Colossal Seebeck Coefficient of Hopping Electrons in ${(\mathrm{TMTSF})}_{2}\text{ }{\mathrm{PF}}_{6}$

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Colossal Seebeck Coefficient of Hopping Electrons in ${(TMTSF)}_{2} {PF}_{6}$

Yo Machida, Xiao Lin, Woun Kang, Koichi Izawa, and Kamran Behnia

Phys. Rev. Lett. 116, 087003 – Published 25 February 2016

Abstract

We report on a study of the Seebeck coefficient and resistivity in the quasi-one-dimensional conductor ${(TMTSF)}_{2} {PF}_{6}$ extended deep into the spin-density-wave state. The metal-insulator transition at $T_{SDW} = 12 K$ leads to a reduction in carrier concentration by 7 orders of magnitude. Below 1 K, charge transport displays the behavior known as variable range hopping. Until now, the Seebeck response of electrons in this regime has barely been explored and is even less understood. We find that, in this system, residual carriers, hopping from one trap to another, generate a Seebeck coefficient as large as $400 k_{B} / e$ . The results provide the first solid evidence for a long-standing prediction according to which hopping electrons in the presence of the Coulomb interaction can generate a sizable Seebeck coefficient in the zero-temperature limit.

Received 6 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.087003

Physics Subject Headings (PhySH)

Seebeck effect Spin density waves

Organic superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yo Machida¹, Xiao Lin², Woun Kang³, Koichi Izawa¹, and Kamran Behnia^2,*

¹Department of Physics, Tokyo Institute of Technology, Meguro 152-8551, Japan
²LPEM (UPMC-CNRS) ESPCI, 75005 Paris, France
³Department of Physics, Ewha Womans University, Seoul 120-750, Korea

^*kamran.behnia@espci.fr

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Vol. 116, Iss. 8 — 26 February 2016

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Figure 1
(a) In a metal, the average thermal energy of a carrier, which sets the Peltier coefficient, $Π$ , is quadratic in temperature. With decreasing temperature, mobile entropy shrinks but carrier number does not change. As a consequence of the kelvin relation ( $Π = S T$ ), the Seebeck coefficient is $T$ linear. (b) In an insulator, the average thermal energy of a carrier is $T$ independent, set by the distance between the occupied level closest to the chemical potential. Both the carrier number and entropy vanish at zero temperature. If the carrier number decreases faster, the Seebeck coefficient will increase with decreasing temperature. (c) Real insulators will eventually enter the variable range hopping regime, where Coulomb interaction opens a soft gap ( $Δ_{ES}$ ) in the vicinity of the chemical potential. What happens to the thermoelectric response at temperatures below this gap?
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Figure 2
(a) Temperature dependence of resistivity along the $a$ axis in a logarithmic plot; resistivity increases by more than 7 orders of magnitude. As seen in the inset, over a wide temperature window (10 to 1 K), it follows an activated behavior. (b),(c) Below 1 K, resistivity displays an $\exp [(T / T_{0})^{- γ}]$ behavior characteristic of VRH. Semilogarithmical plots of $ρ$ vs (b) $T^{- 1 / 3}$ and (c) $T^{- 1 / 2}$ both yield quasistraight lines at the low-temperature end. (d) Crystal structure of the Bechgaard salt ${(TMTSF)}_{2} {PF}_{6}$ .
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Figure 3
(a) Temperature dependence of the Seebeck coefficient along the $a$ axis in the vicinity of the SDW transition. Below the transition temperature, the Seebeck coefficient follows a $T^{- 1}$ dependence, as indicated by a solid line. (Inset) The anomaly at the SDW transition. (b) Temperature dependence of the Seebeck coefficient in a logarithmic plot. The magnitude of the Seebeck coefficient attains $37 mV / K$ at 0.13 K. (Lower left inset) The temperature dependence of the Peltier coefficient $Π = S T$ . (Upper right inset) The data in a linear plot. Solid and empty circles represent data obtained on two different samples with two different setups.
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Figure 4
(a) For measuring the Seebeck coefficient, a heat current was injected into the sample by passing a current though the heater and measuring both the temperature gradient and the voltage difference created by this heat current. (b) For measuring the electrical resistivity, a current was injected into the sample and the voltage difference created by this charge current. In both cases, the voltage was measured in the same way by the same electrodes and the same instrument.
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Physical Review Letters

Colossal Seebeck Coefficient of Hopping Electrons in (TMTSF)2 PF6

Yo Machida, Xiao Lin, Woun Kang, Koichi Izawa, and Kamran Behnia

Phys. Rev. Lett. 116, 087003 – Published 25 February 2016

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Colossal Seebeck Coefficient of Hopping Electrons in ${(TMTSF)}_{2} {PF}_{6}$