An investigation of orientational symmetry-breaking mechanisms in high Landau levels

Cooper, K. B.; Lilly, Michael; Eisenstein, J. P.; Jungwirth, T.; Pfeiffer, L. N.; West, K. W.

doi:10.1016/s0038-1098(01)00212-5

Cited by 50 publications

(97 citation statements)

References 24 publications

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“…Theoretical studies on the influence of a simple periodic modulation on the orientation of the stripes suggest that they prefer to align perpendicular to a weak potential [19,20]. However, a parallel alignment may occur in the strong potential limit [20].Previous experiments that identified the 110 direction as the "easy" axis were limited to fixed densities in the range of 1.5 − 3.0 × 10 11 cm −2 [1,2,17,18]. Furthermore, the correlation between the orientation of the stripes and the native symmetry breaking potential is difficult to deduce since the latter is likely to vary from specimen to specimen.…”

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Density-Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels

et al. 2002

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We observe density induced 90 • rotations of the anisotropy axes in transport measurements at half-filled high Landau levels in the two dimensional electron system, where stripe states are proposed (ν=9/2, 11/2, etc). Using a field effect transistor, we find the transition density to be 2.9×10 11 cm −2 at ν=9/2. Hysteresis is observed in the vicinity of the transition. We construct a phase boundary in the filling factor-magnetic field plane in the regime 4.4 < ν < 4.6. An in-plane magnetic field applied along either anisotropy axis always stabilizes the low density orientation of the stripes. The physics of electrons in higher Landau levels has recently drawn much attention due to the discovery of large transport anisotropies at half fillings (ν = 9/2, 11/2 etc) in high quality two dimensional electron gases (2DEG) in GaAs [1,2]. At these filling factors, longitudinal magneto resistances R xx of samples grown on (001)-oriented GaAs show strong maxima in the 110 direction and deep minima in the 110 direction. The ratio of the resistance values can exceed 1000:1 in high quality samples. This large anisotropy is viewed as strong evidence for the formation of a unidirectional Charge Density Wave or so called "stripe state" around these filling factors [3,4,5,6]. Calculations based on the Hartree-Fock approximation show the stripes to form as the result of the competition between the short-range attractive exchange interaction and the long-range Coulomb repulsion. Recently there appeared calculations beyond the Hartree-Fock approximation [7,8,9,10,11]. Some of them propose the existence of liquid crystalline states with stripe ordering and broken rotational symmetry [7,10]. Employing an edge state transport mechanism, the "easy"(low resistance) axis is along the stripes whereas the "hard" (high resistance) axis is perpendicular to the stripes. This identification is supported by experiments [12].In spite of the strong evidence supporting the formation of a stripe state, the origin of its preferred orientation remains poorly understood [13,14,15]. Theory does not a priori provide a preferred direction for the stripes. However, all previous experiments have identified the 110 direction as the "easy" axis. It is often assumed that anisotropic imperfections at GaAs/AlGaAs interface act as the native symmetry breaking potential. Anisotropic roughness has been observed in GaAs layers grown by Molecular Beam Epitaxy [16]. Two groups have investigated the correlation between the surface roughness and the orientation of the stripes which form a few thousandÅ below the surface. Atomic Force Microscope images reveal the presence of roughness elongated along both the 110 and the 110 directions. However, its correlation with the orientation of the stripes remains controversial [17,18]. Theoretical studies on the influence of a simple periodic modulation on the orientation of the stripes suggest that they prefer to align perpendicular to a weak potential [19,20]. However, a parallel alignment may occur in the strong potential limi...

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Density-Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels

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“…By comparing the in-plane field required to interchange the anisotropy axes with this theory, an estimate of the native anisotropy energy may be obtained: Typical values are around 1 mK per electron. 13 Figures 2͑a͒ and 2͑b͒ display the temperature dependencies of the longitudinal resistance in the hard and easy directions, R hard and R easy , at ϭ9/2. The data in Fig.…”

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“…Below the KT transition temperature, the system is singularly susceptible to external symmetry-breaking fields and is thus readily oriented by some ͑as yet unexplained 13 ͒ weak symmetry breaking field in the GaAs/Al x Ga 1Ϫx As sample. Fradkin et al have modeled the system as a classical 2D XY magnet, modified to accommodate a director field.…”

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Onset of anisotropic transport of two-dimensional electrons in high Landau levels: Possible isotropic-to-nematic liquid-crystal phase transition

et al. 2002

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The recently discovered anisotropy of the longitudinal resistance of two-dimensional electrons near half filling of high Landau levels is found to persist to much higher temperatures T when a large in-plane magnetic field B ʈ is applied. Under these conditions we find that the longitudinal resistivity scales quasilinearly with B ʈ /T. These observations support the notion that the onset of anisotropy at B ʈ ϭ0 does not reflect the spontaneous development of charge density modulations but may instead signal an isotropic-to-nematic liquidcrystal phase transition. DOI: 10.1103/PhysRevB.65.241313 PACS number͑s͒: 73.43.Qt, 73.20.Qt, 73.63.Hs Transport experiments 1,2 on clean two-dimensional electron systems ͑2DES͒ at high perpendicular magnetic field have recently revealed a new class of collective phases at low temperatures. These new phases, which have been observed only when electrons occupy the excited Landau levels, are quite different from the fractional quantized Hall liquids found almost exclusively in the lowest (Nϭ0) Landau level. 3 The new phases exhibit strong electrical transport anisotropies near half filling and curious re-entrant insulating behavior in the flanks of the third and higher (Nу2) Landau level ͑LL͒. At the phenomenological level, these properties are remarkably consistent with those expected from the ''stripe'' and ''bubble'' charge-density waves ͑CDW͒ predicted on the basis of Hartree-Fock ͑HF͒ theory. 4,5 These inhomogeneous states are stabilized by an exchange-energydriven tendency to phase separate which is particularly effective in the excited LLs. Near half filling, the ground state is approximately a unidirectional CDW, i.e., a stripe phase. The anisotropy of the longitudinal resistance observed at this filling is presumed to result from very different electrical conductivities parallel and perpendicular to stripes whose orientation relative to the crystal axes of the host semiconductor is determined by some, as yet unknown, symmetrybreaking field.With the filling factor defined as the ratio of the 2D electron density n s to the degeneracy eB/h of a single-spinresolved LL, the simplest HF stripe state consists of parallel strips in which the filling factor alternates between adjacent integers. For example, at average filling ϭ9/2, corresponding to half filling of the lower spin branch of the N ϭ2 LL, the local filling factor alternates between ϭ4 and ϭ5. The period of this alternation is set by the competition between the direct and exchange Coulomb interactions and is estimated to be on the order of 100 nm in typical samples. These same interactions also determine the temperature at which the stripes form, and HF estimates are in the few Kelvin range. 4 This contrasts with the experimental observation that resistive anisotropy only sets in below about 100 mK. Although disorder in the 2D system may account for some of this discrepancy, a more interesting idea is that the onset of anisotropy does not in fact signal the initial development of charge-density modulation, but instea...

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“…Cooper et al excluded substrate morphology, steps induced by miscuts as well as an anisotropic effective mass as possible explanations [105]. Instead piezoelectric effects have been proposed [106].…”

Section: The Stripe Phasementioning

confidence: 99%

Spin and Charge Ordering in the Quantum Hall Regime

Frieß

2016

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An investigation of orientational symmetry-breaking mechanisms in high Landau levels

Cited by 50 publications

References 24 publications

Density-Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels

Density-Induced Interchange of Anisotropy Axes at Half-Filled High Landau Levels

Onset of anisotropic transport of two-dimensional electrons in high Landau levels: Possible isotropic-to-nematic liquid-crystal phase transition

Spin and Charge Ordering in the Quantum Hall Regime

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