{"title":"Coulomb Drag inGraphene/ℎ−BN/GrapheneMoiré Heterostructures","authors":"Yueyang Wang, Hongxia Xue, Xiong Wang, Kenji Watanabe, Takashi Taniguchi, Dong-Keun Ki","doi":"10.1103/physrevlett.133.186301","DOIUrl":null,"url":null,"abstract":"We report on the observation of Coulomb drag between graphene-hexagonal boron nitride (<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=\"0\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"h\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>-BN) moiré heterostructure with a moiré wavelength of <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 breakable=\"true\" data-semantic-children=\"6,2,3,4\" data-semantic-collapsed=\"(10 (c 7 8 9) 6 2 3 4)\" data-semantic- data-semantic-owns=\"6 2 3 4\" data-semantic-role=\"text\" data-semantic-speech=\"tilde 14 n m\" data-semantic-structure=\"(10 (6 5 0 1) 2 3 4)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"5 0 1\" data-semantic-parent=\"10\" data-semantic-role=\"equality\" data-semantic-type=\"relseq\" inline-breaks=\"true\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-break size=\"0\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,∼\" data-semantic-parent=\"6\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.645em;\">1</mjx-c><mjx-c style=\"padding-top: 0.645em;\">4</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.485em;\">n</mjx-c><mjx-c style=\"padding-top: 0.485em;\">m</mjx-c></mjx-mi></mjx-math></mjx-container> and an intrinsic graphene with a lattice constant of <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 breakable=\"true\" data-semantic-children=\"6,2,3,4\" data-semantic-collapsed=\"(10 (c 7 8 9) 6 2 3 4)\" data-semantic- data-semantic-owns=\"6 2 3 4\" data-semantic-role=\"text\" data-semantic-speech=\"tilde 0.25 n m\" data-semantic-structure=\"(10 (6 5 0 1) 2 3 4)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"5 0 1\" data-semantic-parent=\"10\" data-semantic-role=\"equality\" data-semantic-type=\"relseq\" inline-breaks=\"true\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-break size=\"0\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,∼\" data-semantic-parent=\"6\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><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 noic=\"true\" style=\"padding-top: 0.644em;\">2</mjx-c><mjx-c style=\"padding-top: 0.644em;\">5</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"unknown\" data-semantic-type=\"identifier\" space=\"2\"><mjx-c noic=\"true\" style=\"padding-top: 0.485em;\">n</mjx-c><mjx-c style=\"padding-top: 0.485em;\">m</mjx-c></mjx-mi></mjx-math></mjx-container>. By tuning carrier densities of each graphene layer independently, we find that charge carriers in moiré minibands, i.e., near satellite Dirac point (sDP), can be coupled with massless Fermions near the original Dirac point (oDP), strongly enough to generate a finite drag resistivity. At high temperature (<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-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-math></mjx-container>) and large density (<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-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-role=\"latinletter\" data-semantic-speech=\"n\" data-semantic-type=\"identifier\"><mjx-c>𝑛</mjx-c></mjx-mi></mjx-math></mjx-container>), the drag resistivities near both oDP and sDP follow a typical <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=\"(4 0 (3 1 2))\"><mjx-mrow><mjx-msup data-semantic-children=\"0,3\" data-semantic- data-semantic-owns=\"0 3\" data-semantic-role=\"latinletter\" data-semantic-speech=\"n Superscript negative alpha\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑛</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"4\" data-semantic-role=\"negative\" data-semantic-type=\"prefixop\" size=\"s\"><mjx-mo data-semantic- data-semantic-operator=\"prefixop,−\" data-semantic-parent=\"3\" data-semantic-role=\"subtraction\" 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=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛼</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msup></mjx-mrow></mjx-math></mjx-container> (<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=\"(6 0 1 (5 2 3 4))\"><mjx-mrow data-semantic-children=\"0,5\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 5\" data-semantic-role=\"equality\" data-semantic-speech=\"alpha equals 1.3 en dash 1.7\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝛼</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"6\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"2,4\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 4\" data-semantic-parent=\"6\" data-semantic-role=\"dash\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">1</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-mi data-semantic- data-semantic-operator=\"infixop,–\" data-semantic-parent=\"5\" data-semantic-role=\"dash\" data-semantic-type=\"operator\"><mjx-c>–</mjx-c></mjx-mi><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.639em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.639em;\">.</mjx-c><mjx-c style=\"padding-top: 0.639em;\">7</mjx-c></mjx-mn></mjx-mrow></mjx-mrow></mjx-math></mjx-container>) and <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=\"(2 0 1)\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T squared\" data-semantic-type=\"superscript\"><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: 0.363em; margin-left: 0.052em;\"><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-msup></mjx-math></mjx-container> power law dependence as expected for the momentum transfer process and it also satisfies the layer reciprocity. In contrast, at low <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=\"0\"><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-math></mjx-container>, the layer reciprocity is broken in both oDP-oDP and sDP-oDP coupled regions that suggest dominant energy drag. Furthermore, quantitatively, the drag resistivities near sDPs are smaller than those near oDP and they deviate from <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=\"(2 0 1)\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"latinletter\" data-semantic-speech=\"upper T squared\" data-semantic-type=\"superscript\"><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: 0.363em; margin-left: 0.052em;\"><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-msup></mjx-math></mjx-container> dependence below <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 breakable=\"true\" data-semantic-children=\"6,2,3,4\" data-semantic-collapsed=\"(10 (c 7 8 9) 6 2 3 4)\" data-semantic- data-semantic-owns=\"6 2 3 4\" data-semantic-role=\"text\" data-semantic-speech=\"tilde 100 normal upper K\" data-semantic-structure=\"(10 (6 5 0 1) 2 3 4)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"5,1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"5 0 1\" data-semantic-parent=\"10\" data-semantic-role=\"equality\" data-semantic-type=\"relseq\" inline-breaks=\"true\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-break size=\"0\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,∼\" data-semantic-parent=\"6\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"6\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn></mjx-mrow><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"space\" data-semantic-type=\"text\" 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: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>K</mjx-c></mjx-mi></mjx-math></mjx-container>. Our work demonstrates that the drag experiment can be used to investigate the coupling between the carriers in moiré minibands and those in original Dirac bands which can be extended to other moiré materials.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":"9 1","pages":""},"PeriodicalIF":8.1000,"publicationDate":"2024-10-28","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.133.186301","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
We report on the observation of Coulomb drag between graphene-hexagonal boron nitride (ℎ-BN) moiré heterostructure with a moiré wavelength of ∼14nm and an intrinsic graphene with a lattice constant of ∼0.25nm. By tuning carrier densities of each graphene layer independently, we find that charge carriers in moiré minibands, i.e., near satellite Dirac point (sDP), can be coupled with massless Fermions near the original Dirac point (oDP), strongly enough to generate a finite drag resistivity. At high temperature (𝑇) and large density (𝑛), the drag resistivities near both oDP and sDP follow a typical 𝑛−𝛼 (𝛼=1.3–1.7) and 𝑇2 power law dependence as expected for the momentum transfer process and it also satisfies the layer reciprocity. In contrast, at low 𝑇, the layer reciprocity is broken in both oDP-oDP and sDP-oDP coupled regions that suggest dominant energy drag. Furthermore, quantitatively, the drag resistivities near sDPs are smaller than those near oDP and they deviate from 𝑇2 dependence below ∼100K. Our work demonstrates that the drag experiment can be used to investigate the coupling between the carriers in moiré minibands and those in original Dirac bands which can be extended to other moiré materials.
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