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      Electron–electron interactions and the paired-to-nematic quantum phase transition in the second Landau level

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          Abstract

          In spite of its ubiquity in strongly correlated systems, the competition of paired and nematic ground states remains poorly understood. Recently such a competition was reported in the two-dimensional electron gas at filling factor ν = 5/2. At this filling factor a pressure-induced quantum phase transition was observed from the paired fractional quantum Hall state to the quantum Hall nematic. Here we show that the pressure-induced paired-to-nematic transition also develops at ν = 7/2, demonstrating therefore this transition in both spin branches of the second orbital Landau level. However, we find that pressure is not the only parameter controlling this transition. Indeed, ground states consistent with those observed under pressure also develop in a sample measured at ambient pressure, but in which the electron–electron interaction was tuned close to its value at the quantum critical point. Our experiments suggest that electron–electron interactions play a critical role in driving the paired-to-nematic transition.

          Abstract

          Two-dimensional electron systems at half-filled Landau levels can form unusual electronic states such as paired fractional quantum Hall and nematic phases. Here the authors observe the transition between these two phases at filling factors 5/2 and 7/2 and demonstrate the important influence of interactions.

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          From quantum matter to high-temperature superconductivity in copper oxides.

          The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.
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            Composite-fermion approach for the fractional quantum Hall effect.

            Jain (1989)
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              Electronic Liquid Crystal Phases of a Doped Mott Insulator

              The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charges agglomerate along domain walls at which the spin correlations, which may or may not remain long-ranged, suffer a \(\pi\) phase shift. In two dimensions, these domain walls are ``stripes'' which are either insulating, or conducting, i.e. metallic rivers with their own low energy degrees of freedom. However, quasi one-dimensional metals typically undergo a transition to an insulating ordered charge density wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel, liquid-crystalline low-temperature phases -- an electron smectic, with crystalline order in one direction, but liquid-like correlations in the other, and an electron nematic with orientational order but no long-range positional order. These phases, which constitute new states of matter, can be either high temperature supeconductors or two-dimensional anisotropic ``metallic'' non-Fermi liquids. Evidence for the new phases may already have been obtained by neutron scattering experiments in the cuprate superconductor, La_{1.6-x}Nd_{0.4}Sr_xCuO_{4}.
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                Author and article information

                Contributors
                gcsathy@purdue.edu
                Journal
                Nat Commun
                Nat Commun
                Nature Communications
                Nature Publishing Group UK (London )
                2041-1723
                19 June 2018
                19 June 2018
                2018
                : 9
                : 2400
                Affiliations
                [1 ]ISNI 0000 0004 1937 2197, GRID grid.169077.e, Department of Physics and Astronomy, , Purdue University, ; West Lafayette, IN 47907 USA
                [2 ]ISNI 0000 0004 1937 2197, GRID grid.169077.e, School of Materials Engineering, , Purdue University, ; West Lafayette, IN 47907 USA
                [3 ]ISNI 0000 0004 1937 2197, GRID grid.169077.e, Birck Nanotechnology Center, , Purdue University, ; West Lafayette, IN 47907 USA
                [4 ]ISNI 0000 0004 1937 2197, GRID grid.169077.e, School of Electrical and Computer Engineering, , Purdue University, ; West Lafayette, IN 47907 USA
                [5 ]ISNI 0000 0001 2097 5006, GRID grid.16750.35, Department of Electrical Engineering, , Princeton University, ; Princeton, NJ 08544 USA
                [6 ]ISNI 0000 0001 2097 4740, GRID grid.5292.c, Present Address: QuTech and Kavli Institute of NanoScience, , Delft University of Technology, ; Lorentzweg 1, 2628 CJ Delft, Netherlands
                Article
                4879
                10.1038/s41467-018-04879-1
                6008478
                f2cb4502-13f9-4158-818b-0bd235128d1a
                © The Author(s) 2018

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 6 February 2018
                : 23 May 2018
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