# Physics Research

## Postdoctoral Project

### Germanium Quantum Dot Growth on InAlAs

In this project my postdoc adviser, Christian Ratsch at UCLA, and I were trying to compute the mobility of germanium adatoms on an InAlAs (111)A surface with particular comparison to gallium adatoms as a rough analog for Ge vs GaAs quantum dots.

## Graduate Projects

### Hubbard Dimer

My advisor, Professor Kieron Burke, had a project with collaborators at the Universidad de Oviedo in Spain. They were interested in doing a thorough application of density functional theory (DFT) on the asymmetric two site Hubbard model. In this work we were able to do many exact DFT calculations (a rarity) and compare to approximations. We were able to illustrate a slew of DFT principles and created a nice approximation for the universal functional.

D. Carrascal, J. Ferrer, **J.C. Smith**, and K. Burke, Journal of Physics: Condensed Matter, 27, 393001 (2015).

### Thermal Density functional theory

I became interested in thermal DFT and wanted to apply my well developed experience and intuition on the Hubbard dimer to a problem that has not been thoroughly tackled. In this work I was able to do the first ever exact thermal DFT calculations that provided us with more understanding on how the exchange-correlation (XC) free energy behaves with temperature. Most importantly, we learned that the XC free energy is not bounded by the T=0 value (i.e. the energy)

Additionally, I was able to verify and illustrate new thermal DFT identities that my advisor had derived.

J.C. Smith, A. Pribram-Jones, and K. Burke, Phys. Rev. B 93 245131 (2016).

K. Burke,** J.C. Smith**, P. Grabowski, and A. Pribram-Jones, “ Phys. Rev. B 93, 195132 (2016).**J.C. Smith**, F. Sagredo, and K. Burke, Frontiers of Quantum Chemistry, 249-271 (2018).

### Stitching Potential

Kieron and I have been developing a new theory that is designed to combine results from thermal DFT and path integral Monte Carlo (PIMC). The motivation is that PIMC is highly accurate for temperature values beyond warm dense matter (our interest) while thermal DFT can be run for a huge range of temperatures but lacks the desired accuracy. The effective thermal potential theory allows us to write down a potential that is defined at a low temperature and a high temperature. If we then put this into a PIMC solver at the high temperature then it yields the density and energetics of the system at the low temperature. Typically this effective thermal potential will be constructed from thermal DFT approximations.

**J.C. Smith**, and K. Burke, Physical Review B 98 (7), 075148 (2018).

## Undergraduate Projects

### Electronic Structure of CoSB3

I studied the electronic structure of CoSB3 in collaboration with a graduate student and postdoc. The impetus for this project was a curious feature in the band structure that Professor Warren Pickett had noticed years prior.

We discovered that if you apply strain along one axis that the curious feature forms a semi-dirac cone and the material becomes a topological insulator. This was incredibly well timed with the nascent and rapidly growing popularity of topologically insulating materials.

**J.C. Smith**, S. Banerjee, V. Pardo, and W.E. Pickett, Phys. Rev. Lett. 106 056401 (2011).

V. Pardo, **J.C. Smith**, and W.E. Pickett, Phys. Rev. B 85 214531 (2012).

### Honors Thesis

I set out to follow another lead from Professor Pickett's past. This time we were curious about the interstitial hydrogen impurity in germanium. Unfortunately, this project was plagued with issues since the tools I had learned on the previous project were not applicable here. My honors thesis detailed the issues and still resulted in me graduating *summa cum laude*.