{"title":"磷系量子环的磁性和热性质","authors":"Xilong Bai, Zhensheng Lu, Liu Long","doi":"10.1007/s10910-025-01732-x","DOIUrl":null,"url":null,"abstract":"<div><p>We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 7","pages":"1636 - 1649"},"PeriodicalIF":2.0000,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Magnetic and thermal properties of phosphorene quantum rings\",\"authors\":\"Xilong Bai, Zhensheng Lu, Liu Long\",\"doi\":\"10.1007/s10910-025-01732-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.</p></div>\",\"PeriodicalId\":648,\"journal\":{\"name\":\"Journal of Mathematical Chemistry\",\"volume\":\"63 7\",\"pages\":\"1636 - 1649\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2025-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10910-025-01732-x\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-025-01732-x","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Magnetic and thermal properties of phosphorene quantum rings
We consider an electron confined in a quantum ring (QR) defined electrostatically within the phosphorene monolayer. A confinement potential with an elliptical shape is employed to account for the anisotropy of the effective masses. The Schrödinger equation is solved, leading to the determination of the energy levels. Subsequently, the Shannon formalism is applied to compute the probability distribution and partition function of the system. Finally, the magnetic and thermodynamic properties of the phosphorene QR are analyzed. The results reveal that the magnetic susceptibility exhibits a negative value, indicative of diamagnetic behavior. A maximum value of magnetic susceptibility is observed at low temperatures and high magnetic fields. At elevated magnetic temperatures, the specific heat remains constant, even in the absence of an external magnetic field.
期刊介绍：
The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches.
Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
