M. B. LLWI S In terms of the relative momentum Pss, Pes must be gran' dt' within a solid angle sr2P/ rss(t') ' in the direction rss I (t'), I r»(t') I' which at distances can be replaced sr''/ I large —by rrs(t') I', whe~e rrs(t') =rrs —Psst'/m and r&s —q& —ti&, n+R' Prst/mf rs co—s8 I ' P12= pl —p2. tan r&s(P»/m) (1—cos'8)'t' (1—cos'8)'t' In (31) changing the momentum integration to Pss we have —cos8 -' t —tan (83) (1—cos'8)'" dt' dQI „o., where 8 is the angle between rrs and Prs. Equation (83) approaches a limit as t —+~, according to 1 8($13 8I'1 — ) cy= — d ggdP32P32 . g( . —cos8 0 t9 $1 i9 P1 ——tan ' r&s(P&s/m) (1—cos'8)'" 2 (1—cos'8)'" To obtain the magnitude of (82) we neglect the varia- (1—cos'8) 't' tion of 0. with time and treat it as constant with respect to the angles when it is nonzero. We then have Pgst/mr„ PHYSI GAL R EVI E%V VOLUME 134, QUM B ER 6A J UN E 1964 Possibility of Synthesizing an Organic Superconductor* EV. A. I ITTLK Departntent of Pttysies, Stanford University, Stanford, California (Received 13 November 1963; revised manuscript received 27 January 1964) I.pndon s idea that superconductivity might occur in organic macromolecules is examined in the light of the 3( S theory of superconductivity. It is shown that the criterion for the occurrance of such a state can be met in certain organic polymers. A particular example is considered in detail. From a realistic estima- tion of the matrix elements and density of states in this polymer it is concluded that superconductivity should occur even at temperatures well above room temperature. The physical reason for this remarkable high transition temperature is discussed. It is shown further that the superconducting state of these polymers should be distinguished by certain unique chemical properties which could have considerable biological signi6cance. I. INTRODUCTION attempt to experiment in such an environment. Instead " of attempting this, we shall tackle the N the forward to Vol. j. of his monographs on problem on our own grounds. The BCS theory, while no means - ~ superQuids, F. London' questions whether a by complete and exact, has succeeded in superQuid-like state might occur in certain macro- providing a model with most of the essential features of a molecules which play an important role in biochemical superconductor. In it reactions. If this should be the case, an entirely new and particular, prescribes certain criteria for a system which, if satisfied, should lead to the important consideration would be added to the problem superconducting state. Our approach is to consider how these of understanding living systems. In view of the signifi- criteria might be applied to the design of a cance of such an effect, it appears appropriate a,t this particular organic molecule which, if its synthesis is time, when a theory of superconductivity, the Bardeen- possible, should show the Cooper-Schrieffer (BCS) theory' has been so remark- some of essential features of a superconductor and, as we shall show, some remarkable chemical ably successful in explaining much of the behavior of properties as well. One of the interesting superconductors, to examine in the light of this whether features about the particular class of molecules we or not a superconducting state might occur in certain investigate in detail is macromolecules. In view of the extreme complexity of that the molecules should be superconducting at room biological systems, it would be folly for a physicist to temperature and, indeed, to temperatures well above room temperatures. We can show on simple physical * the National Science Foundation and Supported in part by grounds why this is so and perhaps, with hindsight, why the U. S. Navy OfBce of Naval Research. ' F. London, Sstperftneds {John Wiley k Sons, Inc. , New York, this was to be expected. 1950), Vol. 1. The idea of superconductivity in organic systems is s J. Bsrdeern, L. N. Cooper, and J. R. Schrietier, Phya Rev. 108, f175 (1957). not a new idea& however, there is a considerable amount SYNTHESIZING AN ORGANI C SUPEP~CON DUCTOR of confusion as to the exact meaning of this, The one must provide, therefore, some mechanism snnilar diamagnetic ring currents of aromatic molecules such to this. In our model we do this in the following manner. as benzene, naphthalene, etc., are nondissipative cur- rents similar in many respects to the persistent currents II. MODEL SYSTEM of superconducting rings and, have often been referred to as a form of superconductivity. However, the "super- We shall consider a molecule consisting of two parts, conductivity" of these molecules is not the same as the a long chain called the "spine" in which electrons fill superconductivity of bulk materials. The reason, I the various states and may or may not form a con- believe, is the following. In macroscopically large ducting system; and secondly, a series of arms or side superconductors, if superconductivity exists, then a chains attached to the spine as indicated in Fig. i.. We finite fraction of the charge carriers, in general, the 8CS will show that by appropriate choice of the molecules pairs are in identically the same center-of-mass momen- which constitute the side chains, the virtual oscillation tum state. This state then has a macroscopic occupation. of charge in these side chains can provide an interaction In a magnetic field the canonical momentum of this between the electrons moving in the spine. This can be state remains unchanged, but due to the vector potential made a suKciently attractive interaction so that the term contained in it a current is induced and the energy superconducting state results. We can show further that of the state changes. For a macroscopically large super- even if the spine by itself is initially an insulator due conductor the kinetic energy of the diferent center-of- to the valence band being full and the conduction band mass momentum states of the pairs lie extremely close empty, the addition of side chains can increase the to one another, however, because the coherence energy electron-electron attraction to the point where it of each state depends upon the square of the number of becomes energetically favorable to enter the super- pairs in that state, the state which is macroscopically conducting state by mixing in states of the conduction occupied is appreciably lower in energy than any of the band. The spine thus transforms from the insulating or neighboring states even in a moderate magnetic 6eld. semiconducting state directly to the superconducting It is only by transitions in which practically all the metallic state upon the addition of the side chains. pairs in the macroscopically occupied state simul- Consider a long chain molecule as shown in the left taneously move to another state that a lower energy half of Fig. 1. We will assume this is a conjugated chain final state can be reached. This is obviously highly of double and single bonds resonating between the two forbidden and, consequently, the system of pairs at each link. This corresponds in the band theory of remains in the momentum state into which condensa- metals to a band which is half filled and ideally is a tion originally occurred. Thus, it is the coherence energy metallic conductor. (See, however, Sec. III.) At the which prevents the system from freely adjusting itself points J'„J", , a regular array of side chain mole- to take the lowest possible energy. In the aromatic cules 8 are attached. The individual side-chain ring compounds practically all the molecules are in molecules are chosen to have a low-lying excited state their ground states. In a magnetic field the canonical such that transitions from the ground state to the momentum of the electrons in this state remain un- excited state correspond classically to an oscillation of changed and diamagnetic currents Row in the molecule charge from end to end of the molecule. similar to those of a bulk superconductor. The energy The electrons moving in the spine may be described of the different momentum states of the electrons in each molecule in this case are well separated though, because the molecules are of microscopic size. Thus, the momenta of the electrons do not change because for 6elds as large as those available in the laboratory, the state which evolves out of the original ground state still is lower in energy than any other in the presence of the Fxc. 1. Proposed field. If, however, the aromatic system is made arbi- model of a super- conducting organic trarily large such as in graphite, bulk superconductivity molecule. The mole- does not result because as the system gets bigger, the cule A is a long un- different momentum states of the electrons saturated polyene approach chain called the each other in energy. Transitions can then occur be- "spine. " The mole- tween states and the induced currents are dissipated. cules 8 are side chains attached to So that in order to get superconductivity in a macro- the spine at points molecule or in a bulk xq.aterial, something of the nature P, P', of a coherence energy is required. In conventional superconductor s this is provided by the phonon- induced, electron-electron interaction; in attempting to devise a macromolecule which is to be superconducting W. A. L I T TL E in the tight-binding approximation by eigenfunctions It is convenient to write this as (1/6) V(Q) for the of the form moment.