Gabriele Naselli, György Frank, Dániel Varjas, Ion Cosma Fulga, Gergő Pintér, András Pályi, Viktor Könye
{"title":"对称约束下韦尔节点合并过程的稳定性","authors":"Gabriele Naselli, György Frank, Dániel Varjas, Ion Cosma Fulga, Gergő Pintér, András Pályi, Viktor Könye","doi":"10.1103/physrevlett.133.196602","DOIUrl":null,"url":null,"abstract":"Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this Letter, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a twofold rotation and time-reversal (<mjx-container ctxtmenu_counter=\"25\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 (2 0 1) 4 3)\"><mjx-mrow data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,3\" data-semantic-content=\"4\" data-semantic- data-semantic-owns=\"2 4 3\" data-semantic-role=\"implicit\" data-semantic-speech=\"upper C 2 script upper T\" data-semantic-type=\"infixop\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐶</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.018em;\"><mjx-mrow size=\"s\"><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\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝒯</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>) symmetry. We find that, counterintuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our Letter suggests that multi-Weyl merging may be observed in a large variety of quantum materials, and we discuss <mjx-container ctxtmenu_counter=\"26\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(2 0 1)\"><mjx-mrow><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"unknown\" data-semantic-speech=\"upper S r upper S i 2\" data-semantic-type=\"subscript\"><mjx-mrow><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: 0.673em;\">S</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.673em;\">r</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.673em;\">S</mjx-c><mjx-c style=\"padding-top: 0.673em;\">i</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><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\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> and bilayer graphene as potential candidates.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":"17 1","pages":""},"PeriodicalIF":8.1000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of Weyl Node Merging Processes under Symmetry Constraints\",\"authors\":\"Gabriele Naselli, György Frank, Dániel Varjas, Ion Cosma Fulga, Gergő Pintér, András Pályi, Viktor Könye\",\"doi\":\"10.1103/physrevlett.133.196602\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this Letter, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a twofold rotation and time-reversal (<mjx-container ctxtmenu_counter=\\\"25\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(5 (2 0 1) 4 3)\\\"><mjx-mrow data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,3\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-owns=\\\"2 4 3\\\" data-semantic-role=\\\"implicit\\\" data-semantic-speech=\\\"upper C 2 script upper T\\\" data-semantic-type=\\\"infixop\\\"><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mrow><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝐶</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.018em;\\\"><mjx-mrow size=\\\"s\\\"><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\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"script\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝒯</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>) symmetry. We find that, counterintuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our Letter suggests that multi-Weyl merging may be observed in a large variety of quantum materials, and we discuss <mjx-container ctxtmenu_counter=\\\"26\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(2 0 1)\\\"><mjx-mrow><mjx-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-role=\\\"unknown\\\" data-semantic-speech=\\\"upper S r upper S i 2\\\" data-semantic-type=\\\"subscript\\\"><mjx-mrow><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: 0.673em;\\\">S</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.673em;\\\">r</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.673em;\\\">S</mjx-c><mjx-c style=\\\"padding-top: 0.673em;\\\">i</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow size=\\\"s\\\"><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\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> and bilayer graphene as potential candidates.\",\"PeriodicalId\":20069,\"journal\":{\"name\":\"Physical review letters\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":8.1000,\"publicationDate\":\"2024-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical review letters\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevlett.133.196602\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review letters","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevlett.133.196602","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Stability of Weyl Node Merging Processes under Symmetry Constraints
Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this Letter, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a twofold rotation and time-reversal (𝐶2𝒯) symmetry. We find that, counterintuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our Letter suggests that multi-Weyl merging may be observed in a large variety of quantum materials, and we discuss SrSi2 and bilayer graphene as potential candidates.
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