Designing 1D correlated-electron states by non-Euclidean topography of 2D monolayers

TL;DR

This paper proposes a novel method to create one-dimensional flat electronic bands in 2D materials by patterning their surface with non-Euclidean topographies, enabling exploration of 1D strongly correlated quantum phenomena.

Contribution

It introduces a new approach to generate 1D correlated electron states using surface topography, distinct from twist-based methods in 2D systems.

Findings

Non-Euclidean surface patterns induce pseudo-electric and magnetic fields in 2D monolayers.

These fields lead to anisotropic confinement and 1D flat bands.

Tuning surface undulations can control electronic correlations and phases.

Abstract

Two-dimensional (2D) bilayers, twisted to particular angles to display electronic flat bands, are being extensively explored for physics of strongly correlated 2D systems. However, the similar rich physics of one-dimensional (1D) strongly correlated systems remains elusive as it is largely inaccessible by twists. Here, a distinctive way to create 1D flat bands is proposed, by either stamping or growing a 2D monolayer on a non-Euclidean topography-patterned surface. Using boron nitride (hBN) as an example, our analysis employing elastic plate theory, density-functional and coarse-grained tight-binding method reveals that hBN's bi-periodic sinusoidal deformation creates pseudo-electric and magnetic fields with unexpected spatial dependence. A combination of these fields leads to anisotropic confinement and 1D flat bands. Moreover, changing the periodic undulations can tune the bandwidth, to drive the system to different strongly correlated regimes such as density waves, Luttinger liquid, and Mott insulator. The 1D nature of these states differs from those obtained in twisted materials and can be exploited to study the exciting physics of 1D quantum systems.