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{"title":"Altermagnetism and superconductivity in a multiorbital𝑡−𝐽model","authors":"Anjishnu Bose, Samuel Vadnais, Arun Paramekanti","doi":"10.1103/physrevb.110.205120","DOIUrl":null,"url":null,"abstract":"Motivated by exploring correlated multiorbital altermagnets (<mjx-container ctxtmenu_counter=\"145\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l megaseconds\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unit\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 17px;\" variant=\"-explicitFont\">Ms</mjx-utext></mjx-mtext></mjx-math></mjx-container>) we study minimal <mjx-container ctxtmenu_counter=\"146\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"subtraction\" data-semantic-speech=\"t minus upper J\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑡</mjx-c></mjx-mi><mjx-break size=\"3\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"3\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"3\"><mjx-c>𝐽</mjx-c></mjx-mi></mjx-math></mjx-container> models on the square-octagon lattice, which favors such a collinear magnetic order. While antiferromagnetic order breaks translational and time-reversal symmetries, the <mjx-container ctxtmenu_counter=\"147\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> state (equivalently, a “<mjx-container ctxtmenu_counter=\"148\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"d\" data-semantic-type=\"identifier\"><mjx-c>𝑑</mjx-c></mjx-mi></mjx-math></mjx-container>-wave ferromagnet”) features multipolar order, which separately breaks time-reversal and crystal rotation symmetries but preserves their product leading to spin-split bands with zero net magnetization. We study the mean-field phase diagram of these multiorbital models as we vary doping and interactions, discovering two types of <mjx-container ctxtmenu_counter=\"149\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> order: (i) itinerant weak-coupling <mjx-container ctxtmenu_counter=\"150\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> metals driven by quasi-1D van Hove singularities, as well as (ii) strong <mjx-container ctxtmenu_counter=\"151\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> order at half-filling. We also find regimes of superconductivity including uniform <mjx-container ctxtmenu_counter=\"152\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"0\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"s\" data-semantic-type=\"identifier\"><mjx-c>𝑠</mjx-c></mjx-mi></mjx-math></mjx-container>-wave and <mjx-container ctxtmenu_counter=\"153\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 (4 1 3 2))\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-role=\"latinletter\" data-semantic-speech=\"d Subscript x y\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑑</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"1 3 2\" data-semantic-parent=\"5\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"4\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑦</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub></mjx-math></mjx-container>-wave pairing states, incipient <mjx-container ctxtmenu_counter=\"154\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 (4 1 3 2))\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-role=\"latinletter\" data-semantic-speech=\"d Subscript x y\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑑</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"1 3 2\" data-semantic-parent=\"5\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"4\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑦</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub></mjx-math></mjx-container>-wave pair density wave order, and uniform phases with coexisting singlet-triplet pairing and <mjx-container ctxtmenu_counter=\"155\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> order. Our inhomogeneous mean-field theory approach reveals that the coexistence phases are unstable to phase separation, but longer-range interactions could lead to stripe order. Our results may be relevant to studies of doping and pressure on <mjx-container ctxtmenu_counter=\"156\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"0,1,2\" data-semantic-content=\"3,4\" data-semantic- data-semantic-owns=\"0 3 1 4 2\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper A script l upper M\" data-semantic-structure=\"(5 0 3 1 4 2)\" data-semantic-type=\"infixop\"><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 9px;\" variant=\"-explicitFont\">A</mjx-utext></mjx-mtext><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℓ</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mtext data-semantic-annotation=\"general:text;clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 11px;\" variant=\"-explicitFont\">M</mjx-utext></mjx-mtext></mjx-math></mjx-container> materials.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"11 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.205120","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
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