Abstract
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.
- Received 27 August 2020
- Revised 18 October 2020
- Accepted 9 November 2020
DOI:https://doi.org/10.1103/PhysRevA.102.052229
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