Effective one-dimensional square well for two-dimensional quantum wires

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.

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.

Path integral Monte Carlo on a lattice. II. Bound states

The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.

Resonant Anderson localization in segmented wires

We discuss a model of random segmented wire, with linear segments of two-dimensional wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy, a finite segmented wire typically evolves from localized to diffusive to ballistic behavior in each conductance plateau.

A Model System for Dimensional Competition in Nanostructures: A Quantum Wire on a Surface

The retarded Green’s function (E−H + iε)⁻¹is given for a dimensionally hybrid Hamiltonian which interpolates between one and two dimensions. This is used as a model for dimensional competition in propagation effects in the presence of one-dimensional subsystems on a surface. The presence of a quantum wire generates additional exponential terms in the Green’s function. The result shows how the location of the one-dimensional subsystem affects propagation of particles.