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We have used Bi$_2$Se$_3$ nanoribbons, grown by catalyst-free Physical Vapor Deposition to fabricate high quality Josephson junctions with Al superconducting electrodes. In our devices we observe a pronounced reduction of the Josephson critical current density $J_c$ by reducing the width of the junction, which in our case corresponds to the width of the nanoribbon. Because the topological surface states extend over the entire circumference of the nanoribbon, the superconducting transport associated to them is carried by modes on both the top and bottom surfaces of the nanoribbon. We show that the $J_c$ reduction as a function of the nanoribbons width can be accounted for by assuming that only the modes travelling on the top surface contribute to the Josephson transport as we derive by geometrical consideration. This finding is of a great relevance for topological quantum circuitry schemes, since it indicates that the Josephson current is mainly carried by the topological surface states.
We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe$_2$ nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a f
Using non-equilibrium Greens functions, we studied numerically the transport properties of a Josephson junction, superconductor-topological insulator-superconductor hybrid system. Our numerical calculation shows first that proximity-induced supercond
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the norm
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of
Proximity-induced superconductivity in three dimensional (3D) topological insulators forms a new quantum phase of matter and accommodates exotic quasiparticles such as Majorana bound states. One of the biggest drawbacks of the commonly studied 3D top