Anomalous scaling law for thermoelectric transport of 2D-conﬁned electrons in an organic molecular system Naoki Kouda Kyohei Eguchi Ryuji Okazakiand Masafumi Tamura

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Anomalous scaling law for thermoelectric transport of 2D-conﬁned electrons in an organic

molecular system

Naoki Kouda, Kyohei Eguchi, Ryuji Okazaki,∗and Masafumi Tamura

Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda 278-8510, Japan

Conﬁned electrons in low dimensions host desirable material functions for downscaled electronics as well as

advanced energy technologies. Thermoelectricity is a most fascinating example, since the dimensionality modi-

ﬁes the electron density of states dramatically, leading to enhanced thermopower as experimentally examined in

artiﬁcial two-dimensional (2D) structures. However, it is still an open question whether such an enhanced ther-

mopower in low dimensions is realized in layered materials with strong 2D characters such as cuprates. Here,

we report unusual enhancement of the thermopower in the layered organic compound α-(BEDT-TTF)2I3, where

BEDT-TTF stands for bis(ethylenedithio)-tetrathiafulvalene. We ﬁnd that the slope in the Jonker plot (ther-

mopower Svs. logarithm of electrical conductivity log σ) for α-(BEDT-TTF)2I3is signiﬁcantly larger than that

of conventional semiconductors. Moreover, the large slope is also seen in the related layered salt, demonstrating

the impact of the 2D-conﬁned carriers in the layered organics on thermoelectricity.

I. INTRODUCTION

Thermoelectricity, a fundamental property of solids to gen-

erate the electric ﬁeld Eunder the temperature gradient ∇T

with the proportional coeﬃcient Sknown as the thermopower

or the Seebeck coeﬃcient as E=S∇Tin an open circuit,

oﬀers a simple solid-state technology for the direct heat-to-

electricity conversion, yet it is a very challenging issue to es-

tablish the guiding principles for the high-performance ther-

moelectrics [1, 2]. From a fundamental point of view, the

semiclassical Boltzmann approach gives an approximate for-

mula of the thermopower for a degenerate electron gas, which

is well known as the Mott relation,

S=π2

qkBTdln σ(ε)

dε



ε=µ

,(1)

where kBis the Boltzmann constant, qis the carrier charge, σ

is the electrical conductivity, and µis the chemical potential

[3], signifying a close link to the energy dependence of the

conductivity. Indeed, this relation underlies as a basal guide-

line for various schemes such as the band structure [4] and the

mobility [5] engineering, in which the microscopic parame-

ters in the conductivity formula such as the density of states

(DOS) and the relaxation time are successfully controlled to

increase the thermopower.

Among the various concepts based on the Mott relation,

the reduced dimensionality is a straightforward and intrigu-

ing way as to adopt a step-like singularity in the DOS near the

band edge. If the electron chemical potential is close to the

edge, as in the case of a narrow-gap semiconductor, the energy

derivative of the DOS is expected to diverge so as to aﬀord ex-

traordinarily large thermopower [6]. This theoretical proposal

has motivated well-conceived transport measurements on the

artiﬁcial systems such as the one-dimensional (1D) nanowires

[7, 8] and the two-dimensional (2D) superlattices [9], lead-

ing to the experimental demonstration of the improved dimen-

sionless ﬁgure of merit, ZT =S2σT/κ, where κis the thermal

∗okazaki@rs.tus.ac.jp

conductivity, although these observations seem to come from

the phonon eﬀect [7, 8, 10] rather than the proposed DOS

modiﬁcation. On the other hand, Ohta et al. presented un-

usually large thermopower emerged from the 2D electron gas

(2DEG) in the oxide superlattice [11], indicating a 2D quan-

tum conﬁnement to vary the DOS. Moreover, such a 2DEG

has also been realized at the surface of the three-dimensional

(3D) compounds incorporated into the ﬁeld-eﬀect-transistor

structure, in which a systematic evolution of the thermopower

of the 2D-conﬁned carriers is achieved by the gate voltage

tuning [12, 13].

A key question subsequently arises: does such a drastic

modiﬁcation in DOS enhance thermopower in a bulk ma-

terial with low dimensionality? Many of remarkable phys-

ical phenomena have been found as a result of the low-

dimensional structures. Here, we focus on the charge trans-

fer organic salt α-(ET)2I3[ET being bis(ethylenedithio)-

tetrathiafulvalene (BEDT-TTF)], in which the ET and the I3

anion layers are alternatingly stacked to form the 2D layered

crystal structure as illustrated in Fig. 1(a) [14]. This material

exhibits a charge order transition at TCO =136 K [15, 16],

which is driven by the inter-site Coulomb repulsion [17]. The

two dimensionality in the charge order phase below TCO is

clearly evidenced by the anisotropy in the resistivity [18] as

well as an occurrence of a Kosterlitz-Thouless transition at

TKT ≈35 K [19]. In this study, we performed the elec-

trical conductivity σand the thermopower Smeasurements

on α-(ET)2I3single crystals with a systematic evaluation of

the sample dependence. The thermopower in the charge or-

der phase is unusually large and incompatible with the con-

ventional band picture, but is well scaled in the S-log σplot,

which is strikingly similar to that in the 2D-conﬁned electrons

realized in the oxide superlattices.

II. EXPERIMENTS

Single crystals of α-(ET)2I3were prepared by an electro-

chemical method. The crystal orientation was determined

from the polarized infrared reﬂectivity spectra measured by

using a Fourier transform infrared spectrometer [20]. The re-

arXiv:2210.11631v1 [cond-mat.mtrl-sci] 20 Oct 2022

BEDT-TTF (ET)

BO6octahedron

(a) (b)

anion I3

cation A

FIG. 1. Schematic crystal structures of layered materials. (a) Layered organic salt α-(ET)2I3consisting of planar BEDT-TTF (ET) molecules.

The highest occupied molecular orbital (HOMO) of ET molecule is schematically drawn. The HOMO is spread along the direction normal

to the molecular plane, leading to π-stacked conducting layer with strong two-dimensional character. (b) Layered perovskite oxides A2BO4

consisting of three-dimensional BO6octahedra. Schematic t2gorbital of BO6octahedron is shown.

sistivity and the thermopower were simultaneously measured

by using a conventional four-probe method and a steady-state

method, respectively [21, 22]. For the thermopower measure-

ment, a manganin-constantan diﬀerential thermocouple was

attached to the sample by using a carbon paste and the tem-

perature gradient (|∇T| ≈ 0.5 K/mm) was applied by using

a resistive heater. The thermoelectric voltage from the wire

leads was subtracted. The rate of temperature change is lower

than 0.3 K/min to prevent the damage to the sample.

III. RESULTS AND DISCUSSION

A. Resistivity

Figure 2(a) depicts the temperature dependence of the elec-

trical resistivity ρof α-(ET)2I3single crystals. All the samples

exhibit the metal-insulator transition at TCO =136 K owing

to the charge order. On the other hand, one may ﬁnd the sig-

niﬁcant sample dependence in the magnitude of the resistivity

shown in Fig. 2(a). Although there is an inevitable ambiguity

of the the sample size and the current path in the resistivity

measurement in general, this sample dependence may also be

intrinsic as observed in the thermopower. In the inset of Fig.

2(a), we plot the temperature dependence of the normalized

resistivity by the value at T=160 K. The in-plane anisotropy

between the resistivity data measured for J|| a(ρaa) and for

J|| b(ρbb) is clearly seen just above the transition tempera-

ture TCO: while ρaa exhibits a gradual decrease on heating, ρbb

shows a minimum structure near T=145 K, which has also

been observed in the earlier study [18]. This in-plane resistive

anisotropy may originate from the charge-disproportionation

ﬂuctuations existing even in the high-temperature phase [23]:

the stripe-type charge order along the baxis [24, 25] may in-

duce a smooth charge ﬂow along the same direction but form

strong potential barriers along the a-axis direction to suppress

the conduction.

B. Thermopower

Figures 2(b) displays the temperature dependence of the

thermopower S. The overall behavior of the thermopower is

similar to earlier results that reported this material for the ﬁrst

time [14]: the thermopower is positive and relatively small

value as expected in the metallic state, while it changes its sign

and shows the large absolute value in the insulating phase.

This behavior is also qualitatively consistent with the temper-

ature dependence of the Hall coeﬃcient [18]. On the other

hand, the detailed nature of the thermopower has been not dis-

cussed in the ﬁrst report [14], in which the thermopower was

given as evidence for the metal-insulator transition at TCO. We

also note that the thermopower of α-(ET)2I3has been inten-

sively studied to investigate the exotic Dirac-like electronic

states driven by pressure [26, 27].

The observed sample dependence of the transport prop-

erties may originate from the disorder eﬀect, which is sug-

gested to be intrinsic in this material. This is experimentally

evidenced by the relaxor-type dielectric response [18, 28] in

sharp contrast to the 1D charge order salts [29] and the neg-

ative magnetoresistance in the charge order phase possibly

due to the weak localization [18]. Although it requires de-

tailed future study, the origin of disorders may stem from

the anions layer [18]: the I−

3anions are still chemically re-

active as an oxidant in the crystal. The transition tempera-

ture TCO is, nevertheless, little aﬀected, showing the cohesive

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Anomalousscalinglawforthermoelectrictransportof2D-connedelectronsinanorganicmolecularsystemNaokiKouda,KyoheiEguchi,RyujiOkazaki,andMasafumiTamuraDepartmentofPhysics,FacultyofScienceandTechnology,TokyoUniversityofScience,Noda278-8510,JapanConnedelectronsinlowdimensionshostdesirablematerialfunction...

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Anomalous scaling law for thermoelectric transport of 2D-conﬁned electrons in an organic molecular system Naoki Kouda Kyohei Eguchi Ryuji Okazakiand Masafumi Tamura

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