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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
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