Geometry-Driven Tunability of Edge States in Topological Core–Shell Nanowires

The study of new nanoscopic heterostructures composed of different materials follows the idea that the presence of boundary conditions, interfaces and combinations of materials will produce appropriate spectral properties or quantum states, resulting in new devices. Here, we present a detailed study of two kinds of nanowires formed using topological insulators. First, we consider cylindrical nanowires with a cylindrical core of constant radius along the wire, covered by a shell of uniform width. The core and the shell materials are different topological insulators. We thoroughly study the spectra of distinct wires, considering combinations of materials and sizes of the core and shell radii. We also study the expectation values of the spin operators. Then, we consider wires with only a cylindrical shell. For this case, we pay special attention to the limit when the width of the shell is approximately an order of magnitude smaller than the inner and outer radii of the shell. As we use a high-accuracy variational method to obtain the spectra and quantum states, we also study information-like quantities such as the fidelity and quantum entropy of the topological and normal states of the wires.