Solid State Communications~o1. 15, pp. 269—272, 1974. Pergamon Press. Printed in Great Britain PEIERLS TRANSITION IN A QUASI—ONE DIMENSIONAL SYSTEM* G. Benit Department of Physics, University of California, Los Angeles, California 90024, U.S.A. (Received 8 February 1974 by A.A. Maradudin) We study the thermodynamics of a noninteracting electron system with a half filled strongly anisotropic tight binding band in the mean field approxi- mation. This system may exhibit a structural transition dimerizing along the high conductivity direction. The conditions for the instability to occur are given as a function of the degree of anisotropy. The relationship to the behavior of TCNQ salts is discussed. THE PURPOSE of this communication is to clarify sufficient to produce a similar crystallographic tran- one aspect of the Peierls transition 1 in quasi—one di- sition in a three dimensional system.9”° mensional systems. Physically, quasi—one dimensional systems are realized at least in two classes of compounds, It seems therefore natural to ask whether or not i.e. the charge transfer salts of TCNQ and the mixed a three dimensional, but strongly anisotropic, system valency planar (MVP) transition metal compounds.2’3 would exhibit a Peierls transition. In what follows we Both show columnar stacking with the electrons give an answer to this question within the limits of an localized on parallel chains. The interaction between elementary tight binding model and we find a con- atoms or molecules in a chain is supposed to be much dition for the onset of the instability as a function of larger than the interaction between the chains as mdi- the anisotropy of the interactions. cated for example by conductivity measurements. Thus a number of strictly one dimensional models Consider a single cubic lattice of ions with one have been proposed to explain the remarkable proper- conduction electron per site (Fig. I). In the ~ direc- ties of these systems: simple one electron models,4 tion the ions are harmonically coupled with elastic the Hubbard model,5 the Heisenberg antiferro- constant c. Within the framework of the mean field magnet,6 etc. theory we impose the restriction that the ions may move away from their equilibrium position only in More recently, following some experiments on such a manner that distances between adjacent ions TTF TCNQ,7 a great deal of study has been devoted alternate along the i axis. This restriction is imposed to a variety of models exhibiting a Peierls transition.8 from consideration of the physical systems of interest All these models are strictly one dimensional. How- (TCNQ salts) where a similar alternation of inter- ever, while the strong anisotropy of the interactions ionic distances occurs or might occur. We also remark in TCNQ salts and in MVP compounds is well estab- that with this restriction we neglect fluctuation effects lished, we may argue that the use of a perfectly one and so we favor the occurrence of the phase transition. dimensional model might not be entirely justified. Thus the conditions for the suppression of the insta- This holds especially in connection with the study of biity, which we shall find within this mean field theory, the Peierls transition. In fact, as is well known, the are valid a fortiori when fluctuations are taken into conditions that ensure the occurrence of such tran- account. sition in a one dimensional lattice are in general not The electronic system is described by a simple *Supported in part by the National Science Foundation tight binding model with identical transfer integral t 1 along the ~ and 51 directions. This inter chain transfer tJBM Pre-Doctoral Fellow. t1 is assumed to be much smaller than the transfer 269