Sound Propagation in Cdw and Sdw
- PDF / 273,340 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 35 Downloads / 228 Views
SOUND PROPAGATION IN CDW AND SDW ATTILA VIROSZTEK* AND KAZUMI MAKI** * University of Virginia, Department of Physics, Charlottesville, VA 22901 "**University of Southern California, Department of Physics, Los Angeles, CA 90089-0484 ABSTRACT We present a microscopic theory of the sound propagation in quasi one dimensional charge density wave (CDW), spin density wave (SDW) and field induced spin density wave (FISDW). First, we consider the ideal situation that the phase correlation length in the CDW or the SDW is infinite. In this limit due to the diffusion pole at iw = Dq2 in a variety of correlation functions the sound propagation depends on a) what is the ratio w/Dq2 and b) if the CDW (or the SDW) is pinned or unpinned where D is the diffusion constant. Second, when the CDW (or the SDW) is unpinned, the phason starts to participate in the screening of the ionic potential. However, since the unpinned part is strongly inhomogeneous, the contribution of the phason term depends on the wave vector of q of the sound wave like (1 + (Lq) 2 )- 1 where L is the Fukuyama-Lee-Rice coherence length. The present theory accounts for a variety of features observed in sound propagation in quasi-one dimensional CDW systems like NbSe3 and TaS3 . INTRODUCTION The Fr~hlich conduction is seen in number of quasi-one dimensional CDW and SDW systems [1]. One of its manifestations is the electromechanical effect (i.e. the softening of the elastic constant associated with depinning of CDW or SDW) first established in CDWs in TaS3 and NbSe3 by Brill et al [2] and others [3]. In general, Young's modulus (or the longitudinal sound velocity) increases upon entrance into a CDW [2,31 or a SDW [4]. Then when an electric field exceeding the threshold field ET is applied Young's modulus starts decreasing with increasing electric field E 12,31 though the latter behavior has not been seen in a SDW yet. On the other hand, the shear modulus does not exhibit any anomaly at the CDW transition [5]. However, application of E exceeding ET decreases the shear modulus [5]. More recently, Xiang and Brill [6] observed the strong frequency dependence in this softening in Young's modulus of CDWs in NbSe 3 and TaS3 . The observed softening AY = Y(o) - Y(E) decreases like wwith a ; •-.. This frequency dependence is consistent with an early experiment by Jericho and Simpson [7] who saw only small depinning anomaly at w 110 MHz. We have shown earlier [8] within mean field analysis of the Fr~hlich Hamiltonian for the quasi-one dimensional CDW that the ionic potential in a CDW is screened by both the quasi-particle and the phason. However, when the CDW is pinned the phason cannot participate in the screening. Therefore, in a pinned CDW the increase in the sound velocity is due to the decrease in the quasi particle density in the CDW. On the other hand, when the CDW is completely depinned, by an electric field, both the quasi-particle and the phason participate in the screening resulting in the sound velocity same as in the normal state [8,9]. Though this theory describe
Data Loading...
