Fate of Quadratic Band Crossing under quasiperiodic modulation

TL;DR

This paper investigates how two-dimensional quadratic band crossing topological phases respond to one-dimensional quasiperiodic modulation, revealing stability of the phase and unique topological transitions not seen with regular disorder.

Contribution

It provides a comprehensive numerical analysis of the phase diagram, showing stability of quadratic band crossing under quasiperiodic potential and identifying new topological transition mechanisms.

Findings

Quadratic band crossing is stable against quasiperiodic potential.

Strong quasiperiodic potential can split the band crossing into Dirac cones.

Topological phases with Chern numbers ±1 emerge only at high potential strength.

Abstract

We study the fate of 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 towards 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. With a sufficiently strong quasiperiodic potential, the quadratic band crossing point splits into Dirac cones which enables transitions into gapped phases with Chern numbers $C=\pm1$, absent in the homogeneous limit. This is in sharp contrast with the disordered case, where gapless $C=\pm1$ phases can arise by perturbing the band crossing with any amount of disorder. In the quasiperiodic case, we find that the $C=\pm1$ phases can only become gapless for a very strong potential. Only in this regime, the subsequent quasiperiodic-induced topological transitions into the trivial phase mirror the well-known ``levitation and annihilation'' mechanism in the disordered case.