Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor

TL;DR

This paper introduces a family of two-dimensional aperiodic tilings with tunable geometric properties, enabling control over quantum phases and topological states in quasicrystals and related systems.

Contribution

It presents a novel class of aperiodic tilings where the real-space geometry acts as a control parameter for the quantum geometric tensor, expanding design possibilities.

Findings

Real-space geometry tunes quantum geometric tensor.

Enables access to expanded topological phase space.

Facilitates tunable quantum and many-body physics.

Abstract

The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable family of two-dimensional aperiodic tilings in which the underlying real-space geometry becomes a control knob of the wavefunction's quantum geometric tensor. The real-space geometry can be used to tune into topological phases occupying an expanded phase space compared to crystals, or into a disorder-driven topological Anderson insulator. The quantum metric can also be tuned continuously, opening new routes towards tunable single- and many-body physics in aperiodic solid-state and synthetic systems.