Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials

Abstract

We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-metal transitions are found in this model as the energy is increased in magnitude from the band center (E = 0) to the mobility edges (±Ec2, ±Ec1).

Topological phase transition in the quasiperiodic disordered Su–Schriffer–Heeger chain

“…Due to the slowly varying quasiperiodic disorder accompanied with mobility edges [34][35][36][37][38] , we wonder the location of mobility edges in the spectrum when this type of disorder is introduced in 1D SSH chain. To clarify the localized property of this model we present numerical analysis by applying typical diagnostic technique in disordered systems, the inverse participation ratio (IPR).…”

Mobility edges in $\mathcal{PT}$-symmetric cross-stitch flat band lattices

“…The mobility edge refers to a critical energy-level which separating localized from extended states. In the following study, various AA-like models containing mobility edges are discussed, such as slow-varying potentials 56,57 , offdiagonal disorder 58,59 , long-range hoppings 60 , and other generalized quasiperiodic potentials [61][62][63] . Y. Liu et.al.…”

Invariable mobility edge in a quasiperiodic lattice

“…Therefore, to acquire more insights into the mobility edge and uncover its essence, low-dimensional systems, such as the one-dimensional (1D) systems, are a better choice. After all, there has a long history to search the systems with mobility edge and plenty of theoretical models are proposed and studied in the decades [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Moreover, the mobility edge has been observed in recent experiments by manipulating the cold atoms trapped in 1D quasiperiodic optical lattice [18,19], although there are experimental challenges.…”