Fate of quadratic band crossing under quasiperiodic modulation
Abstract
We study the fate of a two-dimensional quadratic band crossing topological phases under a one-dimensional quasiperiodic modulation. By employing numerically exact methods, we fully characterize the phase diagram of the model in terms of spectral, localization, and topological properties. Unlike in the presence of regular disorder, the quadratic band crossing is stable to the application of the quasiperiodic potential, and most of the topological phase transitions occur through a gap closing and reopening mechanism, as in the homogeneous case. For sufficiently high quasiperiodic potential, the quadratic band crossing point splits into Dirac cones, enabling transitions into gapped phases with Chern numbers C = +/- 1, which are absent in the homogeneous limit. This behavior stands in sharp contrast to the disordered case, where gapless C = +/- 1 phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the C = +/- 1 phases can become gapless only for higher potential strength. Only in this regime do the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known levitation and annihilation mechanism in the disordered case.
