Orbital Description of Landau Levels

TL;DR

This paper constructs a minimal lattice model that accurately describes the lowest and first Landau levels using maximally localized Wannier functions, enabling exploration of topological phenomena in lattice systems.

Contribution

The authors develop a three-orbital lattice model with flat Chern bands and ideal band inversions, providing a concrete orbital description of Landau levels on a lattice.

Findings

The model features two flat Chern bands with Chern number 1.

Many-body calculations show non-Abelian states can emerge at half-filling.

The approach can be extended to higher Landau levels in lattice systems.

Abstract

The pursuit of a lattice analogue for Landau levels has been a central theme in condensed matter physics. Although the correspondence between Chern bands and the lowest Landau level has been widely studied, a lattice realization of the first Landau level remains elusive. Here we construct a minimal lattice model that provides a concrete orbital description of both the lowest and first Landau levels. Using maximally localized Wannier functions with $s$, $p_-$, and $p_+$ orbital character, we develop a three-orbital model in which the two lowest Chern bands are flat and each carries a Chern number $\mathcal{C}=1$. The band topology arises from a sequence of ideal band inversions between Wannier states at the $\Gamma$ and $K$ points in momentum space, establishing an adiabatic connection between the atomic insulator limit and Landau level physics. Notably, many-body exact diagonalization reveals that the non-Abelian state can appear in the half-filled first Chern band. This construction can be further generalized to realize flat Chern bands analogous to higher Landau levels. Our results provide a new perspective on lattice analogues of Landau levels and may enable the exploration of fascinating topological phenomena at elevated temperatures.