Parity‐Time‐Symmetric Bimorphic Topological Insulators

We propose and experimentally realize a parity-time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>PT</mml:mi> <mml:annotation>$\mathcal {PT}$</mml:annotation></mml:semantics> </mml:math> )-symmetric bimorphic topological insulator, characterized by the coexistence of first- and second-order topological phases. Our platform utilizes an anomalous Floquet model implemented in a 2D optical waveguide array, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>PT</mml:mi> <mml:annotation>$\mathcal {PT}$</mml:annotation></mml:semantics> </mml:math> symmetry is maintained via a four-step driving protocol with spatiotemporally engineered loss. Despite the presence of dissipation, we demonstrate that the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>PT</mml:mi> <mml:annotation>$\mathcal {PT}$</mml:annotation></mml:semantics> </mml:math> symmetry ensures a purely real quasienergy spectrum across the topological regime, effectively stabilizing boundary modes against the dynamical instabilities and mode competition typical of non-Hermitian systems. Experimentally, we provide unambiguous evidence of this non-Hermitian bimorphic phase by observing unidirectional, clockwise edge transport in the zero gap and robust corner localization in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>π</mml:mi> <mml:annotation>$\pi$</mml:annotation></mml:semantics> </mml:math> gap. Our findings pave the way for further exploration of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:semantics><mml:mi>PT</mml:mi> <mml:annotation>$\mathcal {PT}$</mml:annotation></mml:semantics> </mml:math> -symmetric and non-Hermitian topological phases in nonlinear and many-body regimes and provide novel insights into the realization of topological insulators in open quantum systems.