Research ArticleCONDENSED MATTER PHYSICS

A cascade of phase transitions in an orbitally mixed half-filled Landau level

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Science Advances  14 Sep 2018:
Vol. 4, no. 9, eaat8742
DOI: 10.1126/sciadv.aat8742
  • Fig. 1 Overview of correlated phases, samples, and the experimental parameter space.

    (A to E) Exemplary magnetotransport sweeps of prominent phases explored in this work. The vertical scale bar corresponds to a longitudinal resistance of 100 ohms. (F) Measurement configuration where a MgZnO/ZnO 2DES device is tilted by θ relative to Bt. (G) Single-particle energy diagram of spin split LLs, where θ is increased and EZ is selectively enhanced relative to Ecyc, with Δ their energy difference. Opposing spin levels of adjacent LLs cross at the jth coincidence position. The chemical potential (μν) is traced as a bold red line for ν = 5/2. (H) Spin susceptibility (g*m*/m0) as a function of charge density (n). (I) T = 450 mK magnetotransport map of sample a (n = 5.8 × 1011 cm−2) with (J) color coding the corresponding orbital and spin character of partially filled levels and j = 1 and 2 coincidence points.

  • Fig. 2 Ground states of sample a.

    (A) T = 20 mK magnetotransport map. (B) Minimum of resistance (δRxx) at ν = 5/2 relative to surrounding fillings as a function of θ. A positive value indicates a minimum at ν = 5/2, as shown in the inset data trace. Close-up mapping of the (C) ICP2 and (D) ICP1 and CP1 phases, with boxes displaying magnetotransport traces at the angle indicated by colored arrows. The box height corresponds to Δ200 ohms.

  • Fig. 3 Ground states and hysteresis of sample b.

    (A and B) Magnetotransport maps (T = 20 mK) for two orthogonal crystal directions, with Rxx associated with IBt and Ryy with I||Bt. (C) Activation energy Δμ of prominent FQH states. (D) Isotropic reentrant integer quantum Hall features at T = 90 mK: mapping of Rxy with reentrant integer quantum Hall features of ν = 2 framed by dotted lines. The subpanels identify their hysteretic behavior, with the scale bar equaling 0.1[h/e2]. (E) Hysteresis at T = 200 mK: mapping of ΔRxx. Individual traces with B-sweep direction–dependent transport are shown for discrete angles in the subpanels. The scale bar corresponds to an Rxx of 10 ohms. Red triangles indicate the j = 1|ν=2 coincidence position.

  • Fig. 4 Phase diagram of ground states.

    (A) Map of the ground states in the (ν-EZ/Ecyc) plane through the transitions from N = 1 (light purple) to 0 (orange) orbital character. The range of FQH features is shown as purple, with the anisotropic CDW-like phase shaded red and isotropic reentrant phases shaded light blue. The range of hysteretic features identified in transport maps is shown as dotted lines for T = 200 mK (red) and 90 mK (blue). (B) Summary of the transitions at ν = 5/2 in terms of EZ/Ecyc|j=2 as a function of n, as per Eq. 1.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/9/eaat8742/DC1

    Section S1. Further discussion on the ground states

    Section S2. Candidate phases

    Fig. S1. Observed sequence of states at filling fraction Formula = 3/2, which corresponds to a total filing ν = 5/2.

    Fig. S2. Continuous depolarization in the auxiliary problem of a two-component half-filled N = 0 LL.

    Fig. S3. Parameters of samples as a function of charge carrier density.

    Fig. S4. Summary of the transitions at ν = 5/2 as a function of n for multiple samples for 1/cosθ.

    Fig. S5. Extended data set from Fig. 1.

    Fig. S6. Mapping of magnetotransport of sample b around ν = 5/2.

    Fig. S7. Temperature-dependent magnetotransport of the ICP1 phase.

    Fig. S8. Temperature dependence of anisotropy.

    Fig. S9. Map of the hysteresis in the data presented in Fig. 3D at T = 90 mK in Rxy.

    Fig. S10. Analysis of exchange energy corrections to single-particle level crossings.

    References (4346)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Further discussion on the ground states
    • Section S2. Candidate phases
    • Fig. S1. Observed sequence of states at filling fraction ν~ = 3/2, which corresponds to a total filing ν = 5/2.
    • Fig. S2. Continuous depolarization in the auxiliary problem of a two-component half-filled N = 0 LL.
    • Fig. S3. Parameters of samples as a function of charge carrier density.
    • Fig. S4. Summary of the transitions at ν = 5/2 as a function of n for multiple samples for 1/cosθ.
    • Fig. S5. Extended data set from Fig. 1.
    • Fig. S6. Mapping of magnetotransport of sample b around ν = 5/2.
    • Fig. S7. Temperature-dependent magnetotransport of the ICP1 phase.
    • Fig. S8. Temperature dependence of anisotropy.
    • Fig. S9. Map of the hysteresis in the data presented in Fig. 3D at T = 90 mK in Rxy.
    • Fig. S10. Analysis of exchange energy corrections to single-particle level crossings.
    • References (4346)

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