Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals

TL;DR

This paper explores the properties of zero-field flat bands on spherical surfaces, revealing unique symmetry-induced electron clustering and proposing experimental setups to study interaction-driven states without magnetic fields.

Contribution

It introduces the concept of zero-field flat bands on spheres, highlighting their symmetry properties and potential for experimental realization, expanding understanding beyond magnetic field-induced flat bands.

Findings

Zero-field flat bands exhibit C(2) symmetry.

Electrons cluster on opposite sides of the sphere's center.

Proposed experimental setup for zero-field flat band exploration.

Abstract

Flat bands result in a divergent density of states and high sensitivity to interactions in physical systems. While such bands are well known in systems under magnetic fields, their realization and behavior in zero-field settings remain largely unexplored. Here we compare the behavior of electrons confined to a single flat band on the surface of a sphere to those in flat bands under a magnetic field. The zero-field flat band exhibits an additional C(2) symmetry, which causes electrons to symmetrically cluster on opposite sides of the sphere's center when a trapping potential is introduced, resulting in a unique form of long-range "entanglement". To explore these findings experimentally, we propose a feasible setup to explore the unique properties of zero-field flat bands on spherical substrates, offering a promising route for studying interaction-driven states in spherical geometry without external fields.