Moving and merging of Dirac points on a square lattice and hidden symmetry protection

TL;DR

This paper investigates how Dirac points in a square lattice move and merge under modifications like staggered potential and diagonal hopping, revealing their protection by hidden symmetries and developing a mapping method to track symmetry evolution.

Contribution

It introduces a mapping method to identify hidden symmetries protecting Dirac points and explains their dynamics under parameter changes in modified lattice models.

Findings

Dirac points move with parameter variation in modified models.

Dirac points merge at critical staggered potential values.

Hidden symmetries evolve with parameters, protecting Dirac points.

Abstract

First, we study a square fermionic lattice that supports the existence of massless Dirac fermions, where the Dirac points are protected by a hidden symmetry. We also consider two modified models with a staggered potential and the diagonal hopping terms, respectively. In the modified model with a staggered potential, the Dirac points exist in some range of magnitude of the staggered potential, and move with the variation of the staggered potential. When the magnitude of the staggered potential reaches a critical value, the two Dirac points merge. In the modified model with the diagonal hopping terms, the Dirac points always exist and just move with the variation of amplitude of the diagonal hopping. We develop a mapping method to find hidden symmetries evolving with the parameters. In the two modified models, the Dirac points are protected by this kind of hidden symmetry, and their moving and merging process can be explained by the evolution of the hidden symmetry along with the variation of the corresponding parameter.