The First plot shows the line gap and point gap topological phases in our system and it's variation due to hopping and the non-hermiticity parameter
The second plot shows the localization of boundary(a) and skin(b) modes in the system.
Anomalous Pumping in Non-Hermitian Rice-Mele Model:
Under the guidance of Dr. Kush Saha and in collaboration with Abhishek Kumar (Ph.D. student at UMass, Amherst, USA) and Dr. S.D. Mahanti, Michigan State University, USA.
The study focuses on the Rice-Mele (RM) model in the presence of an asymmetric hopping-induced non-Hermitian parameter, γ. In particular, we examine the effect of non-Hermiticity on the topological boundary modes and topological pumping. For weak and moderate values of γ, the inherent topological edge modes remain localized at the boundaries, whereas the bulk modes are pumped to the boundary, leading to the typical non-Hermitian skin modes. In both static and dynamic scenarios, we present a topological classification of Point gaps and Line gaps within the system and this classification significantly relies on the hopping parameters and the strength of the non-Hermiticity parameter. Using the finite-size generalized Brillouin zone (GBZ) scheme, we show that the non-Hermiticity-induced skin modes can be distinguished from the topological boundary modes. Upon increasing γ, the topological boundary mode localized at one edge is pumped to the other edge. Furthermore, we have identified a system-size-dependent topological phase transition which results in a novel size-dependent topological pumping transition. The pumping depends upon the driving protocols and strength of the non-Hermiticity. With increasing γ, the adiabatic pumping is destroyed first and then re-emerges as an unconventional/anomalous pumping which does not have any Hermitian counterpart. Utilising the non-Bloch Chern number, we characterise the distinct pumping phases within the system. This characterization enables us to establish a non-Bloch bulk-boundary correspondence within the system.
Study of High-Temperature Cuprate Superconductors:
Under the guidance of Dr. Tanusri Saha-Dasgupta, Director, SNBNCBS, India
The primary focus of this project was to investigate the properties of high-temperature cuprate superconductors using a combination of experimental and theoretical techniques. The research encompassed four main areas: angle-resolved photoemission spectroscopy (ARPES), density functional theory (DFT) calculations, tight binding modelling, and the analysis of spin and charge susceptibilities using the Random phase approximation (RPA). The project aimed to gain insights into the electronic structure, energy dispersion, Van Hove singularities, and the role of electron-electron repulsion (Hubbard parameter U) in cuprate superconductors. Additionally, it explored magnetic properties, revealing information about magnetic interactions and correlations in these materials. Project Report
Analysis of Hubbard Model and strongly correlated Spin-Chain systems with Density Matrix Renormalization Group (DMRG)
Under the guidance of Dr. Anamitra Mukherjee
The density-matrix renormalization group (DMRG) is a numerical technique for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a general decimation prescription. Its algorithm has been extremely successful in computing the ground states of one-dimensional quantum many-body systems. Recently, it has also been extended to compute excited states and to simulate dynamical, finite-temperature, and non-equilibrium systems. As calculation cannot be done analytically, since the Hilbert space exponentially expands with the system’s size. We can numerically examine such systems using DMRG. We have carried out a thorough analysis of the finite and infinite-size DMRG algorithms in this study. We outlined the fundamental limitations and motivating factors behind DMRG. We’ve taken on a number of physical problems like the Hubbard Model, Hardcore Bosons and Spin-Chains. Using a variety of parameters, we produced some excellent results. Furthermore, we produced the correlation results in complex spin systems and Charge Density Profile for the Fermi-Hubbard Model. In the later part, we are able to reproduce the results for Spin-1/2 ladders and analyse several phases like Spin-liquid phase, spin dimer phase and Spin-density profiles that are occurring in the system in different parameter ranges. we also provide a wide range of analyses on the Density Matrix and Entanglement Entropy of the systems. Project Report
Investigation of Quantum Effects of Johnson Nyquist Noise in Graphene
This is basically my project in the Integrated Open-ended Laboratory of our Institute. The aim is to efficiently study the emergence of quantum effects of Johnson Noise in Graphene due to extremely low temperatures (2K-4K) and in Tera-Hertz frequency. I am also planning to examine the required transport properties in single and bi-layer graphene in extreme temperatures along with some varying parameters. All the measurements that we’ve listed here are performed over a sample of Bi-layer Graphene, which has been made by numerous exfoliation attempts with the Highly oriented pyrolytic graphite (HOPG). We’ve also provided the spectroscopic report that convincingly proved the number of layers of Graphene in our sample with Raman Spectroscopy and Atomic Force Microscopy(AFM) images. We have done a detailed analysis of the PeakIntensity to correctly get the number of layers into the sample. We then try to analyse the Impedance of the Graphene layer in the physical property measurement system (PPMS) and its physical behaviour in low temperatures and try to get some physical intuition about the Quantum Effects of Noise. Project Report
Experimental characterization and operation of a diode-pumped Nd: YAG & He: Ne (Helium-Neon) laser system
This comprehensive report presents in-depth studies of two distinct laser systems: the He: Ne (helium-neon) laser and the diode-pumped Nd: YAG laser. The He: Ne system, covers construction, operational theory, and experimental modules, including precise alignment procedures, optical cavity construction, and wavelength measurements. The Nd: YAG section introduces the laser's construction, active medium, and lasing modes, delving into theoretical aspects like optical pumping and rate equations. Detailed experimental modules encompass laser lifetime measurements, cavity construction, and Q-switching. Both sections emphasize the importance of meticulous observation recording and analysis. Project Report
