The double-well problem for the two-dimensional Dirac equation is solved for a family of quasi-one-dimensional potentials in terms of confluent Heun functions. We demonstrate that for a double well separated by a barrier, both the energy-level splitting associated with the wave-function overlap of well states and the gap size of the avoided crossings associated with well and barrier state repulsion can be controlled via the parameters of the potential. The transitions between the two states comprising a doublet, as well as transitions across the pseudogaps are strongly allowed, highly anisotropic, and, for realistic graphene devices, can be tuned to fall within the highly desirable terahertz frequency range.

中文翻译：

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光滑双阱势中二维Dirac费米子的导模和太赫兹跃迁

对于一维准一维势族，根据合流Heun函数，解决了二维Dirac方程的双阱问题。我们证明，对于由势垒分隔的双井，与势态的波函数重叠相关的能级分裂以及与势阱和势垒排斥相关的避免穿越的间隙尺寸都可以通过以下参数控制潜力。强烈允许包含双态的两个状态之间的跃迁以及伪间隙之间的跃迁，高度各向异性，并且对于实际的石墨烯器件，可以将其调整为落入非常理想的太赫兹频率范围内。