Non-linear anelasticity of topological vortex matter in martensites

A number of unusual anelastic phenomena has been observed in the low-temperature non-linear anelasticity of martensitic phases with faulted structure (β′, β′1), typical for binary and ternary Cu-based alloys, when studied at ultrasonic frequencies of around 100 kHz. We suggest to consider interacting and ordered partial dislocations in faulted martensites as a system of elastic topological vortices in a glassy or liquid state. We show that such system of topological vortex matter is remarkably similar to the flux line matter in type-II high temperature superconductors (HTSC). In particular, we found the similarity of intrinsic properties of topological vortices in faulted martensites (self energy of vortices, their interaction) and of extrinsic conditions of their motion (effects of quenched- and thermal-disorder) to those in HTSC. We show that the logarithmic decrement of oscillations in a mechanical system of elastic topological vortices substitutes for the longitudinal resistivity in type-II HTSC. Topological vortices in faulted martensites are convenient objects for experimental studies of vortex matter dynamics due to the high stability of the topological vortices over wide temperature range. They also exemplify a model system of driven elastic strings in a random/correlated potential, which is a subject of intense theoretical investigation.