In-plane sliding ferroelectricity and piezoelectricity in bilayer and trilayer𝑔−C3⁢N4

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.110.174103
Yuhua Wei, Zuhui Hu, Xiaonan Ma, Haotian Wang, Feng Gao, Xiaoxuan Ma, Yin Wang, Wei Ren
{"title":"In-plane sliding ferroelectricity and piezoelectricity in bilayer and trilayer𝑔−C3⁢N4","authors":"Yuhua Wei, Zuhui Hu, Xiaonan Ma, Haotian Wang, Feng Gao, Xiaoxuan Ma, Yin Wang, Wei Ren","doi":"10.1103/physrevb.110.174103","DOIUrl":null,"url":null,"abstract":"The graphenelike form of carbon nitride is known as\n<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=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container>, a single sheet of which may be composed of an <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=\"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>-triazine (<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=\"0\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type) or tri-<mjx-container ctxtmenu_counter=\"46\" 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>-triazine (<mjx-container ctxtmenu_counter=\"47\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type) periodic lattice with a different size of hole. By employing the first-principles calculation, we find that the difference in the out of plane polarization caused by the symmetry breaking of the <mjx-container ctxtmenu_counter=\"48\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type or <mjx-container ctxtmenu_counter=\"49\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type structure of bilayer <mjx-container ctxtmenu_counter=\"50\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> through interlayer sliding may be related to the size of the in-plane hole. The nonpolar bilayer <mjx-container ctxtmenu_counter=\"51\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\"52\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>- or <mjx-container ctxtmenu_counter=\"53\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type) state needs to slide about two bond lengths before it is electrically driven to the polar state, resulting in ferroelectric structures with opposite polarization directions. It has been confirmed experimentally and theoretically [Zelisko <i>et al.</i>, <span>Nat. Commun.</span> <b>5</b>, 4284 (2014)] that the anomalous piezoelectric properties of <mjx-container ctxtmenu_counter=\"54\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type <mjx-container ctxtmenu_counter=\"55\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> monolayer come from their noncentrosymmetric triangular holes. Interestingly, we find here that the <mjx-container ctxtmenu_counter=\"56\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type <mjx-container ctxtmenu_counter=\"57\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> exhibits the opposite piezoelectric property to the <mjx-container ctxtmenu_counter=\"58\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type <mjx-container ctxtmenu_counter=\"59\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container>, that is, a negative longitudinal piezoelectricity (NLP). Our computational analysis shows that the superposition of two reversed triangular holes in the <mjx-container ctxtmenu_counter=\"60\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type <mjx-container ctxtmenu_counter=\"61\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> plane will result in the emergence of NLP. Hence, the origin of different piezoelectric properties between <mjx-container ctxtmenu_counter=\"62\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper S\" data-semantic-type=\"identifier\"><mjx-c>𝑆</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type and <mjx-container ctxtmenu_counter=\"63\" 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-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-type <mjx-container ctxtmenu_counter=\"64\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(10 0 1 (9 (4 2 3) 8 (7 5 6)))\"><mjx-mrow data-semantic-children=\"0,9\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 9\" data-semantic-role=\"subtraction\" data-semantic-speech=\"g minus normal upper C 3 normal upper N 4\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑔</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"10\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" 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: 7px;\" variant=\"-explicitFont\">−</mjx-utext></mjx-mtext><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"4,7\" data-semantic-content=\"8\" data-semantic- data-semantic-owns=\"4 8 7\" data-semantic-parent=\"10\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"2,3\" data-semantic- data-semantic-owns=\"2 3\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>C</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=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>3</mjx-c></mjx-mn></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"9\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msub data-semantic-children=\"5,6\" data-semantic- data-semantic-owns=\"5 6\" data-semantic-parent=\"9\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>N</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=\"7\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>4</mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-mrow></mjx-mrow></mjx-math></mjx-container> is comparatively elucidated. These results provide alternative structural manipulation degrees of freedom for the inherent properties of two-dimensional van der Waals layered semiconductor materials, and expand ferroelectric candidate materials for next-generation nanoelectronic devices.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"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.110.174103","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

The graphenelike form of carbon nitride is known as 𝑔C3N4, a single sheet of which may be composed of an 𝑠-triazine (𝑆-type) or tri-𝑠-triazine (𝑇-type) periodic lattice with a different size of hole. By employing the first-principles calculation, we find that the difference in the out of plane polarization caused by the symmetry breaking of the 𝑆-type or 𝑇-type structure of bilayer 𝑔C3N4 through interlayer sliding may be related to the size of the in-plane hole. The nonpolar bilayer 𝑔C3N4 (𝑆- or 𝑇-type) state needs to slide about two bond lengths before it is electrically driven to the polar state, resulting in ferroelectric structures with opposite polarization directions. It has been confirmed experimentally and theoretically [Zelisko et al., Nat. Commun. 5, 4284 (2014)] that the anomalous piezoelectric properties of 𝑇-type 𝑔C3N4 monolayer come from their noncentrosymmetric triangular holes. Interestingly, we find here that the 𝑆-type 𝑔C3N4 exhibits the opposite piezoelectric property to the 𝑇-type 𝑔C3N4, that is, a negative longitudinal piezoelectricity (NLP). Our computational analysis shows that the superposition of two reversed triangular holes in the 𝑆-type 𝑔C3N4 plane will result in the emergence of NLP. Hence, the origin of different piezoelectric properties between 𝑆-type and 𝑇-type 𝑔C3N4 is comparatively elucidated. These results provide alternative structural manipulation degrees of freedom for the inherent properties of two-dimensional van der Waals layered semiconductor materials, and expand ferroelectric candidate materials for next-generation nanoelectronic devices.
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双层和三层𝑔-C3N4 的面内滑动铁电性和压电性
氮化碳的类石墨烯形式被称为𝑔-C3N4,其单片可能由具有不同孔洞大小的𝑠-三嗪(𝑆型)或三𝑠-三嗪(𝑇型)周期晶格组成。通过第一性原理计算,我们发现双层 𝑔-C3N4 的𝑆型或𝑇型结构通过层间滑动对称性破缺引起的平面外极化差异可能与平面内孔的大小有关。非极性双层 𝑔-C3N4(𝑆- 或 𝑇-型)态需要滑动约两个键长才能电驱动到极性态,从而形成极化方向相反的铁电结构。实验和理论证实 [Zelisko 等人,Nat. Commun. 5, 4284 (2014)],𝑇型 𝑔-C3N4单层的反常压电特性来自于它们的非中心对称三角孔。有趣的是,我们发现𝑆 型 𝑔-C3N4 与 𝑇 型 𝑔-C3N4 具有相反的压电特性,即负纵向压电性 (NLP)。我们的计算分析表明,𝑆 型 𝑔-C3N4 平面上两个反向三角孔的叠加将导致 NLP 的出现。因此,𝑆 型和𝑇 型 𝑔-C3N4 之间不同压电特性的起源得到了比较清晰的阐释。这些结果为二维范德瓦尔斯层状半导体材料的固有特性提供了另一种结构操作自由度,并为下一代纳米电子器件拓展了铁电候选材料。
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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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