Tom Lubensky, Andrea Liu, Arjun Yodh, Shu Yang and Ju Li
An isostatic lattice is one at the threshold of mechanical stability. The square and kagome lattices (see Figure 1a-b) in two dimensions are examples of isostatic lattices. A 2D kagome lattice of N sites has of order N1/2 zero-energy bulk modes under periodic boundary conditions. Theoretical study shows that when neighboring triangles are counter rotated through an arbitrary angle α shown in Figure 1c, the bulk modulus vanishes, making the Poisson’s ratio equal to -1, and all of the bulk zero modes of the α =0 lattice disappear. The study of rigidity and its restoration in these lattices as a function of bending forces or next-nearest-neighbor springs will improve our understanding of jamming of hard spheres systems and of networks of semi-flexible polymers, and offer new paradigms for the microscopic mechanics of disordered media. Taking the general concept of network nstability, we expect to develop a new opto-mechano based materials platform to dynamically tune thephotonic and phononic properties.