Deep-subwavelength interface states in mechanical systems

Topological interface states in mechanical systems are the analogues of the edge modes in topological insulators from the field of condensed matter physics. The interface states produced and reported in the existing literature are located in the Bragg Scattering band gaps of phononic crystals. The corresponding frequencies of the interface states are thus high. This paper proposes a novel mechanical system that can produce an ultra-low frequency interface state in the deepsubwavelength region. Due to the periodic spring connections to the ground, a quasi-static band gap with a starting frequency of 0 Hz can be produced in the proposed system. The spring connections can be tuned to alter the polarization direction of the mode shape. Through a mass-spring model, the formation of an interface state in the quasi-static band gap is demonstrated. Moreover, it is found that by carefully configuring the spring connections to the ground, the interface state in the quasi-static band gap can be tuned to an arbitrarily low frequency. In addition, practical systems based on rod and beam structures are constructed following a similar design methodology. Theoretical analyses demonstrate that for the longitudinal/transverse wave mode in the topological rod/beam structure, a deep-subwavelength interface state can always form in the quasi-static band gap. The possibility of producing the deep-subwavelength interface state at an arbitrarily low frequency is also confirmed in a rod and a beam lattice system.