Seminario di Michele Governale (Victoria U. of Wellington)

30 Novembre 2022 alle ore 16:00
Aula A109
Topological-Insulator Nanowires

Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional
topological insulators (3DTIs) [1-5] have been recently attracting increasing interest,
especially for their optical properties. We present results for the energy spectrum,
the surface states and the dipole matrix elements for optical transitions with in-
plane polarisation of 3DTI nanowires of finite height L and radius R. We first derive
an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem.
We develop two approaches: The first one is an exact numerical tight-binding model
obtained by discretising the Hamiltonian; The second one, which allows us to obtain
analytical results, is an approximated model based on a large-R expansion and on
an effective boundary condition to account for the finite height of the nanowire.
We find that the agreement between the two models, as far as eigenenergies and
eigenfunctions are concerned, is excellent for the lowest absolute value of the
longitudinal component of the angular momentum. Finally, we derive analytical
expressions for the dipole matrix elements by first considering the lateral surface
alone and the bases alone, and then for the whole nanowire. In particular, we focus
on the two limiting cases of tall and squat nanowires. The latter case is compared
with the numerical results finding a good agreement