Manipulation of Dirac Cones in Mechanical Graphene

TL;DR

This paper explores how manipulating spring tension in mechanical graphene alters Dirac cones and topological properties, demonstrating topological transitions and symmetry protection in a classical spring-mass system.

Contribution

It reveals how changing spring tension creates and annihilates Dirac cones and shows topological transitions via Chern number jumps in a classical system.

Findings

Dirac cones are controllably created and annihilated by tension adjustments.

Topological phase transitions are evidenced by Chern number jumps.

Symmetry protection affects edge mode existence depending on boundary conditions.

Abstract

Mechanical graphene, which is a spring-mass model with the honeycomb structure, is investigated. The vibration spectrum is dramatically changed by controlling only one parameter, spring tension at equilibrium. In the spectrum, there always exist Dirac cones at K- and K'-points. As the tension is modified, extra Dirac cones are created and annihilated in pairs. When the time reversal symmetry is broken by uniform rotation of the system, creation and annihilation of the Dirac cones result in a jump of the appropriately defined Chern number. Then, a flip of the propagation direction of the chiral edge modes takes place, which gives an experimental way to detect the topological transition. This is a bulk-edge correspondence of the classical system. We also demonstrate the other important concept, symmetry protection of the topological states, is at work in the classical system. For the time reversal invariant case, the topological edge modes exist for the fixed boundary condition but not for the free boundary condition. This contrast originates from the symmetry breaking at the free boundary.