Research Projects

Recent advances in condensed matter physics have revealed that periodic driving (Floquet engineering), interparticle interactions, superconductivity, and non-Hermitian effects (such as loss, gain, and asymmetric couplings) each give rise to rich and novel quantum phases. These include Floquet-induced Majorana modes, the Josephson diode effect, and exceptional points (EPs) in open systems. However, the combined impact of these elements—Floquet drive, interactions, and non-Hermiticity, remains largely unexplored, especially in superconducting systems where their interplay could lead to fundamentally new topological behavior and device functionalities. This proposal aims to develop a unified theoretical framework to explore how these three mechanisms together generate exotic topological phases and enable application-oriented phenomena. In one dimension, we will study Josephson junctions formed by spinful Kitaev chains or Rashba nanowires connected via quantum dots. These systems will be analyzed under both periodic driving and dissipation, and will include Hubbard-type interactions in the quantum dot. Particular focus will be given to the emergence of ɸ0-junctions, spin-polarized Josephson currents, and the role of Majorana zero and π- modes in diode-like behavior. We will also extend these models to non-Hermitian regimes to explore the appearance and control of exceptional points and topological switching behavior in multiterminal setups. In parallel, we will explore two-dimensional lattice systems (e.g., graphene or 2D Su Schrieffer Heeger model) subjected to structured light, specifically, linearly polarized beams carrying orbital angular momentum (OAM). These systems are known to host Floquet Chern insulating phases even in the absence of magnetic fields. We will investigate how non-Hermitian modifications such as asymmetric hopping or gain/loss affect these phases. Real-space topological markers like the local Chern number and spectral winding will be computed to characterize phase transitions, including the robustness of edge states in the presence of dissipation and interactions. The methodology will combine tight-binding Hamiltonian modeling, Bogoliubov–de Gennes formalism, Floquet theory, Lindblad dynamics, and Green’s function approaches. Both spectral and real-space topological invariants will be used for diagnosis. Expected outcomes include new regimes of nonreciprocal transport, controlled generation of Majorana modes, Floquet-tunable exceptional points, and the design of prototype quantum devices such as spintronic Josephson diodes, topological switches, and EP-based sensors. Long-term goals include laying theoretical foundations for fault-tolerant quantum logic using multiterminal braiding of Floquet Majoranas. This project bridges theoretical physics with potential real-world quantum technologies, combining fundamental insight with application readiness.