Phase diagram of a generalized off-diagonal Aubry–André model withp-wave pairing

Abstract

Off-diagonal Aubry-André (AA) model has recently attracted a great deal of attention as they provide condensed matter realization of topological phases. We numerically study a generalized off-diagonal AA model with p-wave superfluid pairing in the presence of both commensurate and incommensurate hopping modulations. The phase diagram as functions of the modulation strength of incommensurate hopping and the strength of the p-wave pairing is obtained by using the multifractal analysis. We show that with the appearance of the p-wave pairing, the system exhibits mobility-edge phases and critical phases with various number of topologically protected zero-energy modes. Predicted topological nature of these exotic phases can be realized in a cold atomic system of incommensurate bichromatic optical lattice with induced p-wave superfluid pairing by using a Raman laser in proximity to a molecular Bose-Einstein condensation.

Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

“…Moreover, the extended and critical regions as well as their boundaries completely accord with the predictions done by the multifractal analysis [57]. In recent years, the relevant studies has extended to other quasi-periodic generations [58,59], and besides, the quench dynamics [61] and Kibble-Zurek machanism [62] are well investigated.…”

Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation

“…In this work, we are only interested in distinguishing between ergodic, multifractal and localized regions of the phase diagram. For such differentiation, we define below a quantity, the multifractal spectrum [26,50], which we compare to the results obtained using the mean participation ratios.…”

“…We then study the scaling of this quantity as a function of the size of the system. In particular, we study the scaling in terms of the index n of the Fibonacci number that corresponds to the size of the system, similar to [26,28]. This is depicted in Fig.…”

“…In addition, on can also study the effect of interactions. In particular, density-density interactions [22] or Hamiltonians with superconducting pairing term [23][24][25][26][27][28][29][30] have been considered, and lead to an intermediate extended multifractal regime, which exists for a finite range of chemical potential strengths. Other works have considered coupling of more than one Aubry-André-Harper chains [31,32] or two-dimensional Aubry-André-Harper models [33], which leads to hybridization of ergodic and localized bands.…”

Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices

“…We further validate our analysis using the fractal theory, which has been widely applied in the quasiperiodic models 28,56,[61][62][63][64] . The size of the system L is chosen as the jth Fibonacci number F j .…”