# M. Sc. Project

### Thesis Title: Interplay of Charge Density Waves and Superconductivity

My thesis involved performing numerical simulations to model impurity effects in superconductors. Superconductors are materials which lose all electrical resistivity when cooled to a sufficiently low temperature, known as the critical temperature. This was explained in 1957 by John Bardeen, Leon Cooper, and John Robert Schrieffer (BCS) by postulating that electrons in the material form pairs now known as Cooper pairs. The collective motion of these pairs is responsible for the absence of resistivity in the superconducting state.

There is another type of process which can occur when a material is cooled. A charge density wave (CDW) transition occurs when electrons in a material pile up creating regions of alternating charge density. The localization of electrons means they are not free to flow, and as a result CDW materials are typically insulators (bad conductors). Generally, the consensus is that superconductivity should not coexist in a material which exhibits charge density waves.

In a recent experiment on NbSe$$_2$$ they have found that the presence of charge density waves can in fact enhance superconductivity in this material. The goal of my research was to explain these intriguing measurements on NbSe$$_2$$. Due to the large-scale nature of the problem I had to develop parallel algorithms in order to make the calculations feasible. This reduced the time for a typical calculation from a few months to a few days. The calculations for my project were done on a large-scale "Beowulf" class PC cluster, iglu, at the University of Saskatchewan. Iglu has 128 Intel Xeon processors clocked at 3.06 GHz, each with 2 GB of RAM.

### Presentations

I have presented my research at both national and international conferences. In 2010, I travelled to Toronto for the Canadian Association of Physicists annual congress where I received second prize in the student paper oral presentations from the division of condensed matter and materials physics. In 2011, I presented at the American Physical Society's annual March meeting in Dallas TX.

Fermi surface for NbSe$$_2$$, a material which exhibits the coexistence of superconductivity and CDW.