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 inBaFe2Al9","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.
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