Hidden symmetry and protection of Dirac points on the honeycomb lattice

TL;DR

This paper reveals a hidden symmetry in the honeycomb lattice that protects Dirac points, explaining their stability, movement, merging, and associated quantum phase transitions.

Contribution

It uncovers a previously unknown hidden symmetry that precisely accounts for the existence and behavior of Dirac points in honeycomb lattice materials.

Findings

Dirac points are protected by a hidden symmetry.

The movement and merging of Dirac points are explained by symmetry evolution.

Quantum phase transitions are linked to symmetry changes.

Abstract

The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.