Non-Hermitian topology in molecules: Prediction of fractional quantum number

We give a simple toy model to study a famous Jahn-Teller type molecule. Finite lifetime due to non-adiabatic coupling and finite temperature effect results in the effective Hamiltonian to be non-Hermitian. This effect pulls a conical intersection into a pair of connected Weyl points, bridged by a Fermi arc. The length of the Fermi arc depends on the strength of non-hermicity. This is a unique feature of non-Hermitian topology with no Hermitian analogue. We predict the existence of Weyl points in molecules which cause anomalous Jahn-Teller effects and fractional quantum number.