POULOMI CHAKRABORTY

DOS OF 2D TIGHT BINDING ELECTRON IN A SKYRMION TEXTURE

Bachelor's Thesis Project (Academic year 2019-20), Indian Institute of Science, Bangalore

 Under Prof. Sumilan Banerjee, I studied about basics of skyrmions and became familiar with the types of skyrmions, topological quantum numbers, Dresselhaus and Rashba spin-orbit coupling and Dzyaloshinskii-Moriya interactions. I calculated numerically the density of states of 2D electrons with tight binding interactions on a different spin textures (ferromangnetic, antiferromagnetic etc) and compared them to the analytical results. Then, I calculated the density of states for different skyrmion configurations, which were obtained from a paper generating those using conjugate gradient minimization of energy functional. As a warm up, I also studied about Integer Quantum Hall Effect and Hofstadter Butterfly, and formulated a program which generated the graph resembling a butterfly.

FRACTIONAL QUANTUM HALL EFFECT

Summer 2019, Nanyang Technological University, Singapore

Under the guidance of Prof. Yang Bo, I studied the basic theory of Quantum Hall Effect in two dimensional systems, from an article by Dr. Steven Girvin and David Tong's lecture notes. Then, I studied the derivation of the Hamiltonian of the system, using cyclotron coordinates, guiding center coordinates and the ladder operators constructed from them. Next, I became familiar with the pseudopotential approach. After that, I studied the derivation of the second quantized expression of the Hamiltonian and carried out the explicit expressions of the pseudopotential. I have also attempted to calculate the energy levels numerically for a N electron system.

SUPERFLUIDITY

Summer 2018, Indian Institute of Science, Bangalore

Under Prof. Subroto Mukerjee, I have studied of basic properties of superfluidity and superconductivity from Feynman lectures and statistical mechanics Ideal Fermi and Bose gases, Bose-Einstein Condensates and Landau criterion from the book “Statistical Mechanics” by Pathria. Then, I studied the Gross - Pitaevskii equation and its derivation and some experiments involving BECs as well. Using Gross – Pitaevskii equation I simulated the evolution of wave function of BEC (weakly interacting) with time using MATLAB for harmonic potential starting from various initial states (e.g. Gaussian etc).