Magnetotransport in two-dimensional electron systems in high Landau levels

Abstract

The field of condensed matter physics explores the macroscopic and microscopic properties of matter that makes up most of the usual (and unusual) stuff that surrounds us every day. Since the discoveries of integer and fractional quantum Hall effects (Nobel Prizes 1985 and 1999), quantum transport in two-dimensional (2D) carrier systems subjected to low temperatures and magnetic fields has become a fundamental branch in condensed matter physics, intriguing quantum phases arising from the strong electron-electron interaction. Thanks to the advances in nanostructure growth techniques, devices with unparalleled quality allow for new experimental observations and the exploration of the underlying physics. Among many fascinating discoveries, in this thesis, we focus on magnetotransport in 2D electron systems at high Landau levels, specifically the broken-symmetry states at $N \geq 2$ Landau levels, and emergent transport phenomena at weak magnetic fields when the systems are exposed to microwave radiation. I organize the thesis into three parts. The first part includes Chapter 1, where we briefly introduce the fundamentals of magnetotransport in 2D electron systems. The second part includes Chapter 2, Chapter 3, and Chapter 4, where we focus on the transport in the quantum Hall stripe and bubble regimes. More specifically, we introduce our contribution to the experimental observations of three new quantum states. The third part includes Chapter 5 and Chapter 6, where we focus on the experiments related to microwave-induced resistance oscillations (MIRO). We show that MIRO gives us access to several physical parameters and understanding the underlying mechanisms. We summarize each chapter respectively as below. Chapter 1 briefly introduces the fundamentals of magnetotransport in 2D electron systems. We review how to realize a clean two-dimensional electron gas in a GaAs quantum well and how to quantify the quality of a two-dimensional electron gas. Then we introduce the integer and fractional quantum Hall effects, the hallmarks of quantum Hall families. Finally, we review previous theoretical and experimental studies on the quantum Hall stripes and bubbles at $N \geq 2$ Landau levels and microwave-induced resistance oscillations at very high Landau levels. Chapter 2 reports on transport signatures of eight distinct bubble phases in the $N=3$ Landau level of a Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As quantum well with $x = 0.0015$. These phases occur near partial filling factors $\nu^\star \approx 0.2\,(0.8)$ and $\nu^\star \approx 0.3\,(0.7)$ and have $M = 2$ and $M = 3$ electrons (holes) per bubble, respectively. We speculate that a small amount of alloy disorder in our sample helps to distinguish these broken symmetry states in low-temperature transport measurements. Chapter 3 reports on transport signatures of hidden quantum Hall stripe (hQHS) phases in high ($N > 2$) half-filled Landau levels of Al$_{x}$Ga$_{1-x}$As/Al$_{0.24}$Ga$_{0.76}$As quantum wells with varying Al mole fraction $x < 10^{-3}$. Residing between the conventional stripe phases (lower $N$) and the isotropic liquid phases (higher $N$), where resistivity decreases as $1/N$, these hQHS phases exhibit isotropic and $N$-independent resistivity. Using the experimental phase diagram, we establish that the stripe phases are more robust than theoretically predicted, calling for improved theoretical treatment. We also show that, unlike conventional stripe phases, the hQHS phases do not occur in ultrahigh mobility GaAs quantum wells but are likely to be found in other systems. Chapter 4 reports the experimental observations on anomalous nemetic states in high half-filled Landau levels. It is well established that the ground states of a two-dimensional electron gas with half-filled high ($N \ge 2$) Landau levels are compressible charge-ordered states, known as quantum Hall stripe (QHS) phases. The generic features of QHSs are a maximum (minimum) in a longitudinal resistance $R_{xx}$ ($R_{yy}$) and a non-quantized Hall resistance $R_H$. Here, we report on emergent minima (maxima) in $R_{xx}$ ($R_{yy}$) and plateau-like features in $R_H$ in half-filled $N \ge 3$ Landau levels. Remarkably, these unexpected features develop at temperatures considerably lower than the onset temperature of QHSs, suggesting a new ground state. Moreover, we demonstrate that a modest in-plane magnetic field, applied either along $\left < 110 \right >$ or $\left < 1\bar10 \right >$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\left < 110 \right >$ direction. These findings confirm that anomalous nematic states are distinct from other ground states and will assist future theories to identify their origin. Chapter 5 investigates how MIRO evolve with the carrier density $n_e$ in a GaAs/AlGaAs quantum well equipped with an \emph{in situ} grown back gate, an aspect which has not been previously explored. First, we show that the MIRO frequency monotonically decreases with $n_e$. This finding can be linked to the renormalization of the effective mass by electron-electron interactions, which are sensitive both to $n_e$ and to quantum confinement of our 2DEG. Second, we find that the MIRO amplitude substantially increases with $n_e$. Our analysis shows that the anticipated increase in the effective microwave power and quantum lifetime with density is \emph{not} sufficient to explain the observed growth of the amplitude. We further observe that the fundamental oscillation extrema move towards cyclotron resonance with increasing density, which also contradicts theoretical predictions. These unexpected findings reveal that the density dependence is not properly captured by existing theories, calling for further studies. Chapter 6 studies the effect of illumination on the quantum lifetime in GaAs quantum wells. Low-temperature illumination of a two-dimensional electron gas in GaAs quantum wells is known to greatly improve the quality of high-field magnetotransport. The improvement is known to occur even when the carrier density and mobility remain unchanged, but what exactly causes it remains unclear. Here, we investigate the effect of illumination on microwave photoresistance in low magnetic fields. We find that the amplitude of MIRO grows dramatically after illumination. Dingle analysis reveals that this growth reflects a substantial increase in the single-particle (quantum) lifetime, which likely originates from the light-induced redistribution of charge enhancing the screening capability of the doping layers.