Exact multiple anomalous mobility edges in a flat band geometry

TL;DR

This paper constructs exact anomalous mobility edges in a flat band system using a novel quasi-periodic modulation, providing analytical solutions and experimental design insights into localization transitions in quasiperiodic models.

Contribution

It introduces a method to derive exact AMEs in flat band geometries with a new quasi-periodic modulation, advancing understanding of localization transitions.

Findings

Exact analytical solutions for AMEs in flat band models

Identification of conditions for localized and critical states

Proposed classical circuit for experimental realization

Abstract

Anomalous mobility edges(AMEs), separating localized from multifractal critical states, represent a novel form of localization transition in quasiperiodic systems. However, quasi-periodic models exhibiting exact AMEs remain relatively rare, limiting the understanding of these transitions. In this work, we leverage the geometric structure of flat band models to construct exact AMEs. Specifically, we introduce an anti-symmetric diagonal quasi-periodic mosaic modulation, which consists of both quasi-periodic and constant potentials, into a cross-stitch flat band lattice. When the constant potential is zero, the system resides entirely in a localized phase, with its dispersion relation precisely determined. For non-zero constant potentials, we use a simple method to derive analytical solutions for a class of AMEs, providing exact results for both the AMEs and the system's localization and critical properties. Additionally, we propose a classical electrical circuit design to experimentally realize the system. This study offers valuable insights into the existence and characteristics of AMEs in quasi-periodic systems.