{"id":78,"date":"2016-06-14T09:00:38","date_gmt":"2016-06-14T16:00:38","guid":{"rendered":""},"modified":"2024-10-10T11:43:56","modified_gmt":"2024-10-10T18:43:56","slug":"the-half-filled-landau-level-the-case-for-dirac-composite-fermions","status":"publish","type":"post","link":"https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/2016\/06\/14\/the-half-filled-landau-level-the-case-for-dirac-composite-fermions\/","title":{"rendered":"The half-filled Landau level: the case for Dirac composite fermions"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-79\" src=\"https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/wp-content\/uploads\/2017\/09\/img-half-filled-landau-level-2-1-767x383.png\" alt=\"\" width=\"767\" height=\"383\" srcset=\"https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/wp-content\/uploads\/2017\/09\/img-half-filled-landau-level-2-1-767x383.webp 767w, https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/wp-content\/uploads\/2017\/09\/img-half-filled-landau-level-2-1-767x383-300x150.webp 300w, https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/wp-content\/uploads\/2017\/09\/img-half-filled-landau-level-2-1-767x383-330x165.webp 330w, https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/wp-content\/uploads\/2017\/09\/img-half-filled-landau-level-2-1-767x383-400x200.webp 400w\" sizes=\"auto, (max-width: 767px) 100vw, 767px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. At high enough fields, all electrons in a solid can fit in the lowest Landau level. If exactly half of that level is filled with electrons, standard theory predicts that a special fermion liquid phase will form that makes a distinction between the filled and empty states (particles and holes). A recent conjecture, in contrast, predicted a liquid consisting of massless Dirac particles that respects the symmetry between particles and holes. A collaboration led by researchers at Station Q Santa Barbara and the Institute for Quantum Information and Matter at Caltech used sophisticated numerical methods to provide strong evidence for this conjecture. The article appeared recently in Science.<\/p>\n<p><a href=\"http:\/\/science.sciencemag.org\/content\/352\/6282\/197\" target=\"_blank\" rel=\"noopener\">Read the article<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. At high enough fields, all electrons in a solid can fit in the lowest Landau level.<\/p>\n","protected":false},"author":0,"featured_media":13606,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"msxcm_post_with_no_image":false,"ep_exclude_from_search":false,"_classifai_error":"","_classifai_text_to_speech_error":"","footnotes":""},"post_tag":[9],"product":[],"content-type":[1320],"coauthors":[11],"class_list":["post-78","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","tag-quantum-computing","content-type-news"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The half-filled Landau level: the case for Dirac composite fermions - Microsoft Azure Quantum Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/azure.microsoft.com\/en-us\/blog\/quantum\/2016\/06\/14\/the-half-filled-landau-level-the-case-for-dirac-composite-fermions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The half-filled Landau level: the case for Dirac composite fermions - Microsoft Azure Quantum Blog\" \/>\n<meta property=\"og:description\" content=\"&nbsp; In an external magnetic field, the energy of an electron in a two-dimensional system takes discrete values, called Landau levels. 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