Maxwell lattices, where the number of degrees of freedom equals the number of constraints, are known to host topologically protected zero-frequency modes and states of self-stress, characterized by a topological index called topological polarization. In this Letter, we show that in addition to these known topological modes, with the help of a mirror symmetry, the inherent chiral symmetry of Maxwell lattices creates another topological index, the mirror-graded winding number (MGWN). This MGWN is a higher-order topological index, which gives rise to topological zero modes and states of self-stress at mirror-invariant domain walls and corners between two systems with different MGWNs. We further show that two systems with the same topological polarization can have different MGWNs, indicating that these two topological indices are fundamentally distinct.

Close

PrevNext

View figure in article

• Symmetry protected topological states
• Mechanical metamaterials
• Discrete symmetries in condensed matter