Low-frequency response of pinned charge-density-wave condensates

Abstract

The frequency-dependent conductivity \ensuremath{\sigma}(\ensuremath{\omega}) was investigated in the 10 Hz to -500 MHz range in materials with an incommensurate charge-density wave. ${\mathrm{NbSe}}_{3}$, orthorhombic ${\mathrm{TaS}}_{3}$, and (${\mathrm{TaSe}}_{4}$${)}_{2}$I. Over a wide range of frequencies both Re\ensuremath{\sigma}(\ensuremath{\omega}) and Im\ensuremath{\sigma}(\ensuremath{\omega}) are described by the expression \ensuremath{\sigma}(\ensuremath{\omega})=C(i\ensuremath{\omega}/\ensuremath{\omega}\ifmmode\bar\else\textasciimacron\fi{}${)}^{\ensuremath{\alpha}}$ with \ensuremath{\alpha}1, and have different values for each material. The \ensuremath{\omega}-dependent response is in clear disagreement with descriptions which neglect the internal degrees of freedom of the condensate. The excess low-frequency conductivity is due to the disorder caused by random distribution of pinning centers. The results are compared with calculations based on a microscopic phase Hamiltonian, which takes impurity pinning into account. The results are in semiquantitative agreement with a modified form of the Mott-Berezhinskii law for one-dimensional hopping conductivity, and they are in qualitative agreement with the classical, relaxational dynamics approach in the \ensuremath{\omega}\ensuremath{\rightarrow}0 limit. We also discuss the relation of our experimental findings to other studies of the frequency-dependent response in these materials.