Topological zero modes from the interplay of PT symmetry and anti- PT symmetry

Parity-time symmetry and anti-parity-time symmetry are complementary but generally incompatible. In this work, we investigate the coexistence of parity-time symmetry and anti-parity-time symmetry. These symmetries impose intriguing constraints on the spectrum, and the Bloch bands appear in opposite and conjugate tetrads. The bulk states, affected by the non-Hermiticity, are entirely complex; however, the topological edge states, protected by sublattice symmetry, are exactly zero. We demonstrate a two-leg ladder consisting of two Su-Schrieffer-Heeger chains connected by radiative and dissipative cross-couplings. The non-Hermiticity facilitates the formation of a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>2</a:mn><a:mi mathvariant="double-struck">Z</a:mi></a:mrow></a:math> point gap topology, and the topological zero modes are robust against disorder.