{"title":"利用变分优化对角化方法研究量子阱中的激子态和带间吸收光谱","authors":"Shudong Wu","doi":"10.1140/epjb/s10051-024-00854-6","DOIUrl":null,"url":null,"abstract":"<div><p>Previous studies on excitons in quantum wells (QWs) have widely focused on the ground exciton state based on the variational method with the trial wave function. Moreover, it is progressively more difficult to use to find the energies of the excited exciton states. Using a variationally optimized diagonalization method based on a two-dimensional (2D) nonorthogonal Laguerre basis set, we theoretically investigate exciton states and interband absorption spectra with various electron and hole subband indices in QWs with finite potential barriers. The maximum relative error up to <span>\\(10^{ - 4}\\)</span> is obtained at the basis size <span>\\(N = 3\\)</span>, which indicates that the use of <span>\\(N = 10\\)</span> in the basis size is enough large to get the excellent results. Therefore, the 2D nonorthogonal Laguerre basis set is an excellent choice for quasi-2D semiconductor structures. For (<i>n</i><sub><i>e</i></sub> = 2,<i> n</i><sub><i>h</i></sub> = 2) exciton in narrow QWs, there are some small inevitable fluctuations in exciton binding energy and oscillator strength due to the interference between the exciton wave functions in the well and barrier layers. It is clear that sharp interband absorption peaks of HH and LH excitons with <i>n</i><sub><i>e</i></sub> = <i>n</i><sub><i>h</i></sub> = 1 and <i>n</i><sub><i>e</i></sub> = <i>n</i><sub><i>h</i></sub> = 2 can be observed, and distinctive additional small peaks e1-HH1 (2<i>s</i>), e1-HH1 (3<i>s</i>), e1-LH1 (2<i>s</i>), e1-LH1 (3<i>s</i>), e2-HH2 (2<i>s</i>), e2-HH2 (3<i>s</i>), e2-LH2 (2<i>s</i>) and e2-LH2 (3<i>s</i>) excitons are resolved on the high-energy side of each 1<i>s</i> exciton peak in the spectrum. Our results are in good agreement with those obtained from the variational method and the experimental results.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"98 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exciton states and interband absorption spectra in quantum wells using a variationally optimized diagonalization method\",\"authors\":\"Shudong Wu\",\"doi\":\"10.1140/epjb/s10051-024-00854-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Previous studies on excitons in quantum wells (QWs) have widely focused on the ground exciton state based on the variational method with the trial wave function. Moreover, it is progressively more difficult to use to find the energies of the excited exciton states. Using a variationally optimized diagonalization method based on a two-dimensional (2D) nonorthogonal Laguerre basis set, we theoretically investigate exciton states and interband absorption spectra with various electron and hole subband indices in QWs with finite potential barriers. The maximum relative error up to <span>\\\\(10^{ - 4}\\\\)</span> is obtained at the basis size <span>\\\\(N = 3\\\\)</span>, which indicates that the use of <span>\\\\(N = 10\\\\)</span> in the basis size is enough large to get the excellent results. Therefore, the 2D nonorthogonal Laguerre basis set is an excellent choice for quasi-2D semiconductor structures. For (<i>n</i><sub><i>e</i></sub> = 2,<i> n</i><sub><i>h</i></sub> = 2) exciton in narrow QWs, there are some small inevitable fluctuations in exciton binding energy and oscillator strength due to the interference between the exciton wave functions in the well and barrier layers. It is clear that sharp interband absorption peaks of HH and LH excitons with <i>n</i><sub><i>e</i></sub> = <i>n</i><sub><i>h</i></sub> = 1 and <i>n</i><sub><i>e</i></sub> = <i>n</i><sub><i>h</i></sub> = 2 can be observed, and distinctive additional small peaks e1-HH1 (2<i>s</i>), e1-HH1 (3<i>s</i>), e1-LH1 (2<i>s</i>), e1-LH1 (3<i>s</i>), e2-HH2 (2<i>s</i>), e2-HH2 (3<i>s</i>), e2-LH2 (2<i>s</i>) and e2-LH2 (3<i>s</i>) excitons are resolved on the high-energy side of each 1<i>s</i> exciton peak in the spectrum. Our results are in good agreement with those obtained from the variational method and the experimental results.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>\",\"PeriodicalId\":787,\"journal\":{\"name\":\"The European Physical Journal B\",\"volume\":\"98 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The European Physical Journal B\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjb/s10051-024-00854-6\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, CONDENSED MATTER\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal B","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjb/s10051-024-00854-6","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
Exciton states and interband absorption spectra in quantum wells using a variationally optimized diagonalization method
Previous studies on excitons in quantum wells (QWs) have widely focused on the ground exciton state based on the variational method with the trial wave function. Moreover, it is progressively more difficult to use to find the energies of the excited exciton states. Using a variationally optimized diagonalization method based on a two-dimensional (2D) nonorthogonal Laguerre basis set, we theoretically investigate exciton states and interband absorption spectra with various electron and hole subband indices in QWs with finite potential barriers. The maximum relative error up to \(10^{ - 4}\) is obtained at the basis size \(N = 3\), which indicates that the use of \(N = 10\) in the basis size is enough large to get the excellent results. Therefore, the 2D nonorthogonal Laguerre basis set is an excellent choice for quasi-2D semiconductor structures. For (ne = 2, nh = 2) exciton in narrow QWs, there are some small inevitable fluctuations in exciton binding energy and oscillator strength due to the interference between the exciton wave functions in the well and barrier layers. It is clear that sharp interband absorption peaks of HH and LH excitons with ne = nh = 1 and ne = nh = 2 can be observed, and distinctive additional small peaks e1-HH1 (2s), e1-HH1 (3s), e1-LH1 (2s), e1-LH1 (3s), e2-HH2 (2s), e2-HH2 (3s), e2-LH2 (2s) and e2-LH2 (3s) excitons are resolved on the high-energy side of each 1s exciton peak in the spectrum. Our results are in good agreement with those obtained from the variational method and the experimental results.
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