The famous Higgs mechanism is responsible for giving mass to the electro-weak gauge bosons in high energy physics. Associated with this mechanism is the famous Mexican hat potential, where the amplitude oscillations are called the Higgs mode or, in particle physics, the Higgs Boson. While this mode has a fixed symmetry and density of states in the standard model, we have many more options in condensed matter physics. One specific example are the gap oscillations in superconductors. In recent years there has been much effort on the experimental side to use non-linear optical methods to dynamical modify the Mexican hat potential to induce superconducting Higgs oscillations. On the theory side we are still far away from completely understanding the non-equilibrium properties of this phenomenon and different models are discussed to describe the excitation mechanism as well as the symmetry classification of these modes.
The aim of the undergraduate research project is to investigate the non-equilibrium response of different superconductors for various quantum quench scenarios. At first, conventional superconductors should be investigated, in order to understand the general concepts.
Here the focus lies on time dependent quenches induced by light matter interaction, such as a short intense THz laser pulses.
The main goal of the project is the analysis of non-equilibrium Higgs oscillations in unconventional materials, such as d-wave or triplet superconductors. Especially research on the various parameters of the quench are required to obtain a deeper understanding and to make possible predictions to future experiments.
On the methodical site numerical as well as analytical tools can be used to describe the Higgs oscillations in superconductors. The basis for both is the Bardeen-Cooper-Schrieffer Hamiltonian of superconducting condensates. For analytical calculations the Anderson-Pseudo spin formalism is used in combination with a linear analysis based on an expansion of the Bloch equation for small perturbations. For numerical calculations the equations of motion for the time dependent Bogoliubov quasi-particle densities must be implemented and solved for different quantum quenches.