Foreign MNEs and domestic innovative capabilities: are there conditions for reverse spillovers in the spanish industry?

We analyse, over 2004-2008, a sample of approximately 700 foreign subsidiaries and 4,500 domestic firms located in Spain in order to understand the relationship between local R&D cooperation and innovativeness of the firm. Our ultimate objective is to understand whether foreign subsidiaries are likely to make a contribution to local innovative capabilities or if, conversely, they may eventually benefit from conditions for reverse spillovers. Using a variety of specifications for the innovation-related activities of the firm, we find that foreign subsidiaries are more cooperative than the average firm located in Spain, but not necessarily more than affiliated domestic firms (entrepreneurial groups). However, foreign subsidiaries are more cooperative than affiliated domestic firms in sectors considered highly dynamic by international technological standards, whether Spain has a technical advantage in these specific sectors or not. When we focus on companies which are more innovative than the two-digit industries in which they operate, we find that foreign subsidiaries tend to be more cooperative than domestic firms in sectors where Spain displays technological advantage. These sectors comprise traditional industries displaying little innovation dynamism from an international point of view. This finding suggests that there may be conditions for reverse spillovers in these specific Spanish sectors (though measuring them is beyond the objectives of this paper).

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.