Non-hermitian bilayer graphene with non-decaying states: Fractional dimension of electron-hole pairs

Over the past decade, it has been re-considered that non-Hermitian Hamiltonians can exhibit regions with a real spectrum. Two graphene sheets coupled via a non-Hermitian hopping term are studied in this work. The resulting electron-hole spectrum is analyzed, and a gap induced by a gate-energy parameter is essential for the existence of non-decaying states. An analytical expression for the number of electron-hole pair states is derived as a function of energy. In the second part of the work, the fractional spatial dimension of the system is estimated, arising from the excitation of electron-hole pairs. This dimension equals two in the vacuum state increases with the energy of the excited system. This rise in spatial dimension (rugosity) can be attributed to finite temperature effects, as observed in other systems such as monolayer graphene.