{"title":"具有二次带交叉点的二维半金属中自旋电子-电子相互作用诱发的有利相变","authors":"","doi":"10.1016/j.aop.2024.169811","DOIUrl":null,"url":null,"abstract":"<div><div>We study the effects of marginally spinful electron–electron interactions on the low-energy instabilities and favorable phase transitions in a two-dimensional (2D) spin-<span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span> semimetal that owns a quadratic band crossing point (QBCP) parabolically touched by the upper and lower bands. In the framework of a renormalization group procedure, all sorts of interactions are treated on the equal footing to derive the coupled energy-dependent evolutions of all interaction couplings that govern the low-energy properties. Deciphering the essential physical information of such flows, we at first find that the tendencies of interaction parameters fall into three categories including Limit case, Special case, and General case based on the initial conditions. In addition, the 2D QBCP system is attracted to several distinct kinds of fixed points (FPs) in the interaction-parameter space, namely <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>/<span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>/ <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>/<span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, and <span><math><mrow><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>41</mn><mo>,</mo><mn>42</mn><mo>,</mo><mn>43</mn></mrow><mrow><mo>±</mo></mrow></msubsup></mrow></math></span> with the subscripts characterizing the features of FPs for the Limit, Special, and General cases, respectively. Furthermore, as approaching these FPs, we demonstrate that the spinful fermion–fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, and <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, respectively. Rather, QSH becomes anisotropic nearby <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>41</mn><mo>,</mo><mn>42</mn><mo>,</mo><mn>43</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span> with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates around these FPs. Our findings provide valuable insights for further research into the 2D QBCP and similar systems.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Favorable phase transitions induced by spinful electron–electron interactions in two-dimensional semimetal with a quadratic band crossing point\",\"authors\":\"\",\"doi\":\"10.1016/j.aop.2024.169811\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study the effects of marginally spinful electron–electron interactions on the low-energy instabilities and favorable phase transitions in a two-dimensional (2D) spin-<span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span> semimetal that owns a quadratic band crossing point (QBCP) parabolically touched by the upper and lower bands. In the framework of a renormalization group procedure, all sorts of interactions are treated on the equal footing to derive the coupled energy-dependent evolutions of all interaction couplings that govern the low-energy properties. Deciphering the essential physical information of such flows, we at first find that the tendencies of interaction parameters fall into three categories including Limit case, Special case, and General case based on the initial conditions. In addition, the 2D QBCP system is attracted to several distinct kinds of fixed points (FPs) in the interaction-parameter space, namely <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>/<span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>/ <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>/<span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, and <span><math><mrow><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>41</mn><mo>,</mo><mn>42</mn><mo>,</mo><mn>43</mn></mrow><mrow><mo>±</mo></mrow></msubsup></mrow></math></span> with the subscripts characterizing the features of FPs for the Limit, Special, and General cases, respectively. Furthermore, as approaching these FPs, we demonstrate that the spinful fermion–fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, and <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>3</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span>, respectively. Rather, QSH becomes anisotropic nearby <span><math><msubsup><mrow><mi>FP</mi></mrow><mrow><mn>41</mn><mo>,</mo><mn>42</mn><mo>,</mo><mn>43</mn></mrow><mrow><mo>±</mo></mrow></msubsup></math></span> with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates around these FPs. Our findings provide valuable insights for further research into the 2D QBCP and similar systems.</div></div>\",\"PeriodicalId\":8249,\"journal\":{\"name\":\"Annals of Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0003491624002185\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0003491624002185","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Favorable phase transitions induced by spinful electron–electron interactions in two-dimensional semimetal with a quadratic band crossing point
We study the effects of marginally spinful electron–electron interactions on the low-energy instabilities and favorable phase transitions in a two-dimensional (2D) spin- semimetal that owns a quadratic band crossing point (QBCP) parabolically touched by the upper and lower bands. In the framework of a renormalization group procedure, all sorts of interactions are treated on the equal footing to derive the coupled energy-dependent evolutions of all interaction couplings that govern the low-energy properties. Deciphering the essential physical information of such flows, we at first find that the tendencies of interaction parameters fall into three categories including Limit case, Special case, and General case based on the initial conditions. In addition, the 2D QBCP system is attracted to several distinct kinds of fixed points (FPs) in the interaction-parameter space, namely /, / /, and with the subscripts characterizing the features of FPs for the Limit, Special, and General cases, respectively. Furthermore, as approaching these FPs, we demonstrate that the spinful fermion–fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for , , and , respectively. Rather, QSH becomes anisotropic nearby with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates around these FPs. Our findings provide valuable insights for further research into the 2D QBCP and similar systems.
期刊介绍:
Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance.
The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.