A transfer matrix method for the analysis of fractal quantum potentials

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential

Tunable Multifunctional Topological Insulators in Ternary Heusler Compounds

Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare earth element Ln which can realize additional properties ranging from superconductivity (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.Comment: 20 pages, 5 figure