标题： 基于有隙石墨烯在均匀磁场中的罗森-莫尔斯势的大量狄拉克粒子 显示英文标题

标题： Massive Dirac particles based on gapped graphene with Rosen-Morse potential in a uniform magnetic field

摘要： 我们研究在存在Rosen-Morse势和外部均匀磁场的情况下，二维平面中的带隙石墨烯结构。 为了描述相应的结构，我们考虑石墨烯中电子的传播作为相对论费米子准粒子，并使用狄拉克方程中的两分量旋量波函数，利用赝自旋对称性进行分析。 接下来，为了解和分析狄拉克方程，我们使用勒让德微分方程得到本征值和本征向量。 之后，根据主量子数\(n\)和自旋-轨道量子数\(k\)的系数，得到依赖于Rosen-Morse势和磁势系数的能量束缚态。 然后，计算基态和第一激发态的能量谱值，并根据坐标$r$绘制波函数和相应的概率。 随后，我们通过修改的色散关系探索带隙石墨烯的能带结构，并用二维波矢$K_x$和$K_y$表示它。 最后，根据波矢$K_x$和$K_y$绘制有无磁项的能量带。 显示英文摘要

摘要： We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an 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.