Fig. 2: Confirmation of quadrupole and trivial PhCs through nested Wannier bands.
a Wannier bands, νx(ky) and νy(kx), are calculated for the first and second bands of the quadrupole PhC. Results show the bulk dipole momentum is zero (px = py = 0). b Calculations of the nested Wilson loops, \({p}_{y}^{{\nu }_{x}^{-}}={p}_{x}^{{\nu }_{y}^{-}}=0.5\), show the bulk quadrupole momentum qxy is non-trivial and quantized to 0.5. c, d Similar calculations repeated for a trivial PhC, showing zero bulk dipole moments (px = py = 0) and zero quadrupole moments (\({p}_{y}^{{\nu }_{x}^{-}}={p}_{x}^{{\nu }_{y}^{-}}=0\)).
