Research Projects

Quantum geometry (QG) has emerged as a fundamental and powerful concept in condensed matter systems, providing a plethora of intriguing physics in quantum materials. It is encapsulated by the quantum geometric tensor whose real part is known as quantum metric and imaginary part gives rise to Berry curvature. Despite the growing importance of QG in understanding exotic phases of matter, its influence on transport properties in superconducting phases remains an underexplored area. This project seeks to fill this gap by systematically investigating the QG effects on optical and thermoelectric responses in various unconventional superconductors (SCs) with detailed microscopic models, both in the presence and absence of disorder. This project will mainly focus on four types of unconventional SCs: (i) flat-band SCs, (ii) altermagnetic SCs with unconventional pairing, (iii) SCs whose normal state is topological semimetallic in nature, and (iv) time-reversal symmetry breaking SCs and is structured around several key research objectives. First, it aims to develop a theoretical framework that incorporates the quantum metric and Berry curvature into the transport properties of unconventional SCs. The goal is to determine whether QG-induced transport phenomena can serve as reliable probes to distinguish between different superconducting phases. Second, the project will examine the effects of disorder on QG and its role in modifying transport in disordered SCs. The third objective is to investigate the interplay between quantum geometry and non-Hermiticity in SCs, which is of growing interest due to its potential to host robust Majorana zero modes—a key element for fault-tolerant quantum computing. To achieve these objectives, the project will employ a combination of symmetry analysis, model Hamiltonian-based calculations, and DFT. Symmetry analysis will help to identify the symmetry-allowed transport quantities in unconventional SCs, while the quantum kinetic framework will be used to compute transport properties, including both intra- and inter-band contributions from the quantum geometric tensor. The project will also develop computational tools to simulate the effects of disorder on transport in SCs. Finally, DFT calculations will be used to model realistic materials and validate the theoretical predictions, offering concrete guidelines for experimentalists to probe QG effects in existing and future superconducting materials. The expected outcomes of this research include the development of a unified framework for understanding the QG effects in transport properties of unconventional SCs, along with the identification of specific experimental probes that can unambiguously measure QG-induced phenomena. The insights gained from this project will have profound implications for the design of next-generation superconducting materials, with potential applications in quantum computing, energy transmission, and other quantum technologies.