Lead Green's functions from quadratic eigenvalue problems without mode velocity calculations.

In quantum transport calculations, the proper handling of incoming and outgoing modes for retarded Green's functions is achieved via the lead self-energies. Computationally efficient and accurate methods to calculate the self-energies are thus very important. Here we present an alternative method for calculating lead self-energies which improves on a standard approach to solving quadratic eigenvalue problems that arise in quantum transport modeling. The method is based on a perturbative analysis of the generalized Schur decomposition to determine the relevant set of eigenvalues for transmitting modes. This allows us to circumvent finding the velocities of the modes (left- or right-moving) that are needed in order to calculate the lead Green's function from translationally invariant Green's functions. This saves computational time irrespective of the value of the imaginary part added to the energy. We compare our method with two existing methods-a popular iterative method and a standard eigenvalue method that explicitly calculates the velocities of the propagating modes. Our comparison shows that both eigenvalue methods are more robust than the iterative method. Furthermore, the comparison also shows that above a small threshold of propagating modes, the standard eigenvalue method requires extra computation time over our perturbation method. This excess of computation time grows linearly with the number of propagating modes.

Multi-domain electromagnetic absorption of triangular quantum rings.

We present a theoretical study of the unielectronic energy spectra, electron localization, and optical absorption of triangular core-shell quantum rings. We show how these properties depend on geometric details of the triangle, such as side thickness or corners' symmetry. For equilateral triangles, the lowest six energy states (including spin) are grouped in an energy shell, are localized only around corner areas, and are separated by a large energy gap from the states with higher energy which are localized on the sides of the triangle. The energy levels strongly depend on the aspect ratio of the triangle sides, i.e., thickness/length ratio, in such a way that the energy differences are not monotonous functions of this ratio. In particular, the energy gap between the group of states localized in corners and the states localized on the sides strongly decreases with increasing the side thickness, and then slightly increases for thicker samples. With increasing the thickness the low-energy shell remains distinct but the spatial distribution of these states spreads. The behavior of the energy levels and localization leads to a thickness-dependent absorption spectrum where one transition may be tuned in the THz domain and a second transition can be tuned from THz to the infrared range of electromagnetic spectrum. We show how these features may be further controlled with an external magnetic field. In this work the electron-electron Coulomb repulsion is neglected.