{"id":4973,"date":"2025-06-24T12:22:14","date_gmt":"2025-06-24T12:22:14","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=4973"},"modified":"2025-12-26T23:34:43","modified_gmt":"2025-12-26T23:34:43","slug":"the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/","title":{"rendered":"The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"4973\" class=\"elementor elementor-4973\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-734f937 elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"734f937\" data-element_type=\"section\" id=\"ourgoal\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-346ad826\" data-id=\"346ad826\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1ad23bb4 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"1ad23bb4\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations<\/h1>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1486bc93 elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"1486bc93\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4c4454fb\" data-id=\"4c4454fb\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-1aae3a19 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1aae3a19\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6a9968e5 elementor-invisible\" data-id=\"6a9968e5\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e18f46c elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"7e18f46c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2021<\/h2>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-477de57c elementor-invisible\" data-id=\"477de57c\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7e190cb0 elementor-widget elementor-widget-heading\" data-id=\"7e190cb0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">KIBU Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2bc25b94 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"2bc25b94\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Micheal Waswa Nakitare<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-cb1ae74 elementor-invisible\" data-id=\"cb1ae74\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2b370bf elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"2b370bf\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.iosrjournals.org\/iosr-jap\/papers\/Vol13-issue3\/Series-2\/D1303021519.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">VIEW ON PUBLISHER SITE<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-7dd3130 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7dd3130\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-5ab34e9f elementor-invisible\" data-id=\"5ab34e9f\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-32bda8f8 elementor-widget elementor-widget-heading\" data-id=\"32bda8f8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4eb67f23 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"4eb67f23\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Strongly correlated electronic models such as the Hubbard, are often used to describe the properties of cuprates. In most cases, the projected Hubbard operators are normally used to study this models. The Hubbard operators normally give rise to a specific kinematical interaction of electrons with spin and charge fluctuations. These interaction is induced by the intraband hopping with a coupling parameter, W=8t, of the order of the kinetic energy of electrons which is much larger than the antiferromagnetic exchange interaction J induced by the interband hopping. This study presents a theoretical approach to specific heat of a spin fluctuated superconductivity in electron-doped Niodium Cellenium Copper Oxide (Nd2-xCexCuO4 -NCCO) and Praseodymium Cellenium Copper Oxide (Pr2-xCexCuO4-PCCO) and hole-doped Yitrium Barium Copper Oxide (YBa2CuO7-YBCO) and Lanthanum Strontium Copper Oxide (La2-xSrxCuO4-LSCO) where these interactions are taken into account within the Hubbard operator technique. The low-energy spin excitations are considered for the Heisenberg model, while the electronic properties are studied using the two-dimensional Hubbard-Holstein model.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2021 KIBU Authors Micheal Waswa Nakitare VIEW ON PUBLISHER SITE Abstract Strongly correlated electronic models such as the Hubbard, are often used to describe the properties of cuprates. In most cases, the projected Hubbard operators are normally used to study this models. The Hubbard operators normally give rise to a specific kinematical interaction of electrons [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4973","post","type-post","status-publish","format-standard","hentry","category-research-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations - Faculty of Science<\/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:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2021 KIBU Authors Micheal Waswa Nakitare VIEW ON PUBLISHER SITE Abstract Strongly correlated electronic models such as the Hubbard, are often used to describe the properties of cuprates. In most cases, the projected Hubbard operators are normally used to study this models. The Hubbard operators normally give rise to a specific kinematical interaction of electrons [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\" \/>\n<meta property=\"og:site_name\" content=\"Faculty of Science\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-24T12:22:14+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-26T23:34:43+00:00\" \/>\n<meta name=\"author\" content=\"kibabii\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"kibabii\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\"},\"author\":{\"name\":\"kibabii\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#\/schema\/person\/fc9b7f13eeb65cf0be520197c35b17d6\"},\"headline\":\"The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations\",\"datePublished\":\"2025-06-24T12:22:14+00:00\",\"dateModified\":\"2025-12-26T23:34:43+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\"},\"wordCount\":190,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/kibu.ac.ke\/fs\/#organization\"},\"articleSection\":[\"Research List\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\",\"url\":\"https:\/\/kibu.ac.ke\/fs\/the-specific-heat-of-a-spin-fluctuated-cuprate-superconductors-with-strong-electronic-phonon-correlations\/\",\"name\":\"The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations - 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