Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling

ARTICLE DOI: 10.1038/s41467-017-01810-y OPEN Possible nematic to smectic phase transition in a two-dimensional electron gas at half-filling 1234567890 Q. Qian1, J. Nakamura1, S. Fallahi1,2, G.C. Gardner2,3,4 & M.J. Manfra1,2,3,4,5 Liquid crystalline phases of matter permeate nature and technology, with examples ranging from cell membranes to liquid-crystal displays. Remarkably, electronic liquid-crystal phases can exist in two-dimensional electron systems (2DES) at half Landau-level filling in the quantum Hall regime. Theory has predicted the existence of a liquid-crystal smectic phase that breaks both rotational and translational symmetries. However, previous experiments in 2DES are most consistent with an anisotropic nematic phase breaking only rotational symmetry. Here we report three transport phenomena at half-filling in ultra-low disorder 2DES: a non-monotonic temperature dependence of the sample resistance, dramatic onset of large time-dependent resistance fluctuations, and a sharp feature in the differential resistance suggestive of depinning. These data suggest that a sequence of symmetry-breaking phase transitions occurs as temperature is lowered: first a transition from an isotropic liquid to a nematic phase and finally to a liquid-crystal smectic phase. 1 Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA. 2 Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA. 3 Station Q Purdue, Purdue University, West Lafayette, IN 47907, USA. 4 School of Materials Engineering, Purdue University, West Lafayette, IN 47907, USA. 5 School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA. Q. Qian and J. Nakamura contributed equally to this work. Correspondence and requests for materials should be addressed to M.J.M. (email: ) NATURE COMMUNICATIONS | 8: 1536 | DOI: 10.1038/s41467-017-01810-y | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-01810-y A clean two-dimensional electron system (2DES) at halffilling in high-index (N ≥ 2) Landau levels (LLs) has been theoretically predicted1 and experimentally observed2 to enter an anisotropic liquid-crystal phase colloquiually deemed the stripe phase. The designation as a stripe phase stems from early theoretical work based on Hartree–Fock analysis that predicted unidirectional charge density wave (CDW) order. Later treatment taking into account quantum fluctuations and disorder raised the possibility of several electronic crystal phases3. Candidate states at half-filling are distinguished by their symmetries: the nematic liquid crystal breaks rotational symmetry while preserving translational symmetry3–6, the smectic liquid crystal (akin to the CDW) breaks rotational symmetry as well as translational symmetry in one spatial direction3,7–10, and the anisotropic stripe crystal breaks translational symmetry in both directions3,7,11–15. At high temperatures or in samples with high disorder, symmetries are restored and the 2DES becomes an isotropic conducting liquid. A qualitative picture of each state16 is shown in Fig. 1. With multiple candidate states available17, an intriguing question arises: which symmetries are broken in the limit of low temperature and minimal disorder? A prominent signature of broken symmetry phases is dramatic transport anisotropy: under typical experimental conditions, the resistance Rxx parallel to the h110i crystallographic direction of the host gallium arsenide (GaAs) lattice reaches a large peak at halffilling, while the resistance Ryy measured parallel to h110i drops to a low value, indicating that it is much easier for current to flow along the nematic ordering direction rather than perpendicular to it. This orientation can be reversed at high 2DES density18 or by applying a magnetic field in the plane of the 2DES19, but it has been found that the easy transport axis is always oriented along one of the crystallographic directions of the GaAs lattice2,20. The nature of the native symmetry-breaking mechanism in the lattice remains unknown, although progress has been made towards understanding it21. Broken symmetry states are usually observed in high (N ≥ 2) Landau levels, but exotic methods may be used to induce a transition from a fractional quantum Hall state to an anisotropic phase at half-filling in the N = 1 Landau level22–24. Previous experiments for N ≥ 2 showing conductivity saturation at finite values at the lowest temperatures, absence of noise specific to CDW order, and lack of evidence of sharp features in differential resistance measurements have supported the nematic, which exhibits short-range stripe ordering but preserves long-range translational symmetry, as the most likely candidate state at half-filling4,6,25. On the other hand, experiments in high-Tc superconducting cuprate materials have shown a series of transitions from isotropic to nematic to smectic as temperature is lowered, with symmetries broken one at a time26,27. Here, we investigate an ultra-low disorder GaAs 2DES cooled to millikelvin temperatures, and we report three transport a b Isotropic phenomena at half-filling. First, we observe a non-monotonic temperature dependence to the resistance Rxx, with Rxx decreasing as the system is cooled at the lowest temperatures, which is consistent with theoretical predictions for the smectic state. Second, we measure sharp features in the differential resistance suggestive of depinning, which indicates broken translational symmetry. Finally, we observe the onset of time-dependent noise in Rxx, which is a prominent feature in conventional materials exhibiting CDW order. Our measurements are consistent with the 2DES undergoing a sequence of temperature-induced phase transitions as it is cooled, from an isotropic state to a nematic phase and finally to a smectic phase with broken rotational and translational symmetries. Results GaAs heterostructures. A key factor in our experiment is the high quality of our GaAs 2DES. We characterize the sample’s quality by its high mobility μ = 28 × 106 cm2 V−1 s−1 and large energy gap for the fragile ν = 5/2 fractional quantum Hall state, Δ5/2 = 570 mK. Figure 2a displays magnetotransport in the N = 1 LL; fractional states at ν = 5/2 and ν = 12/5 are well developed. The strength of these fragile states indicates low disorder in the 2DES, and suggests the possibility that fragile phases may emerge in high LLs as well. Henceforth, we refer to this sample as Sample A. Temperature dependence of Rxx. At low temperature when the magnetic field is tuned near half-filling of the spin-resolved N = 2 LL, the 2DES exhibits anisotropic conduction, indicating a phase with broken rotational symmetry. The magnetotransport near ν = 9/2 and ν = 11/2 in Sample A is shown in Fig. 2b, c. The fourterminal resistance Rxx measured along the h110i direction (the hard transport axis) of the GaAs lattice reaches a large peak near each (...truncated)