Fig. 3: Simulation of the band gap formation for a staggered lattice and demonstration of a π change in the Zak phase between the two choices of inversion centre.
From: Synthetic band-structure engineering in polariton crystals with non-Hermitian topological phases
a Greyscale colourmap showing the numerically time-resolved dispersion in a complex Gaussian potential lattice representing the experiment in Fig. 2. Zero energy represents bottom of the lower polariton dispersion and 2d is the lattice vector length. Red curves are calculated energies from Eq. (1). b A schematic illustrating the staggered lattice denoted by sublattice indices A and B and the two coupling strengths J±. c Calculated ϕ(q) with solid and dashed curves corresponding to the two distinct centres of inversion in the chain by interchanging the values of J±. d, e Real and imaginary eigenvalues from a finite system of Eq. (7) with 201 sites and a defect at site \(\left|n=101\right\rangle\) connected by two J+ hoppings resulting in a midgap state at E = Ω (see insets). f Spatial density of the defect wavefunction. Edge sites are connected to the bulk by J− hoppings. Parameters are given in the ‘Methods’ section.
