Abstract
We develop an analytic model for an ideal polyyne ring which describes the induced terahertz (THz) gap in the molecular spectrum due to the Stark effect. This simple model can also be used to describe an odd-dimered cyclocarbon which has undergone a spontaneous symmetry-breaking event (due to the Jahn-Teller effect) as an effective dipole across an ideal ring. We show that both the size of the gap and the strength of optical transitions across it can be modulated by varying the external electric field strength. A THz emission scheme based on optical excitation is proposed, thus paving the way for tunable THz emitters based on $\mathrm{cyclo}[n]\mathrm{carbon}$.
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