periodic oscillations of the superconducting gap in proximitized core-shell nanowires are explored. Periodicity of oscillations in the energy spectrum of a cylindrical nanowire is compared with nanowires having hexagonal and square cross-section geometry, along with the effects of Zeeman and Rashba spin-orbit interaction. A transition betweenh/eandh/2eperiodicity is found and shown to be dependent on the chemical potential, with correspondence to degeneracy points of the angular momentum quantum number. For a thin shell of a square nanowire, solelyh/eperiodicity is found in the infinite wire spectrum and shown to result from energy separation between the lowest groups of excited states.

Effect of impurities on charge and heat transport in tubular nanowires.

We calculate the charge and heat currents carried by electrons, originating from a temperature gradient and a chemical potential difference between the two ends of tubular nanowires with different geometries of the cross-sectional areas: circular, square, triangular, and hexagonal. We consider nanowires based on InAs semiconductor material, and use the Landauer-Büttiker approach to calculate the transport quantities. We include impurities in the form of delta scatterers and compare their effect for different geometries. The results depend on the quantum localization of the electrons along the edges of the tubular prismatic shell. For example, the effect of impurities on the charge and heat transport is weaker in the triangular shell than in the hexagonal shell, and the thermoelectric current in the triangular case is several times larger than in the hexagonal case, for the same temperature gradient.

Majorana zero modes in nanowires with combined triangular and hexagonal geometry.

The effects of geometry on the hosting of Majorana zero modes are explored in core-shell nanowires with a hexagonal core and a triangular shell, and vice versa. The energy interval separating electronic states localized in the corners from states localized on the sides of the shell is shown to be larger for a triangular nanowire with a hexagonal core, than a triangular one. We build the topological phase diagram for both cases and compare them to earlier work on prismatic nanowires with matching core and shell geometry. We suggest that a dual core nanowire is needed to allow for braiding operations of Majorana zero modes at the nanowire end plane.

Anisotropic light scattering by prismatic semiconductor nanowires.

Anisotropic transverse light scattering by prismatic nanowires is a natural outcome of their geometry. In this work, we perform numerical calculations of the light scattering characteristics for nanowires in the optical and near-infrared range and explore the possibility of tuning the directivity by changing the angle of light incidence. The scattering cross section and the directivity of the scattered light when it is incident perpendicular to a facet or to an edge of the prism are investigated both with transverse electric and with transverse magnetic polarizations. The phenomenology includes Mie resonances and guided modes yielding together rich and complex spectra. We consider nanowires with hexagonal, square and triangular cross sections. The modes that are most sensitive to the incidence angle are the hexapole for the hexagonal case and the quadrupole for the square case. Higher order modes are also sensitive, but mostly for the square geometry. Our results indicate the possibility of a flexible in-situ tunability of the directivity simply by rotating the nanowire profile relatively to the direction of the incident light which could offer potential advantages in applications such as switching or sensing.

Corner and side localization of electrons in irregular hexagonal semiconductor shells.

We discuss the low energy electronic states in hexagonal rings. These states correspond to the transverse modes in core-shell nanowires built of III-V semiconductors which typically have a hexagonal cross section. In the case of symmetric structures the 12 lowest states (including the spin) are localized in the corners, while the next following 12 states are localized mostly on the sides. Depending on the material parameters, in particular the effective mass, the ring diameter and width, the corner and side states may be separated by a considerable energy gap, ranging from few to tens of meV. In a realistic fabrication process geometric asymmetries are unavoidable, and therefore the particles are not symmetrically distributed between all corner and side areas. Possibly, even small deformations may shift the localization of the ground state to one of the sides. The transverse states or the transitions between them may be important in transport or optical experiments. Still, up to date, there are only very few experimental investigations of the localization-dependent properties of core-shell nanowires.

Breakdown of Corner States and Carrier Localization by Monolayer Fluctuations in Radial Nanowire Quantum Wells.

We report a comprehensive study of the impact of the structural properties in radial GaAs-Al0.3Ga0.7As nanowire-quantum well heterostructures on the optical recombination dynamics and electrical transport properties, emphasizing particularly the role of the commonly observed variations of the quantum well thickness at different facets. Typical thickness fluctuations of the radial quantum well observed by transmission electron microscopy lead to pronounced localization. Our optical data exhibit clear spectral shifts and a multipeak structure of the emission for such asymmetric ring structures resulting from spatially separated, yet interconnected quantum well systems. Charge carrier dynamics induced by a surface acoustic wave are resolved and prove efficient carrier exchange on native, subnanosecond time scales within the heterostructure. Experimental findings are corroborated by theoretical modeling, which unambiguously show that electrons and holes localize on facets where the quantum well is the thickest and that even minute deviations of the perfect hexagonal shape strongly perturb the commonly assumed 6-fold symmetric ground state.

Robust topological phase in proximitized core-shell nanowires coupled to multiple superconductors.

We consider core-shell nanowires with prismatic geometry contacted with two or more superconductors in the presence of a magnetic field applied parallel to the wire. In this geometry, the lowest energy states are localized on the outer edges of the shell, which strongly inhibits the orbital effects of the longitudinal magnetic field that are detrimental to Majorana physics. Using a tight-binding model of coupled parallel chains, we calculate the topological phase diagram of the hybrid system in the presence of non-vanishing transverse potentials and finite relative phases between the parent superconductors. We show that having finite relative phases strongly enhances the stability of the induced topological superconductivity over a significant range of chemical potentials and reduces the value of the critical field associated with the topological quantum phase transition.

Excitons in Core-Shell Nanowires with Polygonal Cross Sections.

The distinctive prismatic geometry of semiconductor core-shell nanowires leads to complex localization patterns of carriers. Here, we describe the formation of optically active in-gap excitonic states induced by the interplay between localization of carriers in the corners and their mutual Coulomb interaction. To compute the energy spectra and configurations of excitons created in the conductive shell, we use a multielectron numerical approach based on the exact solution of the multiparticle Hamiltonian for electrons in the valence and conduction bands, which includes the Coulomb interaction in a nonperturbative manner. We expose the formation of well-separated quasidegenerate levels, and focus on the implications of the electron localization in the corners or on the sides of triangular, square, and hexagonal cross sections. We obtain excitonic in-gap states associated with symmetrically distributed electrons in the spin singlet configuration. They acquire large contributions due to Coulomb interaction, and thus are shifted to much higher energies than other states corresponding to the conduction electron and the vacancy localized in the same corner. We compare the results of the multielectron method with those of an electron-hole model, and we show that the latter does not reproduce the singlet excitonic states. We also obtain the exciton lifetime and explain selection rules which govern the recombination process.

In-gap corner states in core-shell polygonal quantum rings.

We study Coulomb interacting electrons confined in polygonal quantum rings. We focus on the interplay of localization at the polygon corners and Coulomb repulsion. Remarkably, the Coulomb repulsion allows the formation of in-gap states, i.e., corner-localized states of electron pairs or clusters shifted to energies that were forbidden for non-interacting electrons, but below the energies of corner-side-localized states. We specify conditions allowing optical excitation to those states.

Multi-domain electromagnetic absorption of triangular quantum rings.

We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core-shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side thickness or corners' symmetry. For equilateral triangles, the lowest six energy states (including spin) are grouped in an energy shell, are localized only around corner areas, and are separated by a large energy gap from the states with higher energy which are localized on the sides of the triangle. The energy levels strongly depend on the aspect ratio of the triangle sides, i.e., thickness/length ratio, in such a way that the energy differences are not monotonous functions of this ratio. In particular, the energy gap between the group of states localized in corners and the states localized on the sides strongly decreases with increasing the side thickness, and then slightly increases for thicker samples. With increasing the thickness the low-energy shell remains distinct but the spatial distribution of these states spreads. The behavior of the energy levels and localization leads to a thickness-dependent absorption spectrum where one transition may be tuned in the THz domain and a second transition can be tuned from THz to the infrared range of electromagnetic spectrum. We show how these features may be further controlled with an external magnetic field. In this work the electron-electron Coulomb repulsion is neglected.

Few-photon model of the optical emission of semiconductor quantum dots.

The Jaynes-Cummings model provides a well established theoretical framework for single electron two level systems in a radiation field. Similar exactly solvable models for semiconductor light emitters such as quantum dots dominated by many particle interactions are not known. We access these systems by a generalized cluster expansion, the photon-probability cluster expansion: a reliable approach for few-photon dynamics in many body electron systems. As a first application, we discuss vacuum Rabi oscillations and show that their amplitude determines the number of electrons in the quantum dot.