{"title":"Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field","authors":"A. Kalani, Alireza Amani, M. Ramzanpour","doi":"10.1088/1674-1056/ad426b","DOIUrl":null,"url":null,"abstract":"\n In this paper, we explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and the external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of electrons in graphene as relativistic fermion quasi-particles, and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation. Next, to solve and analyze the Dirac equation, we obtain the eigenvalues and eigenvectors using the Legendre differential equation. After that, we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k. Then, the values of the energy spectrum for the ground state and the first excited state are calculated, and the wave functions and the corresponding probabilities are plotted in terms of coordinates r. In what follows, we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K\n \n x\n and K\n \n y\n . Finally, the energy bands are plotted in terms of the wave vectors K\n \n x\n and K\n \n y\n with and without the magnetic term.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":"47 1","pages":""},"PeriodicalIF":16.4000,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1674-1056/ad426b","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and the external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of electrons in graphene as relativistic fermion quasi-particles, and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation. Next, to solve and analyze the Dirac equation, we obtain the eigenvalues and eigenvectors using the Legendre differential equation. After that, we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k. Then, the values of the energy spectrum for the ground state and the first excited state are calculated, and the wave functions and the corresponding probabilities are plotted in terms of coordinates r. In what follows, we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K
x
and K
y
. Finally, the energy bands are plotted in terms of the wave vectors K
x
and K
y
with and without the magnetic term.
本文探讨了在罗森-莫尔斯电势和外部均匀磁场作用下二维平面上的石墨烯间隙结构。为了描述相应的结构,我们将电子在石墨烯中的传播视为相对论费米子准粒子,并通过具有伪自旋对称性的双分量自旋子的波函数,利用狄拉克方程对其进行分析。接下来,为了求解和分析狄拉克方程,我们利用 Legendre 微分方程获得特征值和特征向量。然后,计算基态和第一激发态的能谱值,并以坐标 r 为单位绘制波函数和相应的概率图。接下来,我们通过修正的色散关系探索间隙石墨烯的能带结构,并以二维波矢量 K x 和 K y 为单位将其写入。最后,我们根据 K x 和 K y 的波矢量绘制了有磁项和无磁项的能带。
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.