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Modelling κ Phase Organic Conductors
V. Yartsev, O. Drozdova, V. Semkin, R. Vlasova
To cite this version:
V. Yartsev, O. Drozdova, V. Semkin, R. Vlasova. ModellingκPhase Organic Conductors. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.1673-1681. �10.1051/jp1:1996102�. �jpa-00247273�
Modelling ~-Phase Organic Conductors
V.M. Yartsev (~.*), O.O. Drozdova (~), V.N. Semkin (~) and R-M- Vlasova (~)
(~ Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020-A, Venezuela
(~) A. F. IooEe Physico-Technical Institute, Russian Academy of Sciences, St-Petersburg, Russia
(Received 17 JaJluajv1996, revised 25 March 1996, accepted 27 August 1996)
PACS.71.10.-w Theories and models of many electron systems PACS.78.30.Jw Orgamc sohds, polymers
Abstract. ~-phase organic conductors with bidimensional layers of orthogonal molecular dimers are modelled by tetramers and hexamers of appropriate geometry. The complex con- ductivity is calculated within the Hubbard model including the electron-intramolecular vibra- tion coupling. The polarized optical conductivity data of two ~-phase charge-transfer salts of b~s-(ethylenedithio)-tetrathiafulvalene: ~-(BEDT-TTF)2(Hg(SCN)2Br] and ~-(BEDT-TTF)2 [Hg(SCN)C12), are, discussed.
1. Introduction
A rapidly growing family of organic conductors includes ion-radical salts witu a variety of crystal structurés, wuicu strongly influence tueir puysical properties [ii. Tue so called "~-
phase" witu bidimensional layers of orthogonal dimers is of special interest, because several of tuese salts are superconductors witu a transition temperature above 10 K at ambient pres- sure [2]. But even salts of tue same donor bis-(etuylenedituio)-tetratuiafulvalene (BEDT-
TTF) witu a common pattern of ~-puase may bave ratuer different electrical properties: tue
~-(BEDT-TTF)2Cu(NCS)2 and ~-(BEDT-TTF)2Cu[N(CN)2]X IX
= Br, Bro 5Clo.5 are super- conductors [2,3] wuile tue ~-(BEDT-TTF)2[Hg(SCN)~_~Xn] IX = Cl, Br, n = 1,2) become dielectric at low temperature [4]. Recently, we bave undertaken a comparative spectroscopic study [5-î] of some of tue ~-puase compounds in order to evaluate tue role of electron-molecular
vibration (EMV) coupling, wuicu is believed [8] to be responsible for tue superconductivity puenomenon in organic matenals.
Two alternative approacues are mainly used currently for describing tue optical proper-
ties of low-dimensional molecular crystals [9]: "puase puonon" tueory wuere charge carriers are supposed to be delocalized and tue cluster model wuere tue optical properties are cal-
culated as a superposition of tue optical responses of isolated clusters of finite size. Tue former tueory seems to be more appropnate for describing uiguly conducting matenals, but
a senous disadvantage of tuis model is tuat it is a "one-electron" tueory, wuere electronic
correlation can be taken into account only in tue effective mass approximation. At tue same time low-dimensional molecular crystals are generally classified as strongly-correlated systems,
(*) Author for correspondence: (e-mail: syartsev@pion.ivic.ve)
@ Les Éditions de Physique 1996
1674 JOURNAL DE PHYSIQUE I N°12
t
~) t, -3
t' -4 ,
2~
b) Î~'Î t '~ ~Î
2- t t' -6
3 4
QLi ,
Fig. l. Modelling ~-phase compound as the tetramer (a) and the hexamer (b).
because tue Coulomb on-site repulsion energy of two radical electrons on tue same molecule, U, is known to be of tue order of tue bandwidtu, calculated in a tigut-binding approxima-
tion. In references là-?], we used tue "phase phonon" tueory to interpret our data and found that trie salts ~-(BEDT-TTF)21Hg(SCN)2Br] and ~-(BEDT-TTF)21Hg(SCN)C12] were char- acterized by a smaller oscillator strength of trie conduction electron transitions and plasma frequency wp, compared to trie ones in superconductors ~-(BEDT-TTF)2Cu(NCS)2 (Si and
~-(BEDT-TTF)2Cu[N(CN)2]Bro.5Clo.5 (GI. This observation indicates that electronic correla- tions are more important in trie former salts. Also it bas been noted that trie optical response of trie ~-phase compounds depends on trie polarization of trie incident light with respect to trie
crystallographic axes [10]. In tue cluster approacu, one can model tue actual orientation of molecules by a suitable cuoice of transfer integrals and consider electronic interactions in an ex-
plicit way, usually employing tue Hubbard Hamiltonian Iiii for tue purpose. Unfortunately, as
cluster dimensions increase, tue exact solution of tue Hubbard model becomes matuematically
diflicult.
In tuis paper, we consider a model of ~-puase as two orthogonal dimers for arbitrary values of tue Hubbard model parameters.
2. Theoretical Model
As noted in tue Introduction, tue crystalline structure of ~-puase organic compounds presents weakly interacting layers composed of orthogonal dimers of donor molecules je-g- BEDT-TTF).
Inside eacu layer, short interdimer (S S) distances are observed indicating a ratuer strong interaction between dimers leading to a quasi-bidimensional electronic system. Wituin tue cluster approacu, a simple model for a ~-puase layer is just two orthogonal dimers suown in
Figure la. Short S.. S contacts are represented by transfer integrals t'. Tue ratio of t' to tue intradimer transfer integral t is a convenient parameter to account for interactions of our
dimer witu its neigubours. Tue uexamer suown in Figure 16 will serve to test tue convergence of calculated results as a cluster grows for diiferent t'/t values.
Recently we bave developed [12] a general formalism to descnbe tue optical properties
of molecular clusters witu arbitrary geometry and equilibrium charge density distribution.
Applying tuese results to our model (see Fig. i for notation), we get tue Hamiltonian
H He + Hv + ~ §o~Rz~ni P'E (1)
n,~
Tue first two terms in equation ii) descnbe, respectively, tue radical electrons and tue in- tramolecular vibrations of eacu monomer in tue absence of vibronic coupling. Linear EMV
coupling is described by tue tuird term wuere gm denotes tue EMV coupling constant of tue electron density, n~, on tue site to tue dimensionless coordinate Qm of tue vibrational mode
a of tue same molecule. Tue last term gives tue interaction energy of an external electric field E witu tue induced dipole moment p of tue tetramer.
Tue complex conductivity bas tue form [12]
a(w) = -iwNt (d,II X diagDl~~ X d)
,
(2)
wuere Nt is tue number of tetramers per unit volume, d denotes tue vector witu components (e(a + a'), ea', 0,0), diag D is tue diagonal matrix of
D~(Ld) = ~j 291~L°a~
n
~°Î~ L°~ iuJ~~~' j~~
1 is tue unitary matrix and X denotes tue matrix of electronic polarizabilities witu tue elements
ÎÙij(ld) ~ ~~ )~~~~ 2~~~ ~/~~~ ÎÙP(~d). (~)
p pi
In equation (3), wn~ and ~ai are, respectively, frequency and damping factor for tue a-tu totally symmetric mode ofintramolecular vibration. In equation (4), rp denotes tue puenomenological
natural widtu of tue origmally uncoupled charge transfer excitation witu tue energy uJpi
"
Ep Eii Ep and [fl) are tue exact eigenvalues and eigenfunctions of tue electromc Hamiltoman
He m equation (i). fl = i labels tue ground state.
Tue electronic Hamiltonian He m equation (i) is taken m tue Hubbard approximation
He =
~ ~j n~ an~ -a-t ~j (c)~c2
a + c(~c4
a + h-c-) -t'~j (c(~c3
a
+ c(~c4
a
+ h-c-)
,
(5)
~
~a a
' ' '
a
' ' ' '
wuere cf~ (c~,a) denotes tue operator of tue uole creation (destruction) on tue site witu tue spin projection a, n~,a = c)~c~,a.
Eigenvalues Ep and eigeifunctions fl) of tue Hamiltoman (Si may be found by usmg a series
jàj =
~ apk [ij 16j
k
over tue basis states (Î), wuicu in tue case of two uoles per tetramer mcludes 28 possible dis- tributions. After numerical solution of tuis problem, we calculate tue electronic polanzabilities (4) and finally tue complex conductivity given by equation (2). Figure 2 presents tue real part of tue conductivity calculated for turee values of U. We notice tuat as U increases tue optical conductivity spectrum looks more and more as tue one calculated for tue isolated dimer model.
Of course it is not surpnsing tuat electronic correlations favour effective charge localization: in
1676 JOURNAL DE PHYSIQUE I N°12
200
~( 200
~C
# 100
~
'É
é 0
) 100 ~
0
ioo
c
~
0 2000 4000 6000 8000
Wavenumber(cm")
Fig. 2. Calculated optical conductivity for the tetramer model for the following parameters: t =
0.2 eV; t'/t
= 0A; U/4t
= 0 (a), 1 (b), 1000 (c); r = 2000 cm~~; uJ~ =1455 cm~~; g«
= 300 cm~~,
~~ =10 cm~~;
a = 3.4 À, a'
= 3.58 À, Nt
# 5.5 x 10~° cm~~ The
case of isolated dimer 11'= 0) is shown by the dashed fine.
tue case of large U we can imagine our system as a Wigner lattice of molecular dimers witu one
charge carrier per dimer. It follows from Figure 2, tuat tue curve (c) for U/t = 4000 is mucu doser to tue curve (b) corresponding to U/t
= 4 (typical value for low-dimensional ion-radical
softs) tuan to tue curve (a) calculated witu tue neglect of electronic correlations as is assumed
m tue "puase puonon" tueory. Finite values of U allow uigu energy transitions resulting in two charges witu opposite spms per site, but tue coupling of tuese transitions to intramolec- ular vibrations is mucu weaker compared to tue low energy excitations permitted in systems witu less tuan ualf-filled band occupation (~-puase compounds bave a quarter-filled band). We
conclude tuat electromc correlations are important and suould be taken into account. Figure 3 presents tue calculated spectra for dimer, tetramer and uexamer for t'/t
= 0.2 and Figure 4 shows tue results for t'If
= 0.4. It may be seen tuat for a relatively small value of t'/t
= 0.2
tue resulting spectra seems to converge well witu tue mcrease of tue size of tue cluster, wuile for t'/t
= 0.4 tue convergence is poor and we would expect tuat tue cluster approacu will not be suitable in tuis case.
3. Discussion of the Experimental Data
It is convenient to consider ~-(BEDT-TTF)2 ÎHg(SCN)C12] and ~-(BEDT-TTF)2 ÎHg(SCN)2Br]
salts for a discussion of our tueoretical results. Tue crystal structure of botu compounds [4,13]
is formed by (parallel to bc plane) bidimensional sueets of cation-radicals (BEDT-TTF), wuicu altemate along tue a axis witu layers of polymer anions. Tue cation-radical sueets consist of
oo
~~
~
~$
~~
~
_5 é
~~
b
O
~
Î ~
50
~
0 2000 4000 6000 8000
Wavenumber(cm")
Fig. 3. Calculated optical conductivity m the case U/4t
= 1000 of
an isolated dimer (a), tetramer
(b) and hexamer (c) for t'/t
= 0.2; the rest of parameters are the same as in Figure 2.
(BEDT-TTF)( dimers, packed in a cuaracteristic ~-puase manner. Tue interplanar spacings
between BEDT-TTF cation-radicals mside tue dimer are 3.53 for tue salt witu Br and 3.59
À for tue salt witu C12. Also, m tue former compound, tue dimer contains two suortened
(compared to tue Van.der.Waals values) intermolecular S S contacts, wuicu are absent in tue salt witu C12, so tue intradimer transfer integral t is smaller in tue latter case. Tue cation-
radicals of tue neigubonng dimers bave some suortened S S contacts. Tue cuains of polymer
aurons in tue two compounds are oriented along tue c axis.
Tue experimental room temperature optical conductivity spectra, aexp(w), of K-(BEDT- TTF)21Hg(SCN)2Br] and ~-(BEDT-TTF)21Hg(SCN)C12] m tue range 1000 4500 cm~~ for polanzation E [ b corresponding to tue most intense cuarge-transfer band are suown m Fig-
ures Sa and 5b, respectively. Tue aexp(w) spectra were obtained by Kramers-Kronig transfor- mation of tue relevant reflectance spectra as described in reference Iii. Tue aexp(w) spectra of botu compounds exuibit a broad peak at around 2400 2800 cm~~ clearly demonstrat-
mg tuat tue electronic system m tuese orgamc metals does not follow tue Drude beuavior.
Tue suarp vibrational features observed on tue low frequency slope of tue broad peak is due to tue electron-molecular vibrational (EMV) coupling. A similar but more intense electronic
peak is observed in aexp(w) of superconducting ~-salts là,6,14] and bas been descnbed by
us là,GI in tue frame of tue "puase puonons" tueory as electron interband transitions across tue energy gap 2A. Tue same analysis of aexp(uJ) for conductors ~-(BEDT-TTF)21Hg(SCN)C12]
and K-(BEDT-TTF)2[Hg(SCN)2Br] gives values of plasma frequency uJp smaller than in trie superconductors [5,6,14], and consequently larger optical effective mass m* of charge carriers (w) = 47rNe~/m*, wuere N is tue charge carriers concentration assumed to be equal to tue
1678 JOURNAL DE PHYSIQUE I N°12
ioo
50 a
-- 0
E
~É 100
~
.É 50 b
1 é 8 ~
(a 150
O ioo
50 c
~
0 2000 «où 6000 8000
Wavenumber (cm'~)
Fig. 4. Calculated optical conductivity m the case U/4t
= 1000 of an isolated dimer (a), tetramer (b) and hexamer (c) for t'Ii
= 0A; the rest of parameters are the same as m Figure 2.
(BEDT-TTF)( dimer concentration, Nd " i.i x 10~~ cm~~ ). We bave obtained from tuis rela- tion m*
= 8.4 molI b), for tue conductor ~-(BEDT-TTF)2 ÎHg(SCN)C12], and m*
= 2.6 mo for
tue superconductor ~-(BEDT-TTF)2Cu(NCS)2 (tue latter value found on tue basis of tue data from Ref. [Si for tue corresponding polarization). We can imagine tuat so large a value of m* for tue conductor as compared to m* for tue superconductor migut be due to tue stronger EMV coupling and tue formation of tue molecular polarons. Nevertueless tuis assumption is not
supported by tue values of tue sum of tue dimensionless EMV coupling constants = 0.18 1?i
and 0.25 [Si obtained for ~-(BEDT-TTF)21Hg(SCN)C12] and ~-(BEDT-TTF)2Cu(NCS)2, re-
spectively. Tuerefore one cannot explain trie reason for trie large value of m* within tue frame work of trie "one-electron" band theory for trie mvestigated compounds. Trie quali-
tative comparison of trie expenmental spectra aexp(w) of ~-(BEDT-TTF)21Hg(SCN)C12] and
~-(BEDT-TTF)21Hg(SCN)2Br] with trie spectra atheor(w) calculated on trie basis of trie the- ory developed in trie preceding section (see Figs. 2 to 4) shows that this theory describes trie main features of trie expenmental spectra rather well. Among all spectra calculated for
diiferent parameter values, aexp(w) is much doser (by trie values of aexp(w), by trie location of tue electronic band, as well as by tue relative location of tue electromc band and EMV
coupling feature) to tue atheor(w) suown in Figure 2c for tue tetramer case of tue Coulomb on-site repulsion energy U
= 4000 t and t
= 0.2 eV; t'/t
= 0.4; tue otuer parameters are given
in tue caption to Figure 2. As it was noted above, tuis case is close to tue one of tue isolated dimer, and uence we can mdeed imagine our system as a Wigner lattice of molecular dimers witu one charge carrier per dimer.
Figures Sa and 5b show tuat tue values of aexp(w), including tue intensity of tue elec-
tromc band, for ~-(BEDT-TTF)21Hg(SCN)2Br] are nearly twice greater tuan tue ones for
200
160
120
a 80
'[
"C 40 _2~
81 8
OEÎ ~
40
80
40
c
~
1000 2000 3000 4000
Wavenumber(cm )
Fig. 5. Experimental optical conductivity spectra of (a) (BEDT-TTF)2(Hg(SCN)2Br] and (b) (BEDT-TTF)2(Hg(SCN)C12) single crystals for E
[[ b polarization; (c) calculated spectrum for the
tetramer model (U/4t
= 1000) with t = 0.17 eV, t'Ii
= 0.2, r
= 3000 cm~~, Nt
" 5.5 x 10~° cm~~,
a
= 3.59 À, a'
= 3.6 À and three vibrational modes discussed in the text.
~-(BEDT-TTF)2[Hg(SCN)C12]. We would expect tuis beuavior as a manifestation of tue stronger intra- and interdimer interactions (larger transfer integrals t and t') for tue former salt. Sucu an interpretation of tue diiference between tue optical conductivities of tue two salts is supported by tue crystallograpuic data. Indeed, for tue ~-(BEDT-TTF)2 ÎHg(SCN)2Br]
salt: 1) tue interplanar spacing between tue BEDT-TTF molecules inside tue dimer is smaller;
ii) tuere are two suortened S S contacts m tue dimer wuicu are absent in tue case of tue salt witu Cl; and iii) eacu cation-radical BEDT-TTF bas 8 suortened S S contacts, wuereas
m tue structure of tue ~-(BEDT-TTF)2[Hg(SCN)C12] salt tuere are 7 or 5 (for tue crystallo-
grapuically different BEDT-TTF molecules) sucu contacts. As follows from our calculations
(see Figs. 3 and 4), tue increase of t' leads to tue suift of tue electromc cuarge-transfer band to lower wavenumbers and a significant growtu of its intensity is predicted.
Figure 5c presents tue conductivity spectrum calculated according to tue tueory developed
m tue preceding section m tue case of U/t
= 4000. In tuis calculation, we employed turee vibrational modes at 1468, 1274 and l174 cm~~ witu tue EMV coupling constants 650, 80 and 70 cm~~, respectively, and trie damping factor ~n
= 20 cm~~ for all turee modes. Trie wavenumbers for these vibrations were determined (also for BEDT-TTF+°.~) by Eldridge et
1680 JOURNAL DE PHYSIQUE I N°12
ai. ma trie careful examination [15] of trie infrared and Raman spectra for different isotopes of BEDT-TTF. Tuere is a general agreement to assign tue 1468 and 1276 cm~~ modes to trie
totally symmetric ag ones and tueir linear coupling to tue electromc charge transfer raises no doubt. Tue matter is more complicated for tue i174 cm~~ mode. Eldridge et ai. [15] bas ascribed it to b3u or b2g vibration. According to tue calculations of Meneguetti et ai. [16]
performed for BEDT-TTF assuming a lower D2 symmetry, tuere is a symmetric vibration at 1195 cm~~ for tue neutral BEDT-TTF. Our previous analysis of tue spectra of some conducting
salts of BEDT-TTF là,GI also pointed to tue existence of tue vibration around i170 cm~~
linearly coupled to tue electronic excitation. Tuus, we believe tuat tue indentations in tue
aexp(w) spectra at i179 cm~~ for ~-(BEDT-TTF)21Hg(SCN)C12] and at ii?? cm~~ for ~-
(BEDT-TTF)21Hg(SCN)2Br] are a signature of tue lowering of tue symmetry of tue BEDT- TTF in our crystals witu respect to D2h symmetry of tue isolated molecule.
In conclusion, we bave demonstrated tue importance of electronic correlations m tue optical properties of tue ~-puase molecular conductors. A more detailed quantitative analysis will require calculations of tue transfer integrals t and t' for different crystallograpuic directions.
Acknowledgments
We would like to use tue opportunity of tuis special issue dedicated to tue memory of Prof. I. F.
Scuegolev to acknowledge tuat we all miss uim not only as a superb scientist, but also as a very uuman and sensitive person. Tue group at Ioffe Institute bas benefited a lot from stimulating discussions witu I. F. Scuegolev during many years of our collaboration. O.O. Drozdova, V.N.
Semkin and R-M- Vlasova gratefully acknowledge financial support of tuis work by tue Russian Scientific-Tecunical Programme on Superconductivity, Project No 94055.
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