Incommensurate lattice fluctuations are present in the beta_L phase (T_c =
1.5 K) of ET_2I_3 (where ET is BEDT-TTF -
bis(ethylenedithio)tetrathiafulvalene) but are absent in the beta_H phase (T_c
= 7 K). We propose that the disorder in the conformational degrees of freedom
of the terminal ethylene groups of the ET molecules, which is required to
stabilise the lattice fluctuations, increases the quasiparticle scattering rate
and that this leads to the observed difference in the superconducting critical
temperatures, T_c, of the two phases. We calculate the dependence of T_c on the
interlayer residual resistivity. Our theory has no free parameters. Our
predictions are shown to be consistent with experiment. We describe experiments
to conclusively test our hypothesis.Comment: 4 pages, 1 figur

Powell, B. J.

English

arXiv

Incommensurate lattice fluctuations are present in the $\beta_\textrm{L}$ phase
($T_c\sim1.5$ K) of ET$_2$I$_3$ (where ET is BEDT-TTF -
bis(ethylenedithio)tetrathiafulvalene) but are absent in the $\beta_\textrm{H}$
phase ($T_c\sim7$ K). We propose that the disorder in the
conformational degrees of freedom of the terminal ethylene groups
of the ET molecules, which is required to stabilise the lattice
fluctuations, increases the quasiparticle scattering rate and that
this leads to the observed difference in the superconducting
critical temperatures, $T_c$, of the two phases. We calculate the
dependence of $T_c$ on the interlayer residual resistivity. Our
theory has no free parameters. Our predictions are shown to be
consistent with experiment. We describe experiments to
conclusively test our hypothesis.

B.J. Powell

EDP Sciences OAI-PMH repository (1.2.0)

The origin of the difference in the superconducting critical
temperatures of the ${\beta_{\rm H}}$ and ${\beta_{\rm L}}$ phases of (BEDT-TTF)${_2}$I${_3}$

Incommensurate lattice fluctuations are present in the beta(L) phase (T-c similar to 1.5 K) of ET2I3 (where ET is BEDT-TTF - bis(ethylenedithio)tetrathiafulvalene) but are absent in the beta(H) phase (T-c similar to 7 K). We propose that the disorder in the conformational degrees of freedom of the terminal ethylene groups of the ET molecules, which is required to stabilise the lattice fluctuations, increases the quasiparticle scattering rate and that this leads to the observed difference in the Superconducting critical temperatures, T-c, of the two phases. We calculate the dependence of T-c on the interlayer residual resistivity. Our theory has no free parameters. Our predictions are shown to be consistent with experiment. We describe experiments to conclusively test our hypothesis

University of Queensland eSpace

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03
The origin of the difference in the superconducting critical temperatures of the
βH and βL phases of (BEDT-TTF)2I3
B. J. Powell∗
Department of Physics, University of Queensland, Brisbane, Queensland 4072, Australia
Incommensurate lattice fluctuations are present in the βL phase (Tc ∼ 1.5 K) of ET2I3
(where ET is BEDT-TTF - bis(ethylenedithio)tetrathiafulvalene) but are absent in the βH
phase (Tc ∼ 7 K). We propose that the disorder in the conformational degrees of freedom of
the terminal ethylene groups of the ET molecules, which is required to stabilise the lattice
fluctuations, increases the quasiparticle scattering rate and that this leads to the observed
difference in the superconducting critical temperatures, Tc, of the two phases. We calculate
the dependence of Tc on the interlayer residual resistivity. Our theory has no free parameters.
Our predictions are shown to be consistent with experiment. We describe experiments to
conclusively test our hypothesis.
It has long been known that the application of hydrostatic pressure, P , to β-ET2I3 has a dramatic
effect on the superconducting critical temperature, Tc. At ambient pressure Tc ∼ 1.5 K but when
the applied pressure reaches P ∼ 1 kbar a discontinuous increase in Tc (∼ 7 K) is observed. The
low Tc state (P . 1 kbar) is denoted the βL phase and the high Tc state (P & 1 kbar) is labelled
the βH phase. When the pressure on the βH phase is decreased the material does not return to
the βL phase but rather Tc is seen to further increase. Below T ∼ 130 K the resistivity of the βH
phase is found to undergo a discontinuous decrease while no such anomaly is found in the βL phase
[1]. Incommensurate lattice fluctuations have been observed in the βL phase but they are absent
in the βH phase below T ∼ 130 K [2]. The incommensurate lattice fluctuations are stabilised by
variations in the conformational ordering of the terminal ethylene groups of the ET molecules and
thus can only exist in the presence of disorder [3]. For a recent review of this phenomenology see
[4].
Although the change in resistivity between the βL and βH phases and the incommensurate lattice
fluctuations have been studied both theoretically [3] and experimentally [1, 2, 4], no explanation of
the change in Tc has been forthcoming. In this paper we propose that difference in the Tc’s of the
two phases is due to disorder, we will show that current data is consistent with our explanation and
suggest experiments which could clearly determine whether or not this is the correct explanation
∗ Electronic address: powell@physics.uq.edu.au
of the difference in Tc.
In a recent paper it was shown [5] that intrinsically non-magnetic disorder decreases the Tc of
a wide range of the superconducting salts of ET in line with the Abrikosov–Gorkov (AG) formula:
ln
(
Tc0
Tc
)
= ψ
(
1
2
+
~
4pikBTc
1
τ
)
− ψ
(
1
2
)
, (1)
where Tc0 is the superconducting transition temperature of a pure sample, 1/τ is the quasiparticle
scattering rate and ψ(x) is the digamma function. There are two scenarios compatible with this
observation: either there is opposite spin pairing and the impurities induce localised magnetic
moments, or else there is a finite angular momentum pairing state (most probably d-wave pairing).
In this paper we will not discuss which of these scenarios is realised, but rather make use of this
observation of the effect that increasing 1/τ has on Tc.
In a quasi-two dimensional metal, such as β-ET2I3, the residual interlayer resistivity is given by
ρ0 =
pi~4
2e2m∗ct2
⊥
1
τ
(2)
where m∗ is the quasiparticle effective mass, c (= 15.291 A˚ for β-ET2I3 [4]) is the interlayer lattice
constant and t⊥ is interlayer hopping integral. Substituting (2) into (1) one finds that
ln
(
Tc0
Tc
)
= ψ
(
1
2
+
e2m∗ct2
⊥
2pi2~3kBTc
ρ0
)
− ψ
(
1
2
)
. (3)
from quantum oscillation Wosnitza et al. [6] found that m∗/me = 4.2 ± 0.2, where me is the elec-
tronic rest mass, t⊥/EF = 1/(175± 10), where EF is the Fermi energy, and the Fermi wavevector,
kF = (3.4 ± 0.2) × 10
9 cm−1. Thus taking EF = ~
2k2
F
/2m∗ one finds that t⊥ = 0.59 ± 0.08 meV.
Tc0 = 7.75 K is found from fast electron irradiation experiments [5, 7].
In figure 1 we plot Tc as a function of ρ0. We stress that there are no free parameters in this
plot once the data from Wosnitza et al. and Forro et al. [5, 7] is considered. For comparison
we also plot the data of Tokumoto et al. [8] who deliberately induced impurities in βH-ET2I3 by
fabricating the alloy β-ET2(I3)1−x(IBr2)x. The data is consistent with our theory although clearly
more data is required to properly test our prediction.
We propose that the disorder in the conformational degrees of freedom of the terminal ethylene
groups of the ET molecules which is required to stabilise incommensurate lattice fluctuations in the
βL phase [3], but absent in the βH phase, increases the quasiparticle lifetime. (Either by inducing
localised magnetic moments or causing variation in the site energy, depending on which of the
scenarios proposed in [5] is realised). Note that conformational disorder of the terminal ethylene
groups of κ-ET2Cu[N(CN)2]Br can be controlled by varying the cooling rate and this leads to
variations in Tc which are well described by the AG formula [5].
2
0 0.02 0.04 0.06 0.08 0.1
ρ(Ωcm)
0
2
4
6
8
T c
(K
)
βH-ET2I3
βH-ET2I3
βH-ET2(I3)1-x(IBr2)x
βL-ET2I3
FIG. 1: The variation of the superconducting transition temperature of βH-ET2I3 with the interlayer re-
sistivity. The prediction (solid line) is made from equation (3) taking the measured interlayer hopping
integral, t⊥ [6]. The dotted lines show the effect of changing t⊥ by one standard deviation. The critical
temperature of a pure sample, Tc0, is that found from fast electron irradiation experiments [5, 7], we do not
include the effects of the errors in this measurement. By way of comparison we show data for impurities
induced in βH-ET2I3 by fabricating the alloy β-ET2(I3)1−x(IBr2)x [8] (circles). This data is consistent with
our prediction. The squares are the data [1] for both the βH and βL phases. However, as the size of the
samples was not reported the value of the resistivity contains one free parameter, the relative dimension
of the sample, A/d. However, this data does show that the relative change in resistivity between the βL
and βH phases is consistent with our hypothesis that the disorder required to stabilise the incommensurate
lattice fluctuations observed in the βL phase lowers Tc by increasing the quasiparticle scattering rate, 1/τ .
Unfortunately, we are not aware of any reports of the resistivity of βL-ET2I3 with which to
test our hypothesis. For example Ginodman et al. [1] reported the change in resistance observed
between the βH and βL phases, but did not report the size of their crystals. Taking the relative
dimensions of their sample as a fitting parameter we find good agreement with our prediction (see
figure 1; based on A/d = 0.4 cm, where A is the cross-sectional area of the sample and d is the
length of the sample in the c-axis, this is actually a fairly typical relative dimension for samples of
this material). However, as we do not know the size of the sample this does not represent a very
stringent test of our hypothesis. The resistance data of Ginodman et al. is well described by the
Fermi liquid form R(T ) = R0 + AT
2 in both the βL and βH phases with the same value of A in
3
both phases. This suggests that major difference between the two phases is the scattering rate due
to impurities, in support of our hypothesis.
Systematic measurements of the resistivity of β-ET2I3 in both the βL and βH phases are required
to test our hypothesis. If this were done for several samples with varying amounts of disorder due
to random imperfections produced during the fabrication process then it would be possible to map
out the entire curve of figure 1 for the βH phase. Clearly only the lower part of the curve could be
mapped out for the βL phase because of the disorder in the terminal ethylene groups.
Acknowledgements
I would like to thank Ross McKenzie and Jochen Wosnitza for useful conversations. This work was
supported by the Australian Research Council.
[1] V.B. Ginodman, A.V. Gudenko, L.N. Zherikhina, V.N. Laukhin, E.B. Yagubskii, P.A. Kononovich and
I.F. Shegolev, Acta Poly. 39, 533 (1988)
[2] T.J. Emge, P.C.W. Leung, M.A. Beno, A.J. Schultz, H.H. Wang, L.M. Sowa and J. M. Williams, Phys.
Rev. B 30, 6780 (1984)
[3] S. Ravy, J. P. Pouget, R. Moret and C. Lenoir, Phys. Rev. B, 37, 5113 (1988)
[4] T. Ishiguro, K. Yamaji and G. Saito, Organic Superconductors (Springer Verlag, Heidelberg, 1998)
[5] B.J. Powell and R.H. McKenzie, cond-mat/0306457
[6] J. Wosnitza, G. Goll, D. Beckmann, S. Wanka, D. Schweitzer and W. Strunz, J. Phys. I 6 1597 (1996)
[7] L. Forro, S. Bouffard and D. Schweitzer, Solid State Comm. 65, 1359 (1988)
[8] M. Tokumoto, H. Anzai, K. Murata, K. Kajimura and T. Ishiguro, Japan. J. Appl. Phys. 26, 1977
(1987)
4


The origin of the difference in the superconducting critical temperatures of the beta(H) and beta(L) phases of (BEDT-TTF)(2)I-3

B. J. Powell

Crossref

The origin of the difference in the superconducting critical temperatures of the β
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https://espace.library.uq.edu.au/view/UQ:73325/UQ73325_OA.pdf

The origin of the difference in the superconducting critical temperatures of the beta_H and beta_L phases of (BEDT-TTF)_2I_3

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