The subject of this dissertation is the experimental discovery and investigation of a new class of collective phases in two-dimensional electron systems. The experiments mainly involve magnetotransport measurements in very high quality GaAs/AlGaAs semiconductor heterostructures, where a large perpendicular magnetic field serves to resolve the electrons? energy spectrum into discrete Landau levels. The most dramatic evidence of a new many-body phase is the huge and unprecedented resistance anisotropy observed only below 150 mK and around the half-filling points of the highly excited Landau levels N > 1. Associated with these anisotropic states are other novel electron phases whose transport signature is a vanishing longitudinal conductivity occurring in the flanks of the same excited Landau levels. Although reminiscent of the well-understood integer quantum Hall states, the insulating phases are exceptional for being driven by electron interactions rather than single-particle localization. A persuasive theoretical picture based on "stripe" and "bubble" charge density wave formation in high Landau levels can account for many of the experimental results. For example, the broken orientational symmetry of the stripe state may underlie the observed transport anisotropy, while disorder-induced pinning of the bubble lattice could give rise to the insulating regions in high Landau levels. Further investigation of the anisotropic transport characteristics has elucidated possible symmetry-breaking mechanisms of the purported stripe phase and has provided evidence that the stripes may be more accurately described as a quantum electronic liquid crystal. In addition, experiments involving the breakdown of the insulating regions at high voltage biases may point to a depinning transition of the bubble phase. These results have spurred intense interest in the field of correlated electron systems in two dimensions and may be an indication of the variety of new phenomena in condensed matter systems still awaiting discovery.
Quantum Hall systems have a one-body energy spectrum consisting of dispersion-less Landau levels. Electron-electron interactions thus dominate in partially filled Landau levels, which exhibit a myriad of strongly correlated phases such as quantum hall ferromagnets and fractional quantum Hall phases. We study two examples of these phenomena. In the first project, we explore the ground state of a system with an interface between two semi-infinite regions with fillings ν= 4 and ν= 3 respectively. The width of the interface can be controlled by varying the background potential, which provides an additional tuning parameter. For a certain range of interaction strengths, the ν= 4 bulk is unpolarized whereas the ν= 3 bulk is fully polarized. In the parameter space spanned by the interaction strength and width of the interface, we find two phases at the interface. Phase A has spin as a good quantum number, and the long-wavelength spin edge excitations are gapped. In phase B, spin rotation symmetry is spontaneously broken at the mean-field level. Using symmetry arguments we find the effective theory near the interface of phase B. This effective theory is known to have gapless long-wavelength spin excitations. In the second project, we study the ground state of a tunnel-decoupled double-layer graphene system when both layers are undoped. We find a simple Hamiltonian in the continuum limit from symmetries of the system. Using the Hartree-Fock approximation we find a state with inter-layer coherence with broken layer U(1) symmetry. This phase becomes magnetized in presence of a non-zero Zeeman field. A first-order phase transition can be driven from the ferromagnetic phase to the magnetized inter-layer coherent phase by increasing the Zeeman field. We predict the number of gapless modes in the bulk.
The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the non-perturbative fixed phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the
ν−κ plane, where
ν is the filling factor and
κ is the strength of Landau level mixing. The phase boundary is seen to exhibit a striking
ν dependence, with the states away from the magic filling factors
ν=n/(2pn+1) being much more susceptible to crystallization due to Landau level mixing than those at
ν=n/(2pn+1). Our results explain the qualitative difference between the experimental behaviors observed in n-doped and p-doped GaAs quantum wells, and, in particular, the existence of an insulating state for
ν<1/3 and also for
1/3<ν<2/5 in low density p-doped systems. We predict that in the vicinity of
ν=1/5 and
ν=2/9, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal but rather into a strongly correlated crystal of composite fermions carrying two vortices.
The Hamiltonian describing interacting two-dimensional electrons in a high magnetic field is diagonalized numerically for a small number of particles to obtain the low-lying excitation spectra. The results include estimates of energy gaps for values of $\ensuremath{\nu}$ (the lowest-Landau-level filling factor) equal to certain multiples of
51,
71,
91, and
111. These $\ensuremath{\nu}'\mathrm{s}$ are characterized by the existence of periodic rigid parent states which generate maximum phase space. The even-denominator cases are markedly different.
At low temperatures, two-dimensional electron systems in a perpendicular magnetic field exhibit remarkable quantum phenomena. In these extreme conditions, strongly correlated electron systems stabilize in different quantum phases as the filling factor of Landau levels is varied. In this Brief Report we present finite-size Monte Carlo simulation results for anisotropic quantum Hall liquid states observed at certain even-denominator filling factors. The anisotropic electronic liquid phases are described by a broken rotational symmetry wave function. Our investigations of systems of few electrons in disk geometry indicate that an anisotropic liquid-crystalline quantum Hall phase with broken rotational symmetry is energetically favored relative to an isotropic liquid one.
A transport study of two-dimensional (2D) holes confined to wide GaAs quantum wells provides a glimpse of a subtle competition between different many-body phases at a Landau level filling $\ensuremath{\nu}=3/2$ in tilted magnetic fields. At large tilt angles ($\ensuremath{\theta}$), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at $\ensuremath{\nu}=3/2$ if the quantum well has a symmetric charge distribution. When the charge distribution is made asymmetric, instead of the stripe phase, an even-denominator fractional quantum state appears at $\ensuremath{\nu}=3/2$ in a range of large $\ensuremath{\theta}$, and reverts back to a compressible state at even higher $\ensuremath{\theta}$. We attribute this remarkable evolution to the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields.