Abstract
The kagome lattice has coordination number , and it is mechanically isostatic when nearest-neighbor sites are connected by central-force springs. A lattice of sites has zero-frequency floppy modes that convert to finite-frequency anomalous modes when next-nearest-neighbor (NNN) springs are added. We use the coherent potential approximation to study the mode structure and mechanical properties of the kagome lattice in which NNN springs with spring constant are added with probability , where and is the average coordination number. The effective medium static NNN spring constant scales as for and as for , yielding a frequency scale and a length scale . To a very good approximation at small nonzero frequency, is a scaling function of . The Ioffe-Regel limit beyond which plane-wave states become ill-defined is reached at a frequency of order .
1 More- Received 11 August 2010
DOI:https://doi.org/10.1103/PhysRevE.83.011111
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