Splitting of roton minimum in the ν=5/2 Moore-Read state

We calculate the dynamical structure factor of the ν=5/2 non-abelian quantum Hall state in the dipole approximation, valid for large momenta. Due to the fact that both quasi-particles (qps) and quasi-holes (qhs) have an internal Majorana degree of freedom, a qp-qh pair has a fermionic degree of freedom which can be either empty or occupied, and leads to a splitting of the roton mode. Observation of this splitting by means of finite wavelength optical spectroscopy could provide evidence for Majorana modes in the ν=5/2 quantum Hall state.

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