Executive Summary : | The proposal aims to investigate emergent phases of matter in transport phenomena, focusing on 2 types of systems with non-trivial toppology: 1D and 2D quasicrystals (QCs) with Fibonacci, Thue-morse, Penrose, Ammann-Beenker tilings, and 3D spin-3/2 superconductors (SCs) found in strongly spin-orbit coupled materials like RPtBi and RPdBi materials with rare-earth element R. The emergence of topological states at zero energy in QCs with aperiodic tilings has been predicted recently, and the aim is to find signatures of these critical states in transport phenomena. The proposal also explores emergent phases of matter by novel combinations of global topology and local superconducting order, considering both bare materials and junctions of two materials. The SCs can be traditional Bardeen-Cooper-Schrieffer (BCS) or newly found spin-3/2 SCs, which have strong spin-orbit coupling and allow Cooper pairs to have exotic pair symmetries, spin-quintet, and spin-septet, in addition to spin-singlet and spin-triplet pairings. The plan is to find the signatures of these exotic pair symmetries, the existence of the Bogoliubov Fermi surface (BFS), and their connections in experimentally measurable quantities like Meissner effect, Josephson current, and thermoelectricity. The proposal's significance lies in providing insight into the characteristic features of QCs and spin-3/2 SCs, as well as signatures in transport phenomena, making these systems ready for experiments and practical purposes. |