#### Title

Ground States of the Two-Dimensional Electron System at Half-Filling Under Hydrostatic Pressure

#### Date of Award

5-2018

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### Committee Chair

Gabor A. Csathy

#### Committee Member 1

Michael J. Manfra

#### Committee Member 2

Tongcang Li

#### Committee Member 3

Yuli Lyanda-Geller

#### Abstract

A many-body electron system in two dimensions at high magnetic field hosts a diverse set of electron ground states. Many of these ground states have been well understood for years, yet some continue to challenge researchers. The ν =5/2 fractional quantum Hall state at half-filling is perhaps the most mysterious state. It holds the promise of novel physics such as non-Abelian statistics, and it possesses topological order, both properties of great interest due to potential applications for robust quantum computing. However, despite many experiments to this date, questions surround the exact nature of ν =5/2 fractional quantum Hall state. This unsatisfactory state of affairs in the understanding of ν =5/2 calls for new and refined experimental methods. Hydrostatic pressure is a widely-used tool that provides a great deal of insight into condensed matter physics. By shrinking the lattice constant in crystalline systems, pressure changes the Bloch wavefunction and the band structure. As a result, pressure permits us to tune material parameters in ways not possible with other techniques. In particular, we may tune the energy scales of the fractional quantum Hall states and gather information about these states from their response to pressure. Pressure therefore has the potential to provide new insight of the behavior of the ν =5/2 fractional quantum Hall state. In this thesis, I describe experiments in which I applied up to 12 kbar to two dimensional electron systems hosted in gallium arsenide heterostructures. With the application of pressure, we observed an unexpected result: a never-before-seen phase transition at filling factor ν =5/2 from the fractional quantum

Hall state to the nematic phase. The nematic phase is a phase characterized by spontaneously broken rotational symmetry and highly anisotropic resistances. This represented the first time such a nematic phase developed spontaneously at ν =5/2, without any external symmetry breaking fields. Probing the temperature dependence of the ν =5/2 fractional quantum Hall state and nematic phase at different pressures allowed us to map a stability diagram of the different phases. Evidence suggests that this transition is a quantum phase transition – a phase transition at zero temperature. There are many examples of quantum phase transitions in condensed matter, but the one we have observed at ν =5/2 is unusual. This is a quantum phase transition which changes topological order, as the quantum Hall state is destroyed, as well as nematic order, a traditional Landau order, as rotational symmetry breaks in the transition. This discovery brings about new questions about the instabilities at ν =5/2, and invites further study, both experimental and theoretical. To gain further insight into the underlying mechanism of the fractional quantum Hall state-to-nematic transition, we also studied the filling factor ν =7/2, the closely-related cousin of ν =5/2, under pressure. The fractional quantum Hall state at ν =7/2 is expected to share the same physics as the ν =5/2 fractional quantum Hall state. Importantly, we find that ν =7/2 also undergoes the fractional quantum Hall state-to-nematic transition. The quantum phase transitions at ν =5/2 and ν =7/2 do not occur at the same pressure, but rather the same magnetic field. Because the magnetic field sets the scale for the electron-electron interactions, this suggests that electron-electron interactions are the dominant factor driving this quantum phase transition. Corroborating this conclusion, a specially-engineered sample studied at ambient pressure also revealed a nematic phase at ν =7/2 at a similar magnitude of electron-electron interactions as the pressurized samples.

#### Recommended Citation

Schreiber, Katherine A., "Ground States of the Two-Dimensional Electron System at Half-Filling Under Hydrostatic Pressure" (2018). *Open Access Dissertations*. 1822.

https://docs.lib.purdue.edu/open_access_dissertations/1822