Effective-mass approximation in semiconductor heterostructures: One-dimensional analysis

Edge States and Strain-Driven Topological Phase Transitions in Quantum Dots in Topological Insulators

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band k→·p→ Hamiltonian or by a four-band k→·p→ Bernevig-Hughes-Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir-Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots.

CdTe Quantum Dots Embedded in Multidentate Biopolymer Based on Salep: Characterization and Optical Properties

This paper describes a novel method for surface modification of water soluble CdTe quantum dots (QDs) by using poly(acrylic acid) grafted onto salep (salep-g-PAA) as a biopolymer. As-prepared CdTe-salep-g-PAA QDs were characterized by Fourier transform infrared (FT-IR) spectrum, thermogravimetric (TG) analysis, and transmission electron microscopy (TEM). The absorption and fluorescence emission spectra were measured to investigate the effect of salep-g-PAA biopolymer on the optical properties of CdTe QDs. The results showed that the optical properties of CdTe QDs were significantly enhanced by using salep-g-PAA-based biopolymer.

Calculation of electronic surface states in superlattices via graph formulations

We propose a graph method for the analysis of electronic surface states in a complex basis superlattice terminated by surface with a multilayer clad. Using topology theory, we frame an energy equation for calculating the surface modes based on a graph model. Compared to the traditional methods, the present method does not have the problem of numerical instability for finding out the surface states of the superlattices. The other advantage is that the localized states are directly solved by the present method without spurious solutions, which usually exist in the solutions obtained by traditional methods. Numerical examples show removal of the spurious solutions by traditional methods may cause numerically instable and incorrect results.

Electronic minibands in complex basis superlattices: a numerically stable calculation

A numerically stable method for accurately determining the energy minibands of superlattices with arbitrary numbers of layers per cell is presented. Using a graph model with tangent and secant functions, we derive a set of concise and closed-form miniband edge equations for determining the miniband structure using topology theory. With the present method, it is not necessary to calculate the cosine of the Bloch phase, which may show a numerical overflow in calculation. Numerical results show that use of the miniband edge equations has better numerical stability than traditional methods in calculating the minibands of complex basis superlattices.