TUNABLE JOSEPHSON TRANSPORT THROUGH SINGLE AND DOUBLE QUANTUM DOTS JUNCTION AT INFINITE-U LIMIT

Abstract

This thesis is a theoretical exploration of Josephson transport through QD (quantum dot) junctions, with a particular focus on Andreev bound states (ABS) and their role in Josephson supercurrent at infinite-U limit. Josephson Junctions based on quantum dots are devices made of a small island coupled to two superconducting leads. These devices are based on quantum transport phenomena and are used in Quantum teleportation as well as Quantum information processing. Quantum transport phenomena through QD coupled to normal metallic leads show Coulomb blockade and Kondo effect. Replacing metallic lead with BCS superconducting leads Superconductor-Quantum dot-Superconductor (S-QD-S) junction is formed in which Cooper pair can tunnel from one lead to another lead. Due to Cooper pairs tunneling, supercurrent flow through the junction. Sub-gap states called Andreev bound states are observed in superconducting QD junction which depends on superconducting phase difference between left and right superconducting lead and hence are responsible for Josephson supercurrent. Development in nanofabrication technology have made it possible to form Superconducting quantum dot junction. Experimental methods such as electron beam lithography, chemical beam epitaxy, vapour-liquid-solid growth technique, Scanning electron microscopy have been used to form and charaterize these types of junction. Experimentally, Andreev bound states, Josephson current and 0 to π-phase transition are observed in these types of junctions. Experimental results are verified in different parameter regime from different theoretical methods namely, cotunneling approach, Hartree fock approximation, Non crossing approximation, perturbation theory, Renormalization group approach. However Infinite-U (interaction strength) Slave Boson method to understand the behaviour of Andreev bound states is less addressed, which motivated us to employ this technique for single and parallel double QD junction at infinite-U limit.