Mallesh Baithi, Tuan Dung Nguyen, Seon Je Kim, Young-Min Kim, Dinh Loc Duong, Young Hee Lee
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{"title":"在掺杂空穴的退化自旋谷半导体中观察低温下的线性电阻","authors":"Mallesh Baithi, Tuan Dung Nguyen, Seon Je Kim, Young-Min Kim, Dinh Loc Duong, Young Hee Lee","doi":"10.1021/acs.nanolett.4c04247","DOIUrl":null,"url":null,"abstract":"Linear resistivity–temperature (<i>R</i>–<i>T</i>) at low temperatures, referred to as strange metal (SM), is an unusual characteristic observed in strongly correlated systems. SM is often mingled with superconductivity and magnetism in various materials. Here, we report a linear <i>R</i>–<i>T</i> relation in a hole-doped, degenerate spin-valley (SV) semiconductor, V<sub>0.25</sub>W<sub>0.75</sub>Se<sub>2</sub>, with hole pockets in the valence band. SM emerges over a wide temperature range (1.8–150 K) without any apparent superconductivity down to 110 mK. This SM behavior is suppressed at low temperatures below 20 K in the presence of a magnetic field. The ansatz <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" overflow=\"scroll\"><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></mrow><mo>&#x2212;</mo><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow><mo>&#x221D;</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>&#x3B1;</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>&#x3B3;</mi><msub><mrow><mi>&#x3BC;</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><msub><mrow><mi>&#x3BC;</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span overflow=\"scroll\" style=\"width: 20.969em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 19.037em; height: 0px; font-size: 110%;\"><span style=\"position: absolute; clip: rect(1.139em, 1019.04em, 3.298em, -999.997em); top: -2.554em; left: 0em;\"><span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝑅</span><span><span style=\"font-family: STIXMathJax_Main;\">(</span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝐻<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\"></span></span><span style=\"font-family: STIXMathJax_Main;\">,</span><span style=\"font-family: STIXMathJax_Normal-italic; padding-left: 0.173em;\">𝑇<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.116em;\"></span></span><span style=\"font-family: STIXMathJax_Main;\">)</span></span><span style=\"font-family: STIXMathJax_Main; padding-left: 0.23em;\">−</span><span style=\"font-family: STIXMathJax_Normal-italic; padding-left: 0.23em;\">𝑅</span><span><span style=\"font-family: STIXMathJax_Main;\">(</span><span style=\"font-family: STIXMathJax_Main;\">0</span><span style=\"font-family: STIXMathJax_Main;\">,</span><span style=\"font-family: STIXMathJax_Main; padding-left: 0.173em;\">0</span><span style=\"font-family: STIXMathJax_Main;\">)</span></span><span style=\"font-family: STIXMathJax_Main; padding-left: 0.344em;\">∝</span><span style=\"padding-left: 0.344em;\"><span style=\"display: inline-block; position: relative; width: 10.23em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.901em, 1009.15em, 4.378em, -999.997em); top: -3.974em; left: 1.082em;\"><span><span><span><span style=\"display: inline-block; position: relative; width: 3.412em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1002.9em, 4.321em, -999.997em); top: -3.974em; left: 0em;\"><span><span><span style=\"font-family: STIXMathJax_Main;\">(</span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝛼<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span><span style=\"display: inline-block; position: relative; width: 1.082em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.151em, -999.997em); top: -3.974em; left: 0em;\"><span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝑘</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; top: -3.804em; left: 0.571em;\"><span><span style=\"font-size: 70.7%; font-family: STIXMathJax_Main;\">B</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝑇<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.116em;\"></span></span><span style=\"font-family: STIXMathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; top: -4.372em; left: 2.957em;\"><span><span style=\"font-size: 70.7%; font-family: STIXMathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span><span style=\"font-family: STIXMathJax_Main; padding-left: 0.23em;\">+</span><span style=\"padding-left: 0.23em;\"><span style=\"display: inline-block; position: relative; width: 4.605em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1004.15em, 4.378em, -999.997em); top: -3.974em; left: 0em;\"><span><span><span style=\"font-family: STIXMathJax_Main;\">(</span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝛾<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\"></span></span><span><span style=\"display: inline-block; position: relative; width: 1.139em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.355em, 1000.57em, 4.321em, -999.997em); top: -3.974em; left: 0em;\"><span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝜇</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; top: -3.747em; left: 0.571em;\"><span><span style=\"font-size: 70.7%; font-family: STIXMathJax_Main;\">B</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span><span><span style=\"display: inline-block; position: relative; width: 1.026em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.355em, 1000.57em, 4.321em, -999.997em); top: -3.974em; left: 0em;\"><span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝜇</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; top: -3.747em; left: 0.571em;\"><span><span style=\"font-size: 70.7%; font-family: STIXMathJax_Main;\">0</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span><span style=\"font-family: STIXMathJax_Normal-italic;\">𝐻<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\"></span></span><span style=\"font-family: STIXMathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; top: -4.372em; left: 4.207em;\"><span><span style=\"font-size: 70.7%; font-family: STIXMathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; clip: rect(3.526em, 1009.15em, 3.923em, -999.997em); top: -4.94em; left: 1.082em;\"><span style=\"display: inline-block; position: relative; width: 9.151em; height: 0px;\"><span style=\"position: absolute; font-family: STIXMathJax_Symbols; top: -3.974em; left: 0em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; font-family: STIXMathJax_Symbols; top: -3.974em; left: 8.866em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.23em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.514em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.741em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.026em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.31em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.537em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.821em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.048em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.332em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.56em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.844em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.128em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.355em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.639em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.866em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.151em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.435em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.662em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.946em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.173em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.457em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.741em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.969em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.253em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.48em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.764em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.048em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.276em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.56em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.787em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.071em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.355em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.582em;\">⎯<span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span><span style=\"position: absolute; clip: rect(2.276em, 1001.08em, 4.435em, -999.997em); top: -3.69em; left: 0em;\"><span style=\"font-family: STIXMathJax_Size1;\">√</span><span style=\"display: inline-block; width: 0px; height: 3.98em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.56em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.684em; border-left: 0px solid; width: 0px; height: 2.191em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" overflow=\"scroll\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></mrow><mo>−</mo><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow><mo>∝</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>α</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>γ</mi><msub><mrow><mi>μ</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></span></span><script type=\"math/mml\"><math display=\"inline\" overflow=\"scroll\"><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></mrow><mo>−</mo><mi>R</mi><mrow><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></mrow><mo>∝</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>α</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\"false\">(</mo><mi>γ</mi><msub><mrow><mi>μ</mi></mrow><mrow><mi mathvariant=\"normal\">B</mi></mrow></msub><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></script> yields the γ/α ratio of ∼4, larger than the previous reports. The observed SM over a wide temperature range is explained by a spin–orbit coupling (SOC)-mediated SV pair with strong correlation effects, analogous to a phonon-mediated Cooper pair in superconductivity. This finding opens possible routes for understanding strange metal behavior through the interplay of strong SOC and strong Coulomb interactions.","PeriodicalId":53,"journal":{"name":"Nano Letters","volume":"8 1","pages":""},"PeriodicalIF":9.6000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Observation of Linear Resistance at Low Temperatures in Hole-Doped Degenerate Spin-Valley Semiconductors\",\"authors\":\"Mallesh Baithi, Tuan Dung Nguyen, Seon Je Kim, Young-Min Kim, Dinh Loc Duong, Young Hee Lee\",\"doi\":\"10.1021/acs.nanolett.4c04247\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Linear resistivity–temperature (<i>R</i>–<i>T</i>) at low temperatures, referred to as strange metal (SM), is an unusual characteristic observed in strongly correlated systems. SM is often mingled with superconductivity and magnetism in various materials. Here, we report a linear <i>R</i>–<i>T</i> relation in a hole-doped, degenerate spin-valley (SV) semiconductor, V<sub>0.25</sub>W<sub>0.75</sub>Se<sub>2</sub>, with hole pockets in the valence band. SM emerges over a wide temperature range (1.8–150 K) without any apparent superconductivity down to 110 mK. This SM behavior is suppressed at low temperatures below 20 K in the presence of a magnetic field. The ansatz <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow><mo>&#x2212;</mo><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\\\"false\\\">)</mo></mrow><mo>&#x221D;</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>&#x3B1;</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>&#x3B3;</mi><msub><mrow><mi>&#x3BC;</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><msub><mrow><mi>&#x3BC;</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span overflow=\\\"scroll\\\" style=\\\"width: 20.969em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 19.037em; height: 0px; font-size: 110%;\\\"><span style=\\\"position: absolute; clip: rect(1.139em, 1019.04em, 3.298em, -999.997em); top: -2.554em; left: 0em;\\\"><span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝑅</span><span><span style=\\\"font-family: STIXMathJax_Main;\\\">(</span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝐻<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Main;\\\">,</span><span style=\\\"font-family: STIXMathJax_Normal-italic; padding-left: 0.173em;\\\">𝑇<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.116em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Main;\\\">)</span></span><span style=\\\"font-family: STIXMathJax_Main; padding-left: 0.23em;\\\">−</span><span style=\\\"font-family: STIXMathJax_Normal-italic; padding-left: 0.23em;\\\">𝑅</span><span><span style=\\\"font-family: STIXMathJax_Main;\\\">(</span><span style=\\\"font-family: STIXMathJax_Main;\\\">0</span><span style=\\\"font-family: STIXMathJax_Main;\\\">,</span><span style=\\\"font-family: STIXMathJax_Main; padding-left: 0.173em;\\\">0</span><span style=\\\"font-family: STIXMathJax_Main;\\\">)</span></span><span style=\\\"font-family: STIXMathJax_Main; padding-left: 0.344em;\\\">∝</span><span style=\\\"padding-left: 0.344em;\\\"><span style=\\\"display: inline-block; position: relative; width: 10.23em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.901em, 1009.15em, 4.378em, -999.997em); top: -3.974em; left: 1.082em;\\\"><span><span><span><span style=\\\"display: inline-block; position: relative; width: 3.412em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1002.9em, 4.321em, -999.997em); top: -3.974em; left: 0em;\\\"><span><span><span style=\\\"font-family: STIXMathJax_Main;\\\">(</span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝛼<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span><span><span style=\\\"display: inline-block; position: relative; width: 1.082em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.151em, -999.997em); top: -3.974em; left: 0em;\\\"><span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝑘</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; top: -3.804em; left: 0.571em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: STIXMathJax_Main;\\\">B</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝑇<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.116em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; top: -4.372em; left: 2.957em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: STIXMathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span><span style=\\\"font-family: STIXMathJax_Main; padding-left: 0.23em;\\\">+</span><span style=\\\"padding-left: 0.23em;\\\"><span style=\\\"display: inline-block; position: relative; width: 4.605em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1004.15em, 4.378em, -999.997em); top: -3.974em; left: 0em;\\\"><span><span><span style=\\\"font-family: STIXMathJax_Main;\\\">(</span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝛾<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\\\"></span></span><span><span style=\\\"display: inline-block; position: relative; width: 1.139em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.355em, 1000.57em, 4.321em, -999.997em); top: -3.974em; left: 0em;\\\"><span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝜇</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; top: -3.747em; left: 0.571em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: STIXMathJax_Main;\\\">B</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span><span><span style=\\\"display: inline-block; position: relative; width: 1.026em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.355em, 1000.57em, 4.321em, -999.997em); top: -3.974em; left: 0em;\\\"><span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝜇</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; top: -3.747em; left: 0.571em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: STIXMathJax_Main;\\\">0</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span><span style=\\\"font-family: STIXMathJax_Normal-italic;\\\">𝐻<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.06em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; top: -4.372em; left: 4.207em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: STIXMathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.526em, 1009.15em, 3.923em, -999.997em); top: -4.94em; left: 1.082em;\\\"><span style=\\\"display: inline-block; position: relative; width: 9.151em; height: 0px;\\\"><span style=\\\"position: absolute; font-family: STIXMathJax_Symbols; top: -3.974em; left: 0em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; font-family: STIXMathJax_Symbols; top: -3.974em; left: 8.866em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.23em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.514em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 0.741em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.026em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.31em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.537em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 1.821em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.048em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.332em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.56em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 2.844em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.128em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.355em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.639em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 3.866em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.151em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.435em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.662em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 4.946em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.173em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.457em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.741em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 5.969em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.253em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.48em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 6.764em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.048em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.276em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.56em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 7.787em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.071em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.355em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"font-family: STIXMathJax_Symbols; position: absolute; top: -3.974em; left: 8.582em;\\\">⎯<span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(2.276em, 1001.08em, 4.435em, -999.997em); top: -3.69em; left: 0em;\\\"><span style=\\\"font-family: STIXMathJax_Size1;\\\">√</span><span style=\\\"display: inline-block; width: 0px; height: 3.98em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.56em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.684em; border-left: 0px solid; width: 0px; height: 2.191em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" overflow=\\\"scroll\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow><mo>−</mo><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\\\"false\\\">)</mo></mrow><mo>∝</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>α</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>γ</mi><msub><mrow><mi>μ</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mi>H</mi><mo>,</mo><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow><mo>−</mo><mi>R</mi><mrow><mo stretchy=\\\"false\\\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\\\"false\\\">)</mo></mrow><mo>∝</mo><msqrt><mrow><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>α</mi><msub><mrow><mi>k</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><mi>T</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo><mi>γ</mi><msub><mrow><mi>μ</mi></mrow><mrow><mi mathvariant=\\\"normal\\\">B</mi></mrow></msub><msub><mrow><mi>μ</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>H</mi><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></math></script> yields the γ/α ratio of ∼4, larger than the previous reports. The observed SM over a wide temperature range is explained by a spin–orbit coupling (SOC)-mediated SV pair with strong correlation effects, analogous to a phonon-mediated Cooper pair in superconductivity. This finding opens possible routes for understanding strange metal behavior through the interplay of strong SOC and strong Coulomb interactions.\",\"PeriodicalId\":53,\"journal\":{\"name\":\"Nano Letters\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":9.6000,\"publicationDate\":\"2024-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nano Letters\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1021/acs.nanolett.4c04247\",\"RegionNum\":1,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nano Letters","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1021/acs.nanolett.4c04247","RegionNum":1,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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