Electronic and topological properties of non-Hermitian graphene*

In recent years the study of open systems via non-Hermitian Hamiltonians established itself as a fascinating research topic. Indeed new intriguing features arises, like the presence of a complex spectrum, the loss of bulk-boundary correspondence and the possibility of charge accumulation on one edge of the sample (the latter phenomenon called non-Hermitian skin effect), just to name a few examples.

Non-Hermiticity can actually be implemented in two different ways: by adding a complex on-site potential or by making the Hamiltonian non-symmetric. 

Here we study the non-reciprocal version of the honeycomb lattice. The goal is to analyze the features of this remarkably important geometry when a non-Hermitian flavor is added into its physical characterization, particularly concerning its electronic properties. Hence we show the emergence of the exceptional points and of the Fermi arc and we extensively study the skin effect and how this state is reached by looking at the time evolution. 

Eventually we propose a new way of exploiting the non-Hermitian skin effect to localize the charge in the bulk, showing that is is possible to localize and move these skin modes using a time dependent non-reciprocal matrix.