New topological invariants in non-Hermitian systems

Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian (NH) systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts. Owing to the PT-invariance as well as loss of hermiticity of the Hamiltonians, the usual topological invariants do not necessarily appear in this case. Recalling the fact that in PT-symmetric NH Hamiltonians, positive inner products of the eigenstates require the presence of a hidden symmetry, often termed as ‘C’-symmetry. We show that with the help of the C-symmetry, new topological invariants can be constructed in the NH Hamiltonians. We will present variety of examples with characteristically distinct topological invariants.