Spin-flip transitions induced by time-dependent electric fields in
  surfaces with strong spin-orbit interaction

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Abstract

We present a comprehensive theoretical investigation of the light absorption rate at the Pb/Ge(111) surface with strong spin-orbit coupling. Our calculations show that electron spin-flip transitions cause as much as 6% of the total light absorption, representing one order of magnitude enhancement over Rashba-like systems. Thus, it is demonstrated that a substantial part of the light irradiating this nominally non-magnetic surface is attenuated in spin flip processes. Remarkably, the spin-flip transition probability is structured in well defined hot spots within the Brillouin zone where the electron spin experiences a sudden 90 degree rotation. This mechanism offers the possibility of an experimental approach to the spin-orbit phenomena by optical means.

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\(Z_2\) Topological Order and the Quantum Spin Hall Effect

C. L. Kane, E. Mele (2005)

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel \(Z_2\) topological invariant, which distinguishes it from an ordinary insulator. The \(Z_2\) classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the \(Z_2\) order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multi band and interacting systems.

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Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions

J Yates, N Marzari, I. Souza … (2007)

We present Wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, Wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. Therefore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWF can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, Wannier90 is able to output MLWF for visualisation and other post-processing purposes. Wannier functions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and minimal basis set in the construction of model Hamiltonians for large-scale systems, in linear-scaling quantum Monte Carlo calculations, and for efficient computation of material properties, such as the anomalous Hall coefficient. Wannier90 is freely available under the GNU General Public License from http://www.wannier.org/