# Phase diagram of a generalized off-diagonal Aubry-Andr\'{e} model with p-wave pairing

## TL;DR

This paper explores a generalized off-diagonal Aubry-Andre9 model with p-wave pairing, revealing complex topological phases, mobility edges, and critical states through numerical analysis, with potential realization in cold atomic systems.

## Contribution

It introduces a generalized model with p-wave pairing, mapping its phase diagram and identifying novel topological and critical phases not previously characterized.

## Key findings

- Presence of mobility-edge phases.
- Existence of critical phases with zero-energy modes.
- Topological phases can be realized in cold atomic systems.

## Abstract

Off-diagonal Aubry-Andr\'{e} (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.