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arXiv:2010.00611 · Communications Physics

Charge density waves and their transitions in anisotropic quantum Hall systems

Yuchi He, Kang Yang, M. O. Goerbig, Roger S. K. Mong

Published Jun 10, 2021• 5 citations
arXivHTMLPDF

Abstract

Abstract In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the N = 2 Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

DOI
10.1038/s42005-021-00613-4

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arXiv:cond-mat/0112233•Physical review. B, Condensed matter•Oct 29, 2002•7 citations
Abstract In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the N = 2 Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.
We investigate the quantum Hall charge density wave states in the N=2N=2N=2 Landau level under mass anisotropy. In the absence of anisotropy, there are two first-order phase transitions between the Wigner crystal, the 222-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 222-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.
The ground-state phase diagram of 2D electrons in a high Landau level (index N=2N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2N=2) is studied by the density-matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/8$ to 1/21/21/2. It is shown that the ground-state phase diagram consists of three different charge density wave states called stripe phase, bubble phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be ${\ensuremath{\nu}}_{c}^{\mathrm{s}\mathrm{\ensuremath{-}}\mathrm{b}}\ensuremath{\sim}0.38$, and that for the bubble phase and Wigner crystal is ${\ensuremath{\nu}}_{c}^{\mathrm{b}\mathrm{\ensuremath{-}}\mathrm{W}}\ensuremath{\sim}0.24$. Each transition is of first order.
We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n=1n=1n=1) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.
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.
Recent experiments indicate the presence of new anisotropic fractional quantum Hall states at regimes not anticipated before. These experiments raise many fundamental questions regarding the inner nature of the electronic system that leads to such anisotropic states. Interplay between electron mass anisotropy and electron-electron correlation effects in a magnetic field can create a rich variety of possibilities. Several anisotropic electronic states ranging from anisotropic quantum Hall liquids to anisotropic Wigner solids may stabilize due to such effects. The electron mass anisotropy in a two-dimensional electron gas effectively leads to an anisotropic Coulomb interaction potential between electrons. An anisotropic interaction potential may strongly influence the stability of various quantum phases that are close in energy since the overall stability of an electronic system is very sensitive to local order. As a result there is a possibility that various anisotropic electronic phases may emerge even in the lowest Landau level in regimes where one would not expect them. In this work we study the state with filling factor 1/6 in the lowest Landau level, a state which is very close to the critical filling factor where the liquid-solid transition takes place. We investigate whether an anisotropic Coulomb interaction potential is able to stabilize an anisotropic electronic liquid state at this filling factor. We describe such an anisotropic state by means of a liquid crystalline wave function with broken rotational symmetry which can be adiabatically connected to the actual wave function for the corresponding isotropic phase. We perform quantum Monte Carlo simulations in a disk geometry to study the properties of the anisotropic electronic liquid state under consideration. The findings indicate stability of liquid crystalline order in presence of an anisotropic Coulomb interaction potential. The results are consistent with the existence of an anisotropic electronic liquid state in the lowest Landau level.
We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge-density wave, becomes the true ground state. The projected electron-density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, ${W}_{c}\ensuremath{\sim}{0.12e}^{2}/\ensuremath{\epsilon}\mathcal{l},$ where a transition/crossover to an isotropic phase with strong local electron-density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.