Fig. 1: Supersymmetric transformations and Su-Schrieffer-Heeger model.

a Schematic representation of the eigenvalue spectrum of the Hamiltonian ℋ and two sets of superpartner Hamiltonians {ℋ₁⁽¹⁾, ℋ₁⁽²⁾} and {ℋ_m⁽¹⁾, ℋ_m⁽²⁾}, obtained by removing the eigenvalues λ₁ and λ_m using supersymmetric transformations, respectively. b Representation of a Su-Schrieffer-Heeger lattice implemented using optical waveguides, which are evanescently coupled with alternating couplings c₁ and c₂ (c₁ < c₂). Depending on the termination of the lattice, the structure has Winding number \({\cal{W}}\) = 1 and supports a topological edge state on that edge or \({\cal{W}}\) = 0 and does not support an edge state on that edge.