J. F. Mendez-Valderrama, Dan Mao, Debanjan Chowdhury
{"title":"莫伊里石墨烯中的低能光学和规则","authors":"J. F. Mendez-Valderrama, Dan Mao, Debanjan Chowdhury","doi":"10.1103/physrevlett.133.196501","DOIUrl":null,"url":null,"abstract":"Few layers of graphene at small twist angles have emerged as a fascinating platform for studying the problem of strong interactions in regimes with a nearly quenched single-particle kinetic energy and nontrivial band topology. Starting from the strong-coupling limit of twisted bilayer graphene with a vanishing single-electron bandwidth and interlayer tunneling between the same sublattice sites, we present an <i>exact</i> analytical theory of the Coulomb interaction-induced low-energy optical spectral weight at all <i>integer</i> fillings. In this limit, while the interaction-induced single-particle dispersion is finite, the optical spectral weight vanishes identically at integer fillings. We study corrections to the optical spectral weight by systematically including the effects of experimentally relevant strain-induced renormalization of the single-electron bandwidth and interlayer tunnelings between the same sublattice sites. Given the relationship between the optical spectral weight and the diamagnetic response that controls superconducting <mjx-container ctxtmenu_counter=\"30\" 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-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T Subscript c\" data-semantic-type=\"subscript\"><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>𝑇</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.048em;\"><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\" size=\"s\"><mjx-c>𝑐</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container>, our results highlight the relative importance of specific parent insulating phases in enhancing the tendency towards superconductivity when doped away from integer fillings.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":"26 1","pages":""},"PeriodicalIF":8.1000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Low-Energy Optical Sum Rule in Moiré Graphene\",\"authors\":\"J. F. Mendez-Valderrama, Dan Mao, Debanjan Chowdhury\",\"doi\":\"10.1103/physrevlett.133.196501\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Few layers of graphene at small twist angles have emerged as a fascinating platform for studying the problem of strong interactions in regimes with a nearly quenched single-particle kinetic energy and nontrivial band topology. Starting from the strong-coupling limit of twisted bilayer graphene with a vanishing single-electron bandwidth and interlayer tunneling between the same sublattice sites, we present an <i>exact</i> analytical theory of the Coulomb interaction-induced low-energy optical spectral weight at all <i>integer</i> fillings. In this limit, while the interaction-induced single-particle dispersion is finite, the optical spectral weight vanishes identically at integer fillings. We study corrections to the optical spectral weight by systematically including the effects of experimentally relevant strain-induced renormalization of the single-electron bandwidth and interlayer tunnelings between the same sublattice sites. Given the relationship between the optical spectral weight and the diamagnetic response that controls superconducting <mjx-container ctxtmenu_counter=\\\"30\\\" 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-msub data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-speech=\\\"upper T Subscript c\\\" data-semantic-type=\\\"subscript\\\"><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>𝑇</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.048em;\\\"><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\\\" size=\\\"s\\\"><mjx-c>𝑐</mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math></mjx-container>, our results highlight the relative importance of specific parent insulating phases in enhancing the tendency towards superconductivity when doped away from integer fillings.\",\"PeriodicalId\":20069,\"journal\":{\"name\":\"Physical review letters\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":8.1000,\"publicationDate\":\"2024-11-04\",\"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.133.196501\",\"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.133.196501","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}
Few layers of graphene at small twist angles have emerged as a fascinating platform for studying the problem of strong interactions in regimes with a nearly quenched single-particle kinetic energy and nontrivial band topology. Starting from the strong-coupling limit of twisted bilayer graphene with a vanishing single-electron bandwidth and interlayer tunneling between the same sublattice sites, we present an exact analytical theory of the Coulomb interaction-induced low-energy optical spectral weight at all integer fillings. In this limit, while the interaction-induced single-particle dispersion is finite, the optical spectral weight vanishes identically at integer fillings. We study corrections to the optical spectral weight by systematically including the effects of experimentally relevant strain-induced renormalization of the single-electron bandwidth and interlayer tunnelings between the same sublattice sites. Given the relationship between the optical spectral weight and the diamagnetic response that controls superconducting 𝑇𝑐, our results highlight the relative importance of specific parent insulating phases in enhancing the tendency towards superconductivity when doped away from integer fillings.
期刊介绍:
Physical review letters(PRL)covers the full range of applied, fundamental, and interdisciplinary physics research topics:
General physics, including statistical and quantum mechanics and quantum information
Gravitation, astrophysics, and cosmology
Elementary particles and fields
Nuclear physics
Atomic, molecular, and optical physics
Nonlinear dynamics, fluid dynamics, and classical optics
Plasma and beam physics
Condensed matter and materials physics
Polymers, soft matter, biological, climate and interdisciplinary physics, including networks