Haoyang Liu, Ashwani Kumar, Liuqi Yu, Richard P. Barber, Jr., Peng Xiong
{"title":"超导体-绝缘体转变附近超薄无定形铅薄膜中的超导波动和副导性","authors":"Haoyang Liu, Ashwani Kumar, Liuqi Yu, Richard P. Barber, Jr., Peng Xiong","doi":"10.1103/physrevb.110.174502","DOIUrl":null,"url":null,"abstract":"Superconductivity in two dimensions has attracted renewed interest in the context of two-dimensional (2D) van der Waals materials. Key questions remain regarding the nature and manifestations of the superconductivity in these materials. One open question is whether superconducting fluctuations in such 2D systems can be described by the classic Aslamazov-Larkin (A-L) equation. While the A-L model has long been found to accurately describe the paraconductivity of some conventional 2D superconductors, its applicability in ultrathin limit near the superconductor-insulator transition (SIT) has not been established. Here, we report a systematic study of superconducting fluctuation and paraconductivity in ultrathin 2D amorphous Pb films near the SIT. Pb films were incrementally deposited, and the electrical measurements were performed <i>in situ</i> at each thickness in a dilution refrigerator, resulting in a series of sheet resistance curves <mjx-container ctxtmenu_counter=\"57\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-structure=\"(11 0 (10 (3 1 2) 9 (7 4 5 6)) 8)\"><mjx-mrow data-semantic-children=\"10\" data-semantic-content=\"0,8\" data-semantic- data-semantic-owns=\"0 10 8\" data-semantic-role=\"leftright\" data-semantic-speech=\"left bracket upper R Subscript white square Baseline left parenthesis upper T right parenthesis right bracket\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"11\" 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-annotation=\"clearspeak:simple\" data-semantic-children=\"3,7\" data-semantic-content=\"9,1\" data-semantic- data-semantic-owns=\"3 9 7\" data-semantic-parent=\"11\" data-semantic-role=\"simple function\" data-semantic-type=\"appl\"><mjx-msub data-semantic-children=\"1,2\" data-semantic- data-semantic-owns=\"1 2\" data-semantic-parent=\"10\" data-semantic-role=\"simple function\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"3\" data-semantic-role=\"simple function\" data-semantic-type=\"identifier\"><mjx-c>𝑅</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mo data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"geometry\" data-semantic-type=\"relation\" size=\"s\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"10\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\"5\" data-semantic-content=\"4,6\" data-semantic- data-semantic-owns=\"4 5 6\" data-semantic-parent=\"10\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\" space=\"2\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"7\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"7\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"7\" 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=\"11\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>]</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> across the SIT. Paramagnetic impurities (Cr) were then deposited on the same superconducting film, driving it back to the insulating state and yielding another set of <mjx-container ctxtmenu_counter=\"58\" 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 R Subscript white square\" 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>𝑅</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"geometry\" data-semantic-type=\"relation\" size=\"s\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-math></mjx-container>(<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=\"upper T\" data-semantic-type=\"identifier\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>). Both types 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 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 R Subscript white square\" 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>𝑅</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mo data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"geometry\" data-semantic-type=\"relation\" size=\"s\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-math></mjx-container>(<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=\"0\"><mjx-mrow><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-mrow></mjx-math></mjx-container>) curves were analyzed with the A-L equation. At all film thicknesses (and <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=\"latinletter\" data-semantic-speech=\"upper T Subscript upper 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>'s), we observed a background paraconductivity significantly greater than the A-L value. As the film thickness decreases and the SIT is approached, the paraconductivity increases precipitously, reaching more than an order of magnitude higher than that of the A-L value at the immediate vicinity of the SIT. Accompanying the presence of excess paraconductivity and its increase with decreasing thickness, the paraconductivity exhibits exponential scaling with <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-mrow><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-mrow></mjx-math></mjx-container> above <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=\"(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 upper 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>, whose temperature range and slope show concomitant variations with decreasing film thickness. In contrast, suppression of <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=\"(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 upper 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> by magnetic impurity results in much weaker increase of the excess paraconductivity and little change in the temperature range and slope of the exponential <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=\"0\"><mjx-mrow><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-mrow></mjx-math></mjx-container> scaling. These observations are consistent with the presence of emergent localized superconducting pairing above <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=\"(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 upper 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> in the strongly disordered, morphologically nominally uniform amorphous films. The spatially localized superconductivity likely causes excess paraconductivity beyond the A-L theory and percolative superconducting transitions. Such electronic inhomogeneities proliferate with decreasing film thickness, especially near the SIT.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Superconducting fluctuations and paraconductivity in ultrathin amorphous Pb films near superconductor-insulator transitions\",\"authors\":\"Haoyang Liu, Ashwani Kumar, Liuqi Yu, Richard P. Barber, Jr., Peng Xiong\",\"doi\":\"10.1103/physrevb.110.174502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Superconductivity in two dimensions has attracted renewed interest in the context of two-dimensional (2D) van der Waals materials. Key questions remain regarding the nature and manifestations of the superconductivity in these materials. One open question is whether superconducting fluctuations in such 2D systems can be described by the classic Aslamazov-Larkin (A-L) equation. While the A-L model has long been found to accurately describe the paraconductivity of some conventional 2D superconductors, its applicability in ultrathin limit near the superconductor-insulator transition (SIT) has not been established. Here, we report a systematic study of superconducting fluctuation and paraconductivity in ultrathin 2D amorphous Pb films near the SIT. Pb films were incrementally deposited, and the electrical measurements were performed <i>in situ</i> at each thickness in a dilution refrigerator, resulting in a series of sheet resistance curves <mjx-container ctxtmenu_counter=\\\"57\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-structure=\\\"(11 0 (10 (3 1 2) 9 (7 4 5 6)) 8)\\\"><mjx-mrow data-semantic-children=\\\"10\\\" data-semantic-content=\\\"0,8\\\" data-semantic- data-semantic-owns=\\\"0 10 8\\\" data-semantic-role=\\\"leftright\\\" data-semantic-speech=\\\"left bracket upper R Subscript white square Baseline left parenthesis upper T right parenthesis right bracket\\\" data-semantic-type=\\\"fenced\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"11\\\" 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-annotation=\\\"clearspeak:simple\\\" data-semantic-children=\\\"3,7\\\" data-semantic-content=\\\"9,1\\\" data-semantic- data-semantic-owns=\\\"3 9 7\\\" data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"appl\\\"><mjx-msub data-semantic-children=\\\"1,2\\\" data-semantic- data-semantic-owns=\\\"1 2\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑅</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"geometry\\\" data-semantic-type=\\\"relation\\\" size=\\\"s\\\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"application\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-children=\\\"5\\\" data-semantic-content=\\\"4,6\\\" data-semantic- data-semantic-owns=\\\"4 5 6\\\" data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\" space=\\\"2\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>(</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑇</mjx-c></mjx-mi><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"7\\\" 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=\\\"11\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>]</mjx-c></mjx-mo></mjx-mrow></mjx-math></mjx-container> across the SIT. Paramagnetic impurities (Cr) were then deposited on the same superconducting film, driving it back to the insulating state and yielding another set of <mjx-container ctxtmenu_counter=\\\"58\\\" 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 R Subscript white square\\\" 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>𝑅</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"geometry\\\" data-semantic-type=\\\"relation\\\" size=\\\"s\\\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-math></mjx-container>(<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=\\\"upper T\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑇</mjx-c></mjx-mi></mjx-mrow></mjx-math></mjx-container>). Both types 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 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 R Subscript white square\\\" 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>𝑅</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"geometry\\\" data-semantic-type=\\\"relation\\\" size=\\\"s\\\"><mjx-c>□</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-math></mjx-container>(<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=\\\"0\\\"><mjx-mrow><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-mrow></mjx-math></mjx-container>) curves were analyzed with the A-L equation. At all film thicknesses (and <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=\\\"latinletter\\\" data-semantic-speech=\\\"upper T Subscript upper 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>'s), we observed a background paraconductivity significantly greater than the A-L value. As the film thickness decreases and the SIT is approached, the paraconductivity increases precipitously, reaching more than an order of magnitude higher than that of the A-L value at the immediate vicinity of the SIT. Accompanying the presence of excess paraconductivity and its increase with decreasing thickness, the paraconductivity exhibits exponential scaling with <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-mrow><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-mrow></mjx-math></mjx-container> above <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=\\\"(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 upper 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>, whose temperature range and slope show concomitant variations with decreasing film thickness. In contrast, suppression of <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=\\\"(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 upper 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> by magnetic impurity results in much weaker increase of the excess paraconductivity and little change in the temperature range and slope of the exponential <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=\\\"0\\\"><mjx-mrow><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-mrow></mjx-math></mjx-container> scaling. These observations are consistent with the presence of emergent localized superconducting pairing above <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=\\\"(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 upper 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> in the strongly disordered, morphologically nominally uniform amorphous films. The spatially localized superconductivity likely causes excess paraconductivity beyond the A-L theory and percolative superconducting transitions. Such electronic inhomogeneities proliferate with decreasing film thickness, especially near the SIT.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.174502\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.174502","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
摘要
二维范德华材料的超导性再次引起了人们的兴趣。有关这些材料中超导性的性质和表现形式的关键问题依然存在。一个悬而未决的问题是,这种二维系统中的超导波动是否可以用经典的阿斯拉马佐夫-拉金(A-L)方程来描述。虽然人们早已发现 A-L 模型能准确描述一些传统二维超导体的副导性,但它在超导体-绝缘体转变(SIT)附近的超薄极限中的适用性尚未确定。在此,我们报告了对 SIT 附近超薄二维非晶铅薄膜中超导波动和副导性的系统研究。铅薄膜以递增的方式沉积,在稀释冰箱中对每个厚度进行原位电学测量,从而得到一系列横跨 SIT 的片电阻曲线[𝑅□(𝑇)]。然后,顺磁杂质(Cr)被沉积在同一超导薄膜上,使其回到绝缘状态,并产生了另一组𝑅□(𝑇)。这两种类型的𝑅□(𝑇) 曲线都用 A-L 方程进行了分析。在所有薄膜厚度(和 𝑇𝐶's)下,我们都观察到本底副电导率明显大于 A-L 值。随着薄膜厚度的减小和 SIT 的接近,副电导率急剧上升,在 SIT 附近比 A-L 值高出一个数量级以上。伴随着过剩副电导率的存在及其随厚度减小而增加,副电导率随𝑇高于𝑇𝐶呈指数缩放,其温度范围和斜率随薄膜厚度减小而相应变化。与此相反,磁性杂质对𝑇𝐶的抑制导致过剩副电导率的增加要弱得多,而指数𝑇缩放的温度范围和斜率变化不大。这些观察结果与强烈无序、形态上名义上均匀的非晶态薄膜中出现的高于𝑇𝐶的局部超导配对相一致。空间局域化超导可能会导致超出 A-L 理论的超导和渗流超导跃迁。这种电子不均匀性会随着薄膜厚度的减小而增大,尤其是在 SIT 附近。
Superconducting fluctuations and paraconductivity in ultrathin amorphous Pb films near superconductor-insulator transitions
Superconductivity in two dimensions has attracted renewed interest in the context of two-dimensional (2D) van der Waals materials. Key questions remain regarding the nature and manifestations of the superconductivity in these materials. One open question is whether superconducting fluctuations in such 2D systems can be described by the classic Aslamazov-Larkin (A-L) equation. While the A-L model has long been found to accurately describe the paraconductivity of some conventional 2D superconductors, its applicability in ultrathin limit near the superconductor-insulator transition (SIT) has not been established. Here, we report a systematic study of superconducting fluctuation and paraconductivity in ultrathin 2D amorphous Pb films near the SIT. Pb films were incrementally deposited, and the electrical measurements were performed in situ at each thickness in a dilution refrigerator, resulting in a series of sheet resistance curves [𝑅□(𝑇)] across the SIT. Paramagnetic impurities (Cr) were then deposited on the same superconducting film, driving it back to the insulating state and yielding another set of 𝑅□(𝑇). Both types of 𝑅□(𝑇) curves were analyzed with the A-L equation. At all film thicknesses (and 𝑇𝐶's), we observed a background paraconductivity significantly greater than the A-L value. As the film thickness decreases and the SIT is approached, the paraconductivity increases precipitously, reaching more than an order of magnitude higher than that of the A-L value at the immediate vicinity of the SIT. Accompanying the presence of excess paraconductivity and its increase with decreasing thickness, the paraconductivity exhibits exponential scaling with 𝑇 above 𝑇𝐶, whose temperature range and slope show concomitant variations with decreasing film thickness. In contrast, suppression of 𝑇𝐶 by magnetic impurity results in much weaker increase of the excess paraconductivity and little change in the temperature range and slope of the exponential 𝑇 scaling. These observations are consistent with the presence of emergent localized superconducting pairing above 𝑇𝐶 in the strongly disordered, morphologically nominally uniform amorphous films. The spatially localized superconductivity likely causes excess paraconductivity beyond the A-L theory and percolative superconducting transitions. Such electronic inhomogeneities proliferate with decreasing film thickness, especially near the SIT.
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