{"title":"Quasiperiodic Moiré Reconstruction and Modulation of Electronic Properties in Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride","authors":"Si-yu Li, Zhiyue Xu, Yingbo Wang, Yingzhuo Han, Kenji Watanabe, Takashi Taniguchi, Aisheng Song, Tian-Bao Ma, Hong-Jun Gao, Yuhang Jiang, Jinhai Mao","doi":"10.1103/physrevlett.133.196401","DOIUrl":null,"url":null,"abstract":"Twisted van der Waals systems have emerged as intriguing arenas for exploring exotic strongly correlated and topological physics, with structural reconstruction and strain playing essential roles in determining their electronic properties. In twisted bilayer graphene aligned with hexagonal boron nitride (<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=\"(6 (5 0 1 2) 3 4)\"><mjx-mrow data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper T upper B upper G divided by h minus upper B upper N\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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: 0.669em;\">T</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c style=\"padding-top: 0.669em;\">G</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" space=\"2\"><mjx-c>/</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>), the interplay between the two sets of moiré patterns from graphene-graphene (<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=\"(3 0 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper G minus upper G\" data-semantic-type=\"infixop\"><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>𝐺</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"3\" 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-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>𝐺</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>) and graphene–<mjx-container ctxtmenu_counter=\"65\" 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 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"subtraction\" data-semantic-speech=\"h minus upper B upper N\" data-semantic-type=\"infixop\"><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>ℎ</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"3\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\"66\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 1 2 3 4)\"><mjx-mrow data-semantic-children=\"0,2,4\" data-semantic-content=\"1,3\" data-semantic- data-semantic-owns=\"0 1 2 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper G minus h minus upper B upper N\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐺</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"5\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" space=\"3\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"3\"><mjx-c>ℎ</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"5\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>) interfaces can trigger notable moiré pattern reconstruction (MPR). Here, we present the quasiperiodic MPR in the <mjx-container ctxtmenu_counter=\"67\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 (5 0 1 2) 3 4)\"><mjx-mrow data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper T upper B upper G divided by h minus upper B upper N\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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: 0.669em;\">T</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c style=\"padding-top: 0.669em;\">G</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" space=\"2\"><mjx-c>/</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> with two similar moiré wavelengths, wherein the MPR results from the incommensurate mismatch between the wavelengths of the <mjx-container ctxtmenu_counter=\"68\" 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 1 2)\"><mjx-mrow data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper G minus upper G\" data-semantic-type=\"infixop\"><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>𝐺</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"3\" 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-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>𝐺</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> and <mjx-container ctxtmenu_counter=\"69\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(5 0 1 2 3 4)\"><mjx-mrow data-semantic-children=\"0,2,4\" data-semantic-content=\"1,3\" data-semantic- data-semantic-owns=\"0 1 2 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper G minus h minus upper B upper N\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐺</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"5\" data-semantic-role=\"subtraction\" data-semantic-type=\"operator\" space=\"3\"><mjx-c>−</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"3\"><mjx-c>ℎ</mjx-c></mjx-mi><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"5\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> moiré patterns. The short-range, nearly ordered moiré super-superstructures deviate from moiré quasicrystal and are accompanied by inhomogeneous strain, thereby inducing spatially variable energy separations between the Van Hove singularities (VHs) in the band structures of the TBG near the magic angle. By tuning the carrier densities in our sample, correlated gaps at specific <mjx-container ctxtmenu_counter=\"70\" 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=\"upper A upper A\" data-semantic-type=\"infixop\"><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>𝐴</mjx-c></mjx-mi><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>𝐴</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> sites are observed, uncovering the quantum-dot-like behavior and incoherent characteristics of the <mjx-container ctxtmenu_counter=\"71\" 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=\"upper A upper A\" data-semantic-type=\"infixop\"><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>𝐴</mjx-c></mjx-mi><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>𝐴</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> sites in the TBG. Our findings would give new hints on the microscopic mechanisms underlying the abundant novel quantum phases in the <mjx-container ctxtmenu_counter=\"72\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(6 (5 0 1 2) 3 4)\"><mjx-mrow data-semantic-children=\"5,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"5 3 4\" data-semantic-role=\"subtraction\" data-semantic-speech=\"upper T upper B upper G divided by h minus upper B upper N\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-parent=\"6\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><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: 0.669em;\">T</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.669em;\">B</mjx-c><mjx-c style=\"padding-top: 0.669em;\">G</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"5\" data-semantic-role=\"division\" data-semantic-type=\"operator\" space=\"2\"><mjx-c>/</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow><mjx-mtext data-semantic-annotation=\"general:text\" data-semantic- data-semantic-operator=\"infixop,−\" data-semantic-parent=\"6\" 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-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">B</mjx-c><mjx-c style=\"padding-top: 0.657em;\">N</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":"5 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.133.196401","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}
引用次数: 0
Abstract
Twisted van der Waals systems have emerged as intriguing arenas for exploring exotic strongly correlated and topological physics, with structural reconstruction and strain playing essential roles in determining their electronic properties. In twisted bilayer graphene aligned with hexagonal boron nitride (TBG/ℎ−BN), the interplay between the two sets of moiré patterns from graphene-graphene (𝐺−𝐺) and graphene–ℎ−BN (𝐺−ℎ−BN) interfaces can trigger notable moiré pattern reconstruction (MPR). Here, we present the quasiperiodic MPR in the TBG/ℎ−BN with two similar moiré wavelengths, wherein the MPR results from the incommensurate mismatch between the wavelengths of the 𝐺−𝐺 and 𝐺−ℎ−BN moiré patterns. The short-range, nearly ordered moiré super-superstructures deviate from moiré quasicrystal and are accompanied by inhomogeneous strain, thereby inducing spatially variable energy separations between the Van Hove singularities (VHs) in the band structures of the TBG near the magic angle. By tuning the carrier densities in our sample, correlated gaps at specific 𝐴𝐴 sites are observed, uncovering the quantum-dot-like behavior and incoherent characteristics of the 𝐴𝐴 sites in the TBG. Our findings would give new hints on the microscopic mechanisms underlying the abundant novel quantum phases in the TBG/ℎ−BN.
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