The bilayer quantum Hall state at total filling factor *ν _{T}=1*, where the total electron density matches the degeneracy of the lowest Landau level, is a prominent example of Bose-Einstein condensation of excitons. A macroscopically ordered state is realized where an electron in one layer is tightly bound to a “hole” in the other layer. If exciton transport were the only bulk transportmechanism, a current driven in one layer would spontaneously generate a current of equal magnitude and opposite sign in the other layer. The Corbino Coulomb drag measurements presented in this thesis demonstrate precisely this phenomenon.

Excitonic superfluidity has been long sought in the *ν _{T}=1* state. The tunneling between the two electron gas layers exihibit a

The subject of this thesis is the measurement and interpretation of thermopower in high-mobility two-dimensional electron systems (2DESs). These 2DESs are realized within state-of-the-art GaAs/AlGaAs heterostructures that are cooled to temperatures as low as T = 20 mK. Much of this work takes place within strong magnetic fields where the single-particle density of states quantizes into discrete Landau levels (LLs), a regime best known for the quantum Hall effect (QHE). In addition, we review a novel hot-electron technique for measuring thermopower of 2DESs that dramatically reduces the influence of phonon drag.

Early chapters concentrate on experimental materials and methods. A brief overview of GaAs/AlGaAs heterostructures and device fabrication is followed by details of our cryogenic setup. Next, we provide a primer on thermopower that focuses on 2DESs at low temperatures. We then review our experimental devices, temperature calibration methods, as well as measurement circuits and protocols.

Latter chapters focus on the physics and thermopower results in the QHE regime. After reviewing the basic phenomena associated with the QHE, we discuss thermopower in this regime. Emphasis is given to the relationship between diffusion thermopower and entropy. Experimental results demonstrate this relationship persists well into the fractional quantum Hall (FQH) regime.

Several experimental results are reviewed. Unprecedented observations of the diffusion thermopower of a high-mobility 2DES at temperatures as high as T = 2 K are achieved using our hot-electron technique. The composite fermion (CF) effective mass is extracted from measurements of thermopower at LL filling factor ν = 3/2. The thermopower versus magnetic field in the FQH regime is shown to be qualitatively consistent with a simple entropic model of CFs. The thermopower at ν = 5/2 is shown to be quantitatively consistent with the presence of non-Abelian anyons. An abrupt collapse of thermopower is observed at the onset of the reentrant integer quantum Hall effect (RIQHE). And the thermopower at temperatures just above the RIQHE transition suggests the existence of an unconventional conducting phase.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Eisenstein, James P.}, } @phdthesis{10.7907/PQJV-SB92, author = {Finck, Aaron David Kiyoshi}, title = {Studies of Exciton Condensation and Transport in Quantum Hall Bilayers}, school = {California Institute of Technology}, year = {2012}, doi = {10.7907/PQJV-SB92}, url = {https://resolver.caltech.edu/CaltechTHESIS:09262011-144749993}, abstract = {This thesis is a report of the transport properties of bilayer two-dimensional electron systems found in GaAs/AlGaAs double quantum well semiconductor heterostructures. When a strong perpendicular magnetic field is applied so that the total Landau filling factor is equal to one and if the two layers are close enough together, a novel quantum Hall (QH) state with strong interlayer correlations can form. This QH state is often described as an excitonic condensate, in which electrons in one layer pair with holes in the other. As neutral particles, excitons feel no Lorentz force and are not confined to the edges of the bilayer system like charged quasiparticles are. Instead, excitons are expected to be able to move freely through the bulk and even flow without any dissipation under proper conditions (i.e.,~excitonic superfluidity). Counterflow studies that directly probe the bulk verify this exciton transport in the electrically insulating interior. We also report on studies of the phase boundary between the correlated and uncorrelated phases at total Landau filling factor one as the effective interlayer separation is tuned. When both phases are fully spin polarized at high Zeeman energy, the phase transition is much broader than when the uncorrelated phase is incompletely polarized at low Zeeman energy. This suggests a possible change in the nature of the phase transition in the regime of complete spin polarization.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Eisenstein, James P.}, } @phdthesis{10.7907/E1X6-F676, author = {Tracy, Lisa A}, title = {Studies of Two Dimensional Electron Systems via Surface Acoustic Waves and Nuclear Magnetic Resonance Techniques}, school = {California Institute of Technology}, year = {2008}, doi = {10.7907/E1X6-F676}, url = {https://resolver.caltech.edu/CaltechETD:etd-11032007-160944}, abstract = {This thesis presents measurements investigating the spin degree of freedom in two dimensional electron systems (2DES’s). The measurements use nuclear magnetic resonance (NMR) techniques to study the role of spin in several 2DES states.

We first examine the spin transition that occurs in a half-filled Landau level in a single layer 2DES and compare our measurements to expectations from a composite fermion (CF) model. We show the temperature and density dependence of the nuclear T1 and resistively-detected NMR signal. The T₁ data can be roughly understood via a Korringa-like model of nuclear spin relaxation. However, the observed density dependence of both T₁ and the NMR signal is not explained by conventional CF theory.

We next consider a bilayer 2DES consisting of two closely spaced 2D electron layers, where each of the individual layers contains a half-filled Landau level. In this system, a transition occurs from a compressible single layer-like state to an incompressible correlated bilayer state as a function of the effective spacing between the two layers. When the effective spacing is made small enough, interactions between the two layers lead to the formation of a new state that can be viewed as a Bose condensate of excitons. Using NMR techniques we show that the spin degree of freedom is active during this transition.

In a single-layer 2DES with one completely filled Landau level (ν = 1), charged spin-texture excitations called skyrmions" are expected to exist. We probe the spin dynamics near this state using NMR. We find relatively fast nuclear relaxation rates that are consistent with a theory of spin excitations for a skyrmion solid. Our measurements also provide clues as to the origin of an “anomalous” NMR lineshape seen near ν=1.

We also present surface acoustic wave (SAW) measurements in a low density 2DES at zero magnetic field, under conditions where a 2D metal-insulator transition may occur. We find that our SAW data are consistent with a disorder-driven, percolation-type transition.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Eisenstein, James P.}, } @phdthesis{10.7907/7ZKQ-QD67, author = {Kellogg, Melinda Jane}, title = {Evidence for Excitonic Superfluidity in a Bilayer Two-Dimensional Electron System}, school = {California Institute of Technology}, year = {2005}, doi = {10.7907/7ZKQ-QD67}, url = {https://resolver.caltech.edu/CaltechETD:etd-08102004-204105}, abstract = {

The discovery of the integer quantum Hall effect (QHE) and the fractional quantum Hall effect (FQHE) revealed that unexpected physics could be found in a seemingly very simple system: free electrons constrained to move in only two dimensions. Adding a degree of complexity to this system by bringing two of these layers of two-dimensional electrons into close proximity, multiplies the exciting physical phenomena available for study and discovery. This thesis is a report on electrical transport studies of bilayer two-dimensional electron systems (2DES) found in GaAs/AlGaAs double quantum well semiconductor heterostructures. Through studies at zero magnetic field using a fairly new transport measurement called “Coulomb drag” pure electron-electron scattering is measured with unprecedented accuracy and clarity. In large magnetic fields applied perpendicular to the electron layers, at the right combination of magnetic field strength, electron density and layer separation, a new, uniquely bilayer, many-body quantum ground state exists that can be described alternately as an itinerant pseudospin ferromagnet or as a Bose-Einstein condensate (BEC) of interlayer excitons. This bilayer quantum state was first predicted theoretically fifteen years ago, and its discovery and exploration is the basis of this thesis. In this thesis, transport measurements allow for the direct detection of the BEC of excitons by their ability to flow with vanishing resistance and vanishing influence from the large external magnetic field. Excitonic BEC has been pursued experimentally for almost 40 years, but this thesis likely represents the first detection of the elusive state. Coulomb drag is found to be an excellent probe of the phase transition out of the bilayer quantum state and is used to extend the mapping of the phase diagram into the temperature and layer density imbalance planes.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Eisenstein, James P.}, } @phdthesis{10.7907/JAXZ-YV11, author = {Spielman, Ian Bairstow}, title = {Evidence for the Josephson Effect in Quantum Hall Bilayers}, school = {California Institute of Technology}, year = {2004}, doi = {10.7907/JAXZ-YV11}, url = {https://resolver.caltech.edu/CaltechETD:etd-05192004-092920}, abstract = {
This thesis presents tunneling measurements on bilayer two-dimensional (2D) electrons systems in GaAs/AlGaAs double quantum wells. 2D-2D tunneling is applied here as a probe of the inter-layer correlated quantum Hall state at total Landau level filling factor ν_{T} = 1. This bilayer state is theoretically expected to be an excitonic superfluid with an associated dissipationless current and Josephson effect.

In addition to the conventional signatures of the quantum Hall effect ? a pronounced minimum in R_{xx} and associated quantization of R_{xy} - the strong inter-layer correlations lead to a step-like discontinuity in the tunneling I ? V. Although reminiscent of the DC Josephson effect, the tunneling discontinuity has a finite extent even at the lowest temperatures (the peak in conductance, dI/dV, is strongly temperature dependent even below 15 mK. The correlations develop when the inter- and intra-layer Coulomb interactions become comparable. The relative importance of which is determined by the ratio of layer separation to average electron spacing. Although this state is theoretically expected to be an excitonic superfluid, the degree to which intra-layer tunneling is Josephson-like is controversial. At a critical layer separation the zero-bias tunneling feature is lost, which we interpret as signaling the quantum phase transition to the uncorrelated state. We study the dependence of the phase transition on electron density and relative density imbalance. In the presence of a parallel magnetic field tunneling probes the response of the spectral function at finite wave vector. These tunneling spectra directly detect the expected linearly dispersing Goldstone mode; our measurement of this mode is in good agreement with theoretical expectations. There remains deep theoretical and experimental interest in this state, which represents a unprecedented convergence in the physics of quantum Hall effects and superconductivity.