Research Projects

Rationale: This project targets a rapidly emerging frontier in topological quantum materials, with a focus on both fundamental exploration and potential applications in quantum technologies, goals that align closely with the broader objectives of the National Quantum Mission. We propose to develop theoretical models for realizing robust Majorana zero modes originating from Fulde-Ferrell (FF) superconductors, characterized by finite-momentum Cooper pairs. Unlike conventional systems, such as Rashba nanowires proximized by s-wave superconductors with zero-momentum pairing, where the observed zero-bias peaks may arise from trivial Andreev bound states, the FF pairing mechanism offers a promising alternative route. Since the finite-momentum analogs of topological Majorana modes remain largely unexplored, a systematic theoretical investigation is both timely and critical. This study has the potential to directly inform experimental efforts in topological superconductivity and simultaneously contribute to the conceptual foundations of future quantum technologies based on FF Majorana modes. Scientific Objectives: Our proposal focuses on developing a theoretical understanding of topological FF superconductors and their associated transport signatures and non-equilibrium dynamics. Majorana modes in FF superconductors remain a largely unexplored area, and our objective is to investigate the robustness of this novel topological phase in the presence of disorder and Hermiticity-breaking perturbations. Additionally, we aim to explore the origin of non-reciprocal transport phenomena, such as the superconducting diode effect and the Josephson diode effect, arising from the finite momentum of Cooper pairs. Notably, we also examine the possibility of realizing these effects via an altermagnetic pathway, eliminating the need for external magnetic fields. Finally, the proposal addresses the non-equilibrium generation and control of FF superconductivity as a key goal. Hypothesis/model to be tested: All four objectives, with their highlighted key themes, provide new, alternative, and distinct approaches for finite-momentum Cooper pair to create, enhance, and understand the FF superconducting order in a novel phase of matter that can be significantly different from conventional zero-momentum Cooper pair of BCS superconductor. Therefore, the joint foci of the objectives are to emulate new theoretical modeling and the conception of novel functional quantum devices, empowering the future scopes of quantum materials, thus justifying the overall goal of quantum applications with topological robustness. Main experiments/Technicalities: We employ a range of analytical and numerical methods to achieve our objectives. Analytical tools include self-consistent BdG Hamiltonians, Born approximations, trace distance, spin-wave and Fermi surface analysis, condensation energy, topological invariants, non-equilibrium Green's functions, and the Floquet-Kubo formalism. Numerically, we use Runge-Kutta integration, exact diagonalization, bond current calculations, and simulations via KWANT and t-WANT. Significance: Our findings will offer essential theoretical input for future first-principles studies, experiments, and quantum technology development. Objective [O1] introduces a novel route towards the understanding and manipulation of Majorana braiding in topological FF superconductors. Objective [O2] extends this by linking Majorana physics with superconducting diode and quantum engine efficiency which are useful for low-dissipation quantum circuitry. Objective [O3] leverages altermagnets with unconventional symmetry properties, to accelerate the search for FF Majorana modes. Objective [O4] explores emergent dynamics in Floquet-engineered FF superconductors, drawing analogies with light–matter interaction in solid-state systems, which offers a powerful and tunable platform for investigating emergent topological states and dynamic phase transitions.