Fractional Chern Insulators in Twisted BilayerMoTe2: A Composite Fermion Perspective

IF 8.1 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Tianhong Lu, Luiz H. Santos
{"title":"Fractional Chern Insulators in Twisted BilayerMoTe2: A Composite Fermion Perspective","authors":"Tianhong Lu, Luiz H. Santos","doi":"10.1103/physrevlett.133.186602","DOIUrl":null,"url":null,"abstract":"The discovery of fractional Chern insulators (FCIs) in twisted bilayer <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=\"(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 M o upper T e 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: 0.657em;\">M</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">o</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">T</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</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> has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This Letter examines the impact of these lattice effects on the topological phases in twisted bilayer <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=\"(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 M o upper T e 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: 0.657em;\">M</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">o</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.657em;\">T</mjx-c><mjx-c style=\"padding-top: 0.657em;\">e</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>, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities <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=\"(35 (5 0 (4 1 3 2)) 6 (34 (30 8 (29 9 10 (28 11 (27 (26 12 25 13) 14 15) 16)) 17) 33 (32 18 (31 (21 19 20) 22 23) 24)))\"><mjx-mrow data-semantic-children=\"5,34\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 34\" data-semantic-role=\"equality\" data-semantic-speech=\"sigma Subscript x y Baseline equals left bracket upper C divided by left parenthesis 2 upper C plus 1 right parenthesis right bracket left parenthesis e squared divided by h right parenthesis\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"35\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"1 3 2\" data-semantic-parent=\"5\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" size=\"s\"><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>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"4\" 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=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑦</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"35\" data-semantic-role=\"equality\" data-semantic-type=\"relation\" space=\"4\"><mjx-c>=</mjx-c></mjx-mo><mjx-mspace></mjx-mspace><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"30,32\" data-semantic-content=\"33\" data-semantic- data-semantic-owns=\"30 33 32\" data-semantic-parent=\"35\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"29\" data-semantic-content=\"8,17\" data-semantic- data-semantic-owns=\"8 29 17\" data-semantic-parent=\"34\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"30\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>[</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"9,28\" data-semantic-content=\"10\" data-semantic- data-semantic-owns=\"9 10 28\" data-semantic-parent=\"30\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"29\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐶</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"29\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"27\" data-semantic-content=\"11,16\" data-semantic- data-semantic-owns=\"11 27 16\" data-semantic-parent=\"29\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"26,15\" data-semantic-content=\"14\" data-semantic- data-semantic-owns=\"26 14 15\" data-semantic-parent=\"28\" data-semantic-role=\"addition\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"12,13\" data-semantic-content=\"25\" data-semantic- data-semantic-owns=\"12 25 13\" data-semantic-parent=\"27\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"26\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"26\" 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=\"26\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝐶</mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,+\" data-semantic-parent=\"27\" data-semantic-role=\"addition\" data-semantic-type=\"operator\" space=\"3\"><mjx-c>+</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"27\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"3\"><mjx-c>1</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"28\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"30\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>]</mjx-c></mjx-mo></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"34\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"31\" data-semantic-content=\"18,24\" data-semantic- data-semantic-owns=\"18 31 24\" data-semantic-parent=\"34\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"32\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"21,23\" data-semantic-content=\"22\" data-semantic- data-semantic-owns=\"21 22 23\" data-semantic-parent=\"32\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mjx-msup data-semantic-children=\"19,20\" data-semantic- data-semantic-owns=\"19 20\" data-semantic-parent=\"31\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑒</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mrow size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"21\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"31\" data-semantic-role=\"division\" 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=\"31\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"32\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow></mjx-mrow></mjx-math></mjx-container> linked to partial filling <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=\"(2 0 1)\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-role=\"greekletter\" data-semantic-speech=\"nu Subscript normal h\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>h</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub></mjx-math></mjx-container> of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number <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=\"upper C\" data-semantic-type=\"identifier\"><mjx-c>𝐶</mjx-c></mjx-mi></mjx-math></mjx-container> within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities <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=\"(22 (5 0 (4 1 3 2)) 6 (21 (20 (18 7 (17 8 9 10) 11) 19 (14 12 13)) 15 16))\"><mjx-mrow data-semantic-children=\"5,21\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 21\" data-semantic-role=\"equality\" data-semantic-speech=\"sigma Subscript x y Baseline equals left parenthesis 2 divided by 3 right parenthesis e squared divided by h\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"22\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"1 3 2\" data-semantic-parent=\"5\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" size=\"s\"><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>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"4\" 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=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑦</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"22\" 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=\"20,16\" data-semantic-content=\"15\" data-semantic- data-semantic-owns=\"20 15 16\" data-semantic-parent=\"22\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"18,14\" data-semantic-content=\"19\" data-semantic- data-semantic-owns=\"18 19 14\" data-semantic-parent=\"21\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"17\" data-semantic-content=\"7,11\" data-semantic- data-semantic-owns=\"7 17 11\" data-semantic-parent=\"20\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"18\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"8,10\" data-semantic-content=\"9\" data-semantic- data-semantic-owns=\"8 9 10\" data-semantic-parent=\"18\" data-semantic-role=\"division\" data-semantic-type=\"infixop\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"17\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"17\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>3</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"18\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"20\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msup data-semantic-children=\"12,13\" data-semantic- data-semantic-owns=\"12 13\" data-semantic-parent=\"20\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mjx-mrow><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑒</mjx-c></mjx-mi></mjx-mrow><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mrow size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msup></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"21\" data-semantic-role=\"division\" 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=\"21\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow></mjx-mrow></mjx-math></mjx-container> and <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 breakable=\"true\" data-semantic-children=\"5,21\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 21\" data-semantic-role=\"equality\" data-semantic-speech=\"sigma Subscript x y Baseline equals left parenthesis 3 divided by 5 right parenthesis e squared divided by h\" data-semantic-structure=\"(22 (5 0 (4 1 3 2)) 6 (21 (20 (18 7 (17 8 9 10) 11) 19 (14 12 13)) 15 16))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"22\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜎</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-annotation=\"clearspeak:simple;clearspeak:unit\" data-semantic-children=\"1,2\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"1 3 2\" data-semantic-parent=\"5\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" size=\"s\"><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>𝑥</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"4\" 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=\"4\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑦</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"22\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"20,16\" data-semantic-content=\"15\" data-semantic- data-semantic-owns=\"20 15 16\" data-semantic-parent=\"22\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"18,14\" data-semantic-content=\"19\" data-semantic- data-semantic-owns=\"18 19 14\" data-semantic-parent=\"21\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"17\" data-semantic-content=\"7,11\" data-semantic- data-semantic-owns=\"7 17 11\" data-semantic-parent=\"20\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"18\" 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data-semantic-operator=\"fenced\" data-semantic-parent=\"18\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,⁢\" data-semantic-parent=\"20\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c>⁢</mjx-c></mjx-mo><mjx-msup data-semantic-children=\"12,13\" data-semantic- data-semantic-owns=\"12 13\" data-semantic-parent=\"20\" data-semantic-role=\"latinletter\" data-semantic-type=\"superscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑒</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.363em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"21\" data-semantic-role=\"division\" 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=\"21\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>ℎ</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container> at fractional fillings <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 breakable=\"true\" data-semantic-children=\"2,7\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 7\" data-semantic-role=\"equality\" data-semantic-speech=\"nu Subscript normal h Baseline equals 2 divided by 3\" data-semantic-structure=\"(8 (2 0 1) 3 (7 4 5 6))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>h</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"8\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-owns=\"4 5 6\" data-semantic-parent=\"8\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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\"><mjx-c>2</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"7\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><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\"><mjx-c>3</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> and <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 breakable=\"true\" data-semantic-children=\"2,7\" data-semantic-content=\"3\" data-semantic- data-semantic-owns=\"2 3 7\" data-semantic-role=\"equality\" data-semantic-speech=\"nu Subscript normal h Baseline equals 3 divided by 5\" data-semantic-structure=\"(8 (2 0 1) 3 (7 4 5 6))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"8\" data-semantic-role=\"greekletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"greekletter\" data-semantic-type=\"identifier\"><mjx-c>𝜈</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow size=\"s\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>h</mjx-c></mjx-mi></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"8\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"4,6\" data-semantic-content=\"5\" data-semantic- data-semantic-owns=\"4 5 6\" data-semantic-parent=\"8\" data-semantic-role=\"division\" data-semantic-type=\"infixop\" space=\"4\"><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\"><mjx-c>3</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"infixop,/\" data-semantic-parent=\"7\" data-semantic-role=\"division\" data-semantic-type=\"operator\"><mjx-c>/</mjx-c></mjx-mo><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\"><mjx-c>5</mjx-c></mjx-mn></mjx-mrow></mjx-math></mjx-container> observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This Letter offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.","PeriodicalId":20069,"journal":{"name":"Physical review letters","volume":null,"pages":null},"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.133.186602","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

The discovery of fractional Chern insulators (FCIs) in twisted bilayer MoTe2 has sparked significant interest in fractional topological matter without external magnetic fields. Unlike the flat dispersion of Landau levels, moiré electronic states are influenced by lattice effects within a nanometer-scale superlattice. This Letter examines the impact of these lattice effects on the topological phases in twisted bilayer MoTe2, uncovering a family of FCIs with Abelian anyonic quasiparticles. Using a composite fermion approach, we identify a sequence of FCIs with fractional Hall conductivities 𝜎𝑥𝑦=[𝐶/(2𝐶+1)](𝑒2/) linked to partial filling 𝜈h of holes of the topmost moiré valence band. These states emerge from incompressible composite fermion bands of Chern number 𝐶 within a complex Hofstadter spectrum. This approach explains FCIs with Hall conductivities 𝜎𝑥𝑦=(2/3)𝑒2/ and 𝜎𝑥𝑦=(3/5)𝑒2/ at fractional fillings 𝜈h=2/3 and 𝜈h=3/5 observed in experiments, and uncovers other fractal FCI states. The Hofstadter spectrum reveals new phenomena, distinct from Landau levels, including a higher-order Van Hove singularity (HOVHS) at half-filling, leading to novel quantum phase transitions. This Letter offers a comprehensive framework for understanding FCIs in transition metal dichalcogenide moiré systems and highlights mechanisms for topological quantum criticality.
扭曲双层碲化镉中的分数切尔绝缘体:复合费米子视角
在扭曲双层 MoTe2 中发现的分数切尔绝缘体(FCIs)引发了人们对无外部磁场的分数拓扑物质的极大兴趣。与朗道水平的平面弥散不同,摩尔电子态受到纳米级超晶格内晶格效应的影响。这封信研究了这些晶格效应对扭曲双层 MoTe2 中拓扑相的影响,发现了一系列具有阿贝尔任意子准粒子的 FCI。利用复合费米子方法,我们发现了一系列具有分数霍尔电导率𝜎𝑥𝑦=[𝐶/(2𝐶+1)](𝑒2/)的 FCIs,它们与最顶端摩尔价带空穴的部分填充𝜈h 有关。这些态是在复杂的霍夫斯塔特谱中由不可压缩的、切尔诺数为 𝐶 的复合费米子带产生的。这种方法解释了在实验中观察到的霍尔电导率𝜎𝑥𝑦=(2/3)𝑒2/楣和分数填充𝜎𝑥𝑦=(3/5)𝑒2/楣在分数填充𝜈h=2/3和𝜈h=3/5时的FCI态,并揭示了其他分形FCI态。霍夫斯塔特谱揭示了不同于朗道水平的新现象,包括半填充时的高阶范霍夫奇点(HOVHS),从而导致新的量子相变。这封信为理解过渡金属二卤化摩尔体系中的 FCI 提供了一个全面的框架,并突出了拓扑量子临界的机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review letters
Physical review letters 物理-物理:综合
CiteScore
16.50
自引率
7.00%
发文量
2673
审稿时长
2.2 months
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
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