Orbital Description of Landau Levels

Area of Science:

• Condensed matter physics
• Topological materials

Background:

• Landau levels are fundamental in understanding electron behavior in magnetic fields.
• A lattice analog for Landau levels, particularly the first Landau level, has been a long-standing challenge.
• Existing research primarily focuses on the correspondence between Chern bands and the lowest Landau level.

Purpose of the Study:

• To construct a minimal lattice model for Landau levels.
• To provide a concrete orbital description for both the lowest and first Landau levels.
• To explore topological phenomena in condensed matter systems.

Main Methods:

• Utilized maximally localized Wannier functions with s, p-, and p+ orbital character.
• Developed a three-orbital model exhibiting flat Chern bands.
• Employed band inversion analysis between Wannier states at Γ and K points.
• Performed many-body exact diagonalization.

Main Results:

• Successfully constructed a lattice model for the lowest and first Landau levels.
• The model features two flat Chern bands, each with a Chern number C=1.
• Demonstrated an adiabatic connection between atomic insulator and Landau level physics.
• Observed the emergence of non-Abelian states in the half-filled first Chern band.

Conclusions:

• The developed model offers a novel perspective on lattice analogs of Landau levels.
• This work facilitates the study of topological phenomena in condensed matter systems.
• The construction can be extended to realize higher Landau level analogs and flat Chern bands.