#### Date of Degree

5-2015

#### Document Type

Dissertation

#### Degree Name

Ph.D.

#### Program

Physics

#### Advisor

Sergey Vitkalov

#### Subject Categories

Condensed Matter Physics | Physics

#### Keywords

2DEG; nonlinear; quantum; semiconductors; transport; two-dimensional

#### Abstract

Heterostructures made of semiconductor materials may be one of most versatile environments for the study of the physics of electron transport in two dimensions. These systems are highly customizable and demonstrate a wide range of interesting physical phenomena. In response to both microwave radiation and DC excitations, strongly nonlinear transport that gives rise to non-equilibrium electron states has been reported and investigated. We have studied GaAs quantum wells with a high density of high mobility two-dimensional electrons placed in a quantizing magnetic field. This study presents the observation of several nonlinear transport mechanisms produced by the quantum nature of these materials.

The quantum scattering rate, $1/\tau_q$, is an important parameter in these systems, defining the width of the quantized energy levels. Traditional methods of extracting $1/\tau_q$ involve studying the amplitude of Shubnikov-de Haas oscillations. We analyze the quantum positive magnetoresistance due to the cyclotron motion of electrons in a magnetic field. This method gives $1/\tau_q$ and has the additional benefit of providing access to the strength of electron-electron interactions, which is not possible by conventional techniques. The temperature dependence of the quantum scattering rate is found to be proportional to the square of the temperature and is in very good agreement with theory that considers electron-electron interactions in 2D systems. In quantum wells with a small scattering rate - which corresponds to well-defined Landau levels - quantum oscillations of nonlinear resistance that are independent of magnetic field strength have been observed. These oscillations are periodic in applied bias current and are connected to quantum oscillations of resistance at zero bias: either Shubnikov-de Haas oscillations for single subband systems or magnetointersubband oscillations for two subband systems. The bias-induced oscillations can be explained by a spatial variation of electron density across the sample. The theoretical model predicts the period of these oscillations to depend on the total electron density, which has been confirmed by controlling the density through a voltage top-gate on the sample.

The peculiar nonlinear mechanism of quantal heating has garned much attention recently. This bulk phenomenon is a quantum manifestation of Joule heating where an applied bias current causes selective flattening in the electron distribution function but conserves overall broadening. This produces a highly non-equilibrium distribution of electrons that drastically effects the transport properties of the system. Recent studies have proposed contributions from edge states and/or skipping orbitals. We have shown that these contributions are minimal by studying the transition to the zero differential conductance state and comparing results between Hall and Corbino geometries. This demonstrated quantal heating as the dominant nonlinear mechanism in these systems. To study the dynamics of quantal heating, we applied microwave radiation simultaneously from two sources at frequencies $f_1$ and $f_2$ and measured the response of the system at the difference frequency, $f=\left|f_1-f_2\right|$. This provides direct access to the rate of inelastic scattering processes, $1/\tau_{in}$, that tend to bring the electron distribution back to thermal equilibrium. While conventional measurements of the temperature dependence indicate that $1/\tau_{in}$ is proportional to temperature, recent DC investigations and our new dynamic measurements show either $T^2$ or $T^3$ dependence in different magnetic fields. Our microwave experiment is the first $direct$ access to the inelastic relaxation rate and confirms the non-linear temperature dependence.

This work was supported by the National Science Foundation (Division of Material Research - 1104503).

#### Recommended Citation

Dietrich, Scott A., "A Static and Dynamic Investigation of Quantum Nonlinear Transport in Highly Dense and Mobile 2D Electron Systems" (2015). *CUNY Academic Works.*

https://academicworks.cuny.edu/gc_etds/906