{"72404":{"#nid":"72404","#data":{"type":"news","title":"A Two-Dimensional Electron Liquid Solidifies in a Magnetic Field","body":[{"value":"\u003Cp\u003EPhysicists\nfrom the Georgia Institute of Technology have developed a theory that describes,\nin a unified manner, the coexistence of liquid and pinned solid phases of\nelectrons in two dimensions under the influence of a magnetic field. The theory\nalso describes the transition between these phases as the field is varied. The\ntheoretical predictions by Constantine Yannouleas and Uzi Landman, from Georgia\nTech\u2019s School of Physics, aim to explain and provide insights into the origins\nof experimental findings published last year by a team of researchers from\nPrinceton, Florida State and Purdue universities. The research appears in the\nOctober 27 edition of the journal \u003Cem\u003EPhysical\nReview B\u003C\/em\u003E. \u003C\/p\u003E\n\n\u003Cp\u003EThe\nexperimental discovery in 1982 of a new Hall conductance step at a fraction\n\u03bd=1\/m with m=3, that is at\u0026nbsp; (1\/3)e\u003Csup\u003E2\u003C\/sup\u003E\/h\n(with more conductance steps, at other m, found later) \u2013 where h is the Planck\nconstant and e is the electron charge \u2013 was made for\u0026nbsp; two-dimensional electrons at low temperatures\nand strong magnetic fields and was greeted with great surprise.\u0026nbsp; The theoretical explanation of this finding a\nyear later by Robert Laughlin in terms of a new form of a quantum fluid, earned\nhim and the experimentalists Horst St\u00f6rmer and Daniel Tsui the 1998 Nobel Prize\nwith the citation \u201cfor the discovery of a new form of quantum fluid with fractionally\ncharged excitations.\u201d These discoveries represent conceptual breakthroughs in\nthe understanding of matter, and the fractional quantum Hall effect (FQHE) liquid\nstates, originating from the highly correlated nature of the electrons in these\nsystems, have been termed as new states of matter. \n\n\u003C\/p\u003E\u003Cp\u003E\u201cThe\nquantum fluid state at the 1\/3 primary fraction is the hallmark of the FQHE,\nwhose theoretical understanding has been formulated around the antithesis\nbetween a new form of quantum fluid and the pinned Wigner crystal,\u201d said Landman,\nRegents\u2019 and Institute Professor in the School of\nPhysics, F.E. Callaway Chair and director of the Center for Computational\nMaterials Science (CCMS) at Georgia Tech. \u201cTherefore, the\ndiscovery of pinned crystalline signatures in the neighborhood of the 1\/3 FQHE fraction,\nmeasured as resonances in the microwave spectrum of the two-dimensional\nelectron gas and reported in the Physical Review Letters in September 2010 by a\ngroup of researchers headed by Daniel Tsui, was rather surprising,\u201d he added. \n\n\u003C\/p\u003E\u003Cp\u003EIndeed,\nformation of a hexagonally ordered two-dimensional electron solid phase, a so\ncalled Wigner crystal (WC) named after the Nobel laureate physicist Eugene\nWigner who predicted its existence in 1934, has been anticipated for smaller\nquantum Hall fractional fillings, \u03bd, of the lowest Landau level populated by\nthe electrons at high magnetic fields, for example \u03bd = 1\/9, 1\/7 and even 1\/5.\nHowever, the electrons in the \u03bd=1\/3 fraction were believed to resist\ncrystallization and remain liquid. \n\n\u003C\/p\u003E\u003Cp\u003EThe\nGeorgia Tech physicists developed a theoretical formalism that, in conjunction\nwith exact numerical solutions, provides a unified microscopic approach to the\ninterplay between FQHE liquid and Wigner solid states in the neighborhood of\nthe 1\/3 fractional filling. A major advantage of their approach is the use of a\nsingle class of variational wave functions for description of both the quantum\nliquid and solid phases.\u0026nbsp; \n\n\u003C\/p\u003E\u003Cp\u003E\u201cLiquid\ncharacteristics of the fractional quantum Hall effect states are associated\nwith symmetry-conserving vibrations and rotations of the strongly interacting\nelectrons and they coexist with intrinsic correlations that are crystalline in\nnature,\u201d Senior Research Scientist Yannouleas and Landman wrote in the opening section of their paper.\n\u201cWhile the electron densities of the fractional quantum Hall effect liquid\nstate do not exhibit crystalline patterns, the intrinsic crystalline\ncorrelations which they possess are reflected in the emergence of a sequence of\nliquid states of enhanced stability, called cusp states, that correspond in the\nthermodynamic limit to the fractional quantum Hall effect filling fractions\nobserved in Hall conductance measurements,\u201d they added.\n\n\u003C\/p\u003E\u003Cp\u003EThe\nkey to their explanation of the recent experimental observations pertaining to\nthe appearance of solid characteristics for magnetic fields in the neighborhood\nof the 1\/3 filling fraction is their finding that \u201caway from the exact\nfractional fillings, for example near \u03bd=1\/3, weak pinning perturbations, due to\nweak disorder, may overcome the energy gaps between adjacent good angular\nmomentum symmetry-conserving states. The coupling between these states\ngenerates broken-symmetry ground states whose densities exhibit spatial\ncrystalline patterns. At the same time, however, the energy gap between the\nground state at \u03bd=1\/3 and adjacent states is found to be sufficiently large to\nprevent disorder-induced mixing, thus preserving its quantum fluid nature.\u201d\u0026nbsp; \n\n\u003C\/p\u003E\u003Cp\u003EFurthermore,\nthe work shows that the emergence of the crystalline features, via the pinning\nperturbations, is a consequence of the aforementioned presence of crystalline\ncorrelations in the symmetry-conserving states. Consequently, mixing rules that\ngovern the nature of the disorder-pinned crystalline states have been\nformulated and tested.\u0026nbsp; Extrapolation of\nthe calculated results to the thermodynamic limit shows development of a\nhexagonal Wigner crystal with enhanced stability due to quantum correlations.\n\n\u003C\/p\u003E\u003Cp\u003E\u201cIn\nclosing, the nature of electrons in the fractional quantum Hall regime continues\nnow for close to three decades to be a subject of great fascination, a research\nfield that raises questions whose investigations can lead to deeper conceptual\nunderstanding of matter and many-body phenomena, and a rich\u0026nbsp; source of surprise and discovery,\u201d said\nLandman.\n\n\u003C\/p\u003E\u003Cp\u003EThis work was\nsupported by the Office of Basic Energy\nSciences of the US Department of Energy.\n\n\u003C\/p\u003E\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003EPhysicists from the Georgia Institute of\nTechnology have developed a theory that describes, in a unified manner, the\ncoexistence of liquid and pinned solid phases of electrons in two dimensions\nunder the influence of a magnetic field. The theory also describes the\ntransition between these phases as the field is varied.\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Physicists from the Georgia Institute of Technology have developed a theory that describes, in a unified manner, the coexistence of liquid and pinned solid phases of electrons in two dimensions under the influence of a magnetic field."}],"uid":"27560","created_gmt":"2011-11-04 09:05:37","changed_gmt":"2016-10-08 03:10:38","author":"Jason Maderer","boilerplate_text":"","field_publication":"","field_article_url":"","dateline":{"date":"2011-11-04T00:00:00-04:00","iso_date":"2011-11-04T00:00:00-04:00","tz":"America\/New_York"},"extras":[],"hg_media":{"72403":{"id":"72403","type":"image","title":"Two-Dimensional Electron Liquid Solidifies in a Magnetic Field","body":null,"created":"1449177930","gmt_created":"2015-12-03 21:25:30","changed":"1475894656","gmt_changed":"2016-10-08 02:44:16","alt":"Two-Dimensional Electron Liquid Solidifies in a Magnetic Field","file":{"fid":"193672","name":"uzi_.jpg","image_path":"\/sites\/default\/files\/images\/uzi__0.jpg","image_full_path":"http:\/\/hg.gatech.edu\/\/sites\/default\/files\/images\/uzi__0.jpg","mime":"image\/jpeg","size":354099,"path_740":"http:\/\/hg.gatech.edu\/sites\/default\/files\/styles\/740xx_scale\/public\/images\/uzi__0.jpg?itok=7lVQIWoA"}},"40073":{"id":"40073","type":"image","title":"Uzi Landman","body":null,"created":"1449174146","gmt_created":"2015-12-03 20:22:26","changed":"1475894231","gmt_changed":"2016-10-08 02:37:11","alt":"Uzi Landman","file":{"fid":"189593","name":"tsm23821.jpg","image_path":"\/sites\/default\/files\/images\/tsm23821.jpg","image_full_path":"http:\/\/hg.gatech.edu\/\/sites\/default\/files\/images\/tsm23821.jpg","mime":"image\/jpeg","size":1903110,"path_740":"http:\/\/hg.gatech.edu\/sites\/default\/files\/styles\/740xx_scale\/public\/images\/tsm23821.jpg?itok=29GUIZ6M"}}},"media_ids":["72403","40073"],"related_links":[{"url":"http:\/\/www.cos.gatech.edu\/","title":"College of Sciences"},{"url":"http:\/\/www.physics.gatech.edu\/","title":"Georgia Tech School of Physics"},{"url":"http:\/\/www.prism.gatech.edu\/~ph274cy\/","title":"Constantine Yannouleas"},{"url":"https:\/\/www.physics.gatech.edu\/user\/uzi-landman","title":"Uzi Landman"}],"groups":[{"id":"1214","name":"News Room"}],"categories":[{"id":"135","name":"Research"},{"id":"150","name":"Physics and Physical Sciences"}],"keywords":[{"id":"608","name":"electrons"},{"id":"166937","name":"School of Physics"},{"id":"9180","name":"Uzi Landman"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cp\u003EJason Maderer\u003C\/p\u003E\u003Cp\u003EGeorgia Tech Media Relations\u003C\/p\u003E\u003Cp\u003E404-385-2966\u003C\/p\u003E\u003Cp\u003E\u003Ca href=\u0022mailto:maderer@gatech.edu\u0022\u003Emaderer@gatech.edu\u003C\/a\u003E\u003C\/p\u003E","format":"limited_html"}],"email":["jason.maderer@comm.gatech.edu"],"slides":[],"orientation":[],"userdata":""}}}