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arXiv:1607.03956 · Physical review. B./Physical review. B

Morphing of two-dimensional hole systems at ν=3/2 in parallel magnetic fields: Compressible, stripe, and fractional quantum Hall phases

Yang Liu, M. A. Mueed, Md Shafayat Hossain, S. Hasdermir, Loren N. Pfeiffer, K. W. West, K. W. Baldwin, MANSOUR SHAYEGAN

Published Oct 31, 2016• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.94.155312

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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 \ensuremathν=3/2\ensuremath{\nu}=3/2\ensuremathν=3/2 in tilted magnetic fields. At large tilt angles (\ensuremathθ\ensuremath{\theta}\ensuremathθ), an anisotropic, stripe (or nematic) phase replaces the isotropic compressible Fermi sea at \ensuremathν=3/2\ensuremath{\nu}=3/2\ensuremathν=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 \ensuremathν=3/2\ensuremath{\nu}=3/2\ensuremathν=3/2 in a range of large \ensuremathθ\ensuremath{\theta}\ensuremathθ, and reverts back to a compressible state at even higher \ensuremathθ\ensuremath{\theta}\ensuremathθ. We attribute this remarkable evolution to the significant mixing of the excited and ground-state Landau levels of 2D hole systems in tilted fields.
We investigated the behavior of fractional quantum Hall (FQH) states in a two-dimensional electron system with layer thickness and an in-plane magnetic field. Our comparisons across various filling factors within the first Landau level revealed a crucial observation. A slight in-plane magnetic field specifically enhances the nematic order of the ν=7/3ν= 7/3ν=7/3 FQH state. For this particular filling, through calculating the energy gap, the Ising nematic order parameter, the pair-correlation function, and the static structure factor, we observed that as the in-plane magnetic field increases, the system first enters into an anisotropic FQH phase without closing the spectrum gap, then the FQH nematic (FQHN) phase after neutral gap closing. The system eventually enters a gapless one-dimensional charge density wave (CDW) phase for a large in-plane field. We thus provide a full phase diagram of the ν=7/3ν= 7/3ν=7/3 state in a tilted magnetic field, demonstrating the existence of the FQHN, which aligns with recent resonant inelastic light scattering (RILS) experimental observations.
By exactly solving the effective two-body interaction for two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopotentials (PPs) without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and first Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values. While the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 13\frac{1}{3}31​ and 12\frac{1}{2}21​ filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.
The $\ensuremath{\nu}=5/2$ fractional quantum Hall effect is a system of intense experimental and theoretical interest as its ground state may host non-Abelian excitations, but the exact nature of the ground state is still undetermined. We present the results of an exact diagonalization study of an electron system in the disk configuration, including the effects of Landau level (LL) mixing and the finite thickness of the quantum well confining the electrons. The degeneracy between the two leading candidates for the ground state, the Pfaffian and anti-Pfaffian, is broken by interactions with a neutralizing background, in addition to the inclusion of two- and three-body interactions via LL mixing. As a result of the neutralizing background in the disk configuration, there is a phase transition from the anti-Pfaffian to the Pfaffian as LL mixing is turned on, in stark contrast to what is observed in spherical geometry. This behavior is in agreement with existing experiments, showing the appearance of the Pfaffian state at strong LL mixing before the system enters a compressible phase. The inclusion of LL mixing leads to an increased charge e/4e/4e/4 quasihole size. LL mixing interactions are also shown to overcome the effects of edge reconstruction. Due to finite thickness effects, these properties are enhanced dramatically. We also find that only the Pfaffian and anti-Pfaffian states continue to possess energy gaps at finite width, while gaps for compressible stripe states close, which is in agreement with available experimental data.
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.
The fractional quantum Hall (FQH) nematic state is a conjectured state of matter in which FQH topological order coexists with spontaneously broken rotation symmetry. Recent experiments on GaAs quantum wells suggest this state, as well as the concomitant isotropic-nematic phase transition, may be realized in a two-dimensional electron gas at certain rational filling factors. Although effective field theories of the FQH nematic state have been constructed, there has been so far no explicit realization of this state as the ground state of a microscopic model of interacting electrons. The authors show via a variational approach and numerical exact diagonalization that tuning Haldane pseudopotentials in a model of interacting electrons in the lowest Landau level induces a quantum phase transition out of the isotropic Laughlin FQH liquid and into the FQH nematic state.