Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential

TL;DR

This paper analytically solves the double-well problem for 2D Dirac fermions, showing how potential parameters control energy splitting and transitions, enabling tunable terahertz frequency applications in graphene.

Contribution

It provides an exact solution for 2D Dirac fermions in a double-well potential using confluent Heun functions, revealing controllable energy levels and transitions.

Findings

Energy level splitting can be tuned via potential parameters.

Transitions are highly anisotropic and tunable to terahertz frequencies.

Transitions across pseudo-gaps are strongly allowed.

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 wavefunction 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 pseudo-gaps are strongly allowed, highly anisotropic, and for realistic graphene devices can be tuned to fall within the highly desirable terahertz frequency range.