Gapless chiral excitons in thin films of topological insulators

In a nanoscopic thin film of a strong topological insulator (TI) the Coulomb interaction in the channel that exchanges the two electrons with the same chirality in two different planes of the slab takes advantage of the minus sign resulting from such "exchange" and gives rise to a bound state between the positive energy states in one surface and the negative energy states in the opposite surfaces. Therefore particle and hole pairs in the {\em undoped} Dirac cone of the TI thin film form an inter-surface spin-singlet state that lies below the continuum of free particle-hole pairs. This mode is similar to the excitons of semiconductors, albeit formed between the electron and hole pairs from two different two-dimensional surfaces. For low-momenta the dispersion relation characterizing this collective mode is linear. Experimental comparison of two slabs with different thicknesses can capture the exponential dependence of the present effect on the slab thickness.Comment: Comments are welcom

Josephson super-current in graphene-superconductor junction

Within the tunneling Hamiltonian formulation for the eight-component spinors,the Josephson critical super-current has been calculated in a planar superconductor-normal graphene-superconductor junction. Coupling between superconductor regions and graphene is taken into account by a tunneling Hamiltonian which contains two types of tunneling, intra-valley and inter-valley tunneling. Within the present tunneling approach, we find that the contributions of two kinds of tunneling to the critical super-current, are completely separable. Therefore, it is possible to consider the effect of the inter-valley tunnelings in the critical super-current. The incorporation of these type of processes into the tunneling Hamiltonian, exposes a special feature of the graphene Josephson junctions. The effect of inter-valley tunneling appears in the length dependence plot of critical current in the form of oscillations. We also present the results for temperature dependence of critical super-current and compare with experimental results and other theoretical calculations