Hall transport in the topological non-Hermitian checkerboard lattice

The checkerboard lattice is a two-dimensional non-trivial structure usually seen as a planar version of the pyrochlore lattice. This geometry supports a two-band insulating electronic system with Chern topology induced by a complex hopping parameter. Inspired by the recent advances in the topology of non-Hermitian systems, in this work we study a non-Hermitian version of the topological checkerboard lattice. The complex band structure and Berry curvature are calculated. In the insulating phase, the Chern number is the same as in the Hermitian version, but the Hall conductivity is no longer quantized. The dependence of the Hall conductivity with the non-Hermitian parameters is investigated. The non-Hermiticity can be seen as a result of dissipation caused by coupling the system to the environment, so this study casts light on the topology of open systems in condensed matter physics.