Origin of the charge density wave state inBaFe2⁢Al9

IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Physical Review B Pub Date : 2024-11-06 DOI:10.1103/physrevb.110.195118
Yuping Li, Mingfeng Liu, Jiangxu Li, Jiantao Wang, Junwen Lai, Dongchang He, Ruizhi Qiu, Yan Sun, Xing-Qiu Chen, Peitao Liu
{"title":"Origin of the charge density wave state inBaFe2⁢Al9","authors":"Yuping Li, Mingfeng Liu, Jiangxu Li, Jiantao Wang, Junwen Lai, Dongchang He, Ruizhi Qiu, Yan Sun, Xing-Qiu Chen, Peitao Liu","doi":"10.1103/physrevb.110.195118","DOIUrl":null,"url":null,"abstract":"Recently, a first-order phase transition associated with charge density wave (CDW) has been observed at low temperatures in intermetallic compound <mjx-container ctxtmenu_counter=\"33\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>. However, this transition is absent in its isostructural sister compound <mjx-container ctxtmenu_counter=\"34\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper C o 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">o</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>. Consequently, an intriguing question arises as to the underlying factors that differentiate <mjx-container ctxtmenu_counter=\"35\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> from <mjx-container ctxtmenu_counter=\"36\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper C o 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">o</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> and drive the CDW transition in <mjx-container ctxtmenu_counter=\"37\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>. Here, we set out to address this question by conducting a comparative <i>ab initio</i> study of the electronic structures, lattice dynamics, and electron-phonon interactions of their high-temperature phases. We find that both compounds are dynamically stable with similar phonon dispersions. The electronic structure calculations reveal that both compounds are nonmagnetic metals; however, they exhibit distinct band structures around the Fermi level. In particular, <mjx-container ctxtmenu_counter=\"38\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> exhibits a higher density of states at the Fermi level with dominant partially filled Fe-<mjx-container ctxtmenu_counter=\"39\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(3 0 2 1)\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"0,1\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"0 2 1\" data-semantic-role=\"implicit\" data-semantic-speech=\"3 d\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>3</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"3\" 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=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑑</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> states and a more intricate Fermi surface. This leads to an electronic instability of <mjx-container ctxtmenu_counter=\"40\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> toward the CDW transition, which is manifested by the diverged electronic susceptibility at the CDW wave vector <mjx-container ctxtmenu_counter=\"41\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(13 (2 0 1) 3 (12 4 (11 5 6 7 8 9) 10))\"><mjx-mrow data-semantic-children=\"2,12\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 12\" data-semantic-role=\"equality\" data-semantic-speech=\"bold q Subscript upper C upper D upper W Baseline equals left parenthesis 0.5 comma 0 comma 0.3 right parenthesis\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"bold\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐪</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" size=\"s\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">D</mjx-c><mjx-c style=\"padding-top: 0.669em;\">W</mjx-c></mjx-mi></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"13\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"11\" data-semantic-content=\"4,10\" data-semantic- data-semantic-owns=\"4 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"4\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,6,7,8,9\" data-semantic-content=\"6,8\" data-semantic- data-semantic-owns=\"5 6 7 8 9\" data-semantic-parent=\"12\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"2\"><mjx-c>0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"11\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">.</mjx-c><mjx-c style=\"padding-top: 0.644em;\">3</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"12\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-math></mjx-container>, observable in both the real and imaginary parts. Conversely, <mjx-container ctxtmenu_counter=\"42\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper C o 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">o</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> does not display such behavior, aligning well with experimental observations. Although the electron-phonon interactions in <mjx-container ctxtmenu_counter=\"43\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> surpass those in <mjx-container ctxtmenu_counter=\"44\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper C o 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">C</mjx-c><mjx-c style=\"padding-top: 0.669em;\">o</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> by two orders of magnitude, the strength is relatively weak at the CDW wave vector, suggesting that the CDW in <mjx-container ctxtmenu_counter=\"45\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(7 (2 0 1) 6 (5 3 4))\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"2 6 5\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper B a upper F e 2 upper A l 9\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">a</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">F</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"7\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"7\" data-semantic-role=\"unknown\" data-semantic-type=\"subscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">A</mjx-c><mjx-c style=\"padding-top: 0.706em;\">l</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>9</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> is primarily driven by electronic factors.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"8 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2024-11-06","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.110.195118","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}
引用次数: 0

Abstract

Recently, a first-order phase transition associated with charge density wave (CDW) has been observed at low temperatures in intermetallic compound BaFe2Al9. However, this transition is absent in its isostructural sister compound BaCo2Al9. Consequently, an intriguing question arises as to the underlying factors that differentiate BaFe2Al9 from BaCo2Al9 and drive the CDW transition in BaFe2Al9. Here, we set out to address this question by conducting a comparative ab initio study of the electronic structures, lattice dynamics, and electron-phonon interactions of their high-temperature phases. We find that both compounds are dynamically stable with similar phonon dispersions. The electronic structure calculations reveal that both compounds are nonmagnetic metals; however, they exhibit distinct band structures around the Fermi level. In particular, BaFe2Al9 exhibits a higher density of states at the Fermi level with dominant partially filled Fe-3𝑑 states and a more intricate Fermi surface. This leads to an electronic instability of BaFe2Al9 toward the CDW transition, which is manifested by the diverged electronic susceptibility at the CDW wave vector 𝐪CDW=(0.5,0,0.3), observable in both the real and imaginary parts. Conversely, BaCo2Al9 does not display such behavior, aligning well with experimental observations. Although the electron-phonon interactions in BaFe2Al9 surpass those in BaCo2Al9 by two orders of magnitude, the strength is relatively weak at the CDW wave vector, suggesting that the CDW in BaFe2Al9 is primarily driven by electronic factors.
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BaFe2Al9 中电荷密度波态的起源
最近,在金属间化合物 BaFe2Al9 中观察到低温下与电荷密度波(CDW)相关的一阶相变。然而,在其等结构姊妹化合物 BaCo2Al9 中却没有出现这种转变。因此,一个耐人寻味的问题出现了,即区分 BaFe2Al9 与 BaCo2Al9 并驱动 BaFe2Al9 中 CDW 转变的潜在因素是什么。在这里,我们通过对这两种化合物高温相的电子结构、晶格动力学和电子-声子相互作用进行比较性的 ab initio 研究来解决这个问题。我们发现,这两种化合物都具有类似的声子色散,动态稳定。电子结构计算显示,这两种化合物都是非磁性金属;但是,它们在费米级附近表现出不同的带状结构。其中,BaFe2Al9 在费米水平表现出更高的态密度,主要是部分填充的 Fe-3𝑑态和更复杂的费米面。这导致 BaFe2Al9 在向 CDW 转变时出现电子不稳定性,具体表现为在 CDW 波矢量 𝐪CDW=(0.5,0,0.3) 处的电子易感性发散,在实部和虚部均可观察到。相反,BaCo2Al9 没有显示出这种行为,这与实验观察结果非常吻合。虽然 BaFe2Al9 中的电子-声子相互作用比 BaCo2Al9 高出两个数量级,但在 CDW 波矢处的强度相对较弱,这表明 BaFe2Al9 中的 CDW 主要由电子因素驱动。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical Review B
Physical Review B 物理-物理:凝聚态物理
CiteScore
6.70
自引率
32.40%
发文量
0
审稿时长
3.0 months
期刊介绍: Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide. PRB covers the full range of condensed matter, materials physics, and related subfields, including: -Structure and phase transitions -Ferroelectrics and multiferroics -Disordered systems and alloys -Magnetism -Superconductivity -Electronic structure, photonics, and metamaterials -Semiconductors and mesoscopic systems -Surfaces, nanoscience, and two-dimensional materials -Topological states of matter
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