Hysteresis in thermal expansion of the quasi 1-dimensional conductor TaS$_3$: Coupling of the underlying and the electronic crystals

An interferometer-based setup for measurements of length of needle-like samples is developed, and thermal expansion of o-TaS$_3$ crystals is studied. Below the Peierls transition the temperature hysteresis of length $L$ is observed, the width of the hysteresis loop $\delta L/L$ being up to $5\times 10^{-5}$. Curiously, $L(T)$ changes so that it is in front of its equilibrium value. The hysteresis loop couples with that of conductivity. With lowering $T$ the charge-density waves' (CDW) elastic modulus grows and at 100 K becomes comparable with that of the lattice $Y_l$. The results justify the assumption about the strain dependence of the CDW wave vector and clarify the nature of the anomalies of $Y_l$ which occur on the CDW depinning. In particular, $Y_l$, is expected to show a strong drop in the static regime, if measured at sufficiently small sample elongation $(\delta L/L < 10^{ -5}) $