Topological constraints on the electronic band structure of hexagonal lattice in a magnetic field

TL;DR

This paper explores how projective lattice symmetry influences the topological features of electronic band structures in hexagonal lattices under magnetic fields, revealing unique Dirac points and Chern number constraints.

Contribution

It uncovers novel topological constraints on band structures in hexagonal lattices with magnetic flux, extending understanding beyond square lattice models.

Findings

At pi flux, symmetry enforces Dirac band touchings at E ≠ 0.

For rational flux, symmetry constrains the number of Dirac points at E = 0.

Constraints on Chern numbers differ significantly from those in square lattices.

Abstract

The impact of projective lattice symmetry on electronic band structures has attracted significant attention in recent years, particularly in light of growing experimental studies of two-dimensional hexagonal materials in magnetic fields. Yet, most theoretical work to date has focused on the square lattice due to its relative simplicity. In this work, we investigate the role of projective lattice symmetry in a hexagonal lattice with rational magnetic flux, emphasizing the resulting topological constraints on the electronic band structure. We show that, at pi flux, the symmetry in the hexagonal lattice enforces novel Dirac band touchings at E not equal to zero, and for general rational flux it constrains the number of Dirac points at E = 0. We further analyze the symmetry-imposed constraints on the Chern numbers of both isolated gapped bands and band multiplets connected by Dirac-point touchings. Our results demonstrate that these constraints in the hexagonal lattice differ substantially from those in the square lattice.