Giant thermoelectric power factor in ultrathin FeSe superconductor

The thermoelectric effect is attracting a renewed interest as a concept for energy harvesting technologies. Nanomaterials have been considered a key to realize efficient thermoelectric conversions owing to the low dimensional charge and phonon transports. In this regard, recently emerging two-dimensional materials could be promising candidates with novel thermoelectric functionalities. Here we report that FeSe ultrathin films, a high-Tc superconductor (Tc; superconducting transition temperature), exhibit superior thermoelectric responses. With decreasing thickness d, the electrical conductivity increases accompanying the emergence of high-Tc superconductivity; unexpectedly, the Seebeck coefficient α shows a concomitant increase as a result of the appearance of two-dimensional natures. When d is reduced down to ~1 nm, the thermoelectric power factor at 50 K and room temperature reach unprecedented values as high as 13,000 and 260 μW cm−1 K−2, respectively. The large thermoelectric effect in high Tc superconductors indicates the high potential of two-dimensional layered materials towards multi-functionalization.

T wo-dimensional (2D) materials are expanding their arena in terms of richness in material type, properties, and functions, which range from electronic devices to catalysts and medicines 1,2 . Thermoelectric generation is one of the physical functions in which 2D materials are anticipated to be superior in comparison with their bulk counterparts. The density of states (DOS) in 2D semiconductors is considerably different from that of three-dimensional (3D) materials at the band edge singularity 3 . As the Seebeck coefficient α is related to the profile of the DOS at the Fermi energy, 2D or low dimensional structures are considered to be advantageous for enhancing thermoelectric performance. Such a concept was proposed originally for semiconductor quantum wells and superlattices; 4 however, recently emerging 2D-layered materials provide naturally formed atomic layers and their hetero-structures 5 , which are an ideal platform to elicit their intrinsic 2D nature. For characterization of thermoelectric properties of nanomaterials, on-chip device measurements have been often utilized [6][7][8] . Although the device configuration used for the measurements is not directly adapted to practical applications, it is highly powerful for realizing ideal conditions including the structures free from significant disorder and the tunable carrier density and thus for elucidating the intrinsic performance of materials. This method also fits the thermoelectric characterization of 2D materials in the present study.
The performance of thermoelectric semiconductors is measured by the figure of merit ZT = α 2 Τ/ρκ (where ρ is the electrical resistivity, κ is the thermal conductivity, and T is the absolute temperature). Therefore, materials with the large power factor α 2 / ρ can be candidates for high ZT. In order to maximize α 2 /ρ, we propose to extensively investigate recent 2D layered materials. In addition to the possible enhancement of the Seebeck effect in 2D DOS, an important characteristic of the recent 2D materials is their excellent crystallinity, which is preferable for keeping a large conductivity even in nano-thick monolayers.
For our purpose, 3d transition-metal-based compounds should be more favorable than 4d and 5d counterparts because the wave functions of 3d-based compounds are more localized, generally causing a larger effective mass m* and thus the larger DOS. Among 3d-based materials, we chose FeSe, first because a relatively large m* ranging from 2 to 4 m e has been reported in heavily electron-doped regions 9,10 , where m e is the free electron mass. The physical properties of ultrathin FeSe have attracted much attention because of the appearance of the unexpected high-T c superconducting phase by reducing the film thickness down to a monolayer, the T c of which reaches 65 K 11,12 or 100 K 13 . Surprisingly, the high conductivity value survives even in monolayer FeSe; 11,14,15 this is in stark contrast to conventional semiconductor thin films, where the resistance increases with reducing the thickness.
Here we report simultaneous measurements of α and ρ while controlling the thickness d of FeSe films on SrTiO 3 (001) substrates in an electric double-layer transistor configuration 16 . In previous studies, we succeeded in optimization of α 2 /ρ with controlling n through the gate bias V G and applied this technique to various materials 16 (see Methods). When V G is applied at 220 K, which is just above the glass transition temperature of the ionic liquid used in this study (see Methods), the cations or anions are self-aligned on the surface of FeSe; thus, charge carriers are electrostatically accumulated to form the electric double layer 17,18 . On the other hand, when a certain level of V G is applied at higher temperatures such as~245 K or above, an electrochemical reaction takes place at the liquid-solid interface, and the topmost FeSe layer dissolves into the ionic liquid in a pseudo layer-by-layer manner 15 . Therefore, systematic investigation of the thermoelectric properties from bulk to ultrathin FeSe now becomes possible at a wide temperature range from 10 K to around room temperature. We found that the thermoelectric effect is dramatically enhanced with reducing d down to~1 nm and thermoelectric power factor at 50 K and room temperature reach unprecedented values as high as 13,000 and 260 μW cm −1 K −2 , respectively. The coexistence of giant thermoelectric power factor and high-T c superconductivity indicates the high potential of 2D layered materials towards multi-functionalization.

Results
Electrochemically enhanced Seebeck effect in FeSe thin film. Dimensionality is a possible key factor to induce the evolution of the thermoelectric response owing to the characteristic DOS ( Fig. 1a, b). The electric double layer transistor configuration shown in Fig. 1c enables us to control the film thickness d through the electrochemical etching on the surface of the FeSe films (Fig. 1d). Figure  substrate as a source of the large Seebeck response is also definitely ruled out as the large α is observed only under gate bias and is suppressed to bulk-like small values by switching off V G to 0 V, as seen in the main panel of Fig. 2b. Importantly, the high-T c superconductivity appears by applying V G = 5 V and disappears by removing V G 15,17,18 , as shown in the inset of Fig. 2b. The simultaneous emergence of the giant thermoelectric response and Superconductivity appeared when V G = 5 V was applied. c Variation of sheet resistance ρ 2D 200 K at 200 K as a function of d. The value of ρ 2D 200 K for V G = 5 V showed a weak d dependence (blue circles), whereas that for V G = 0 V increased with decreasing d (gray circles). d Thickness d dependence of thermoelectric power factor α 2 /ρ exhibiting anomalous enhancement in the ultrathin limit. Here, ρ is the electrical resistivity, which is estimated as ρ = ρ 2D × d. The value of α 2 /ρ at 200 K in the thick region is comparable to that in bulk FeSe 19  the high-T c superconductivity proves that these two transport properties arise from the same electronic state of FeSe thin films.
Another noticeable feature of FeSe thin films is the low electrical resistance realized even in ultrathin regions. Figure 2c shows the 2D sheet resistance ρ 2D of Sample A for V G = 0 V (gray circles) and 5 V (blue circles) as a function of d. When starting from the initial state with d~18 nm, the sheet resistance at 200 K, ρ 2D 200 K , first increased with decreasing d for both V G = 0 V and 5 V. With further decreasing d, ρ 2D 200 K at V G = 5 V showed a small peak at around d~11 nm and kept small values down to d~1 nm because the gated topmost layer of FeSe and the charge transfer layer at the FeSe/SrTiO 3 interface dominate the electrical transport of the thin film (see Supplementary Figure 3 and Supplementary Note 2 for the details of the d dependence of ρ 2D 200 K ). Such a low electrical resistance irrespective of the film thickness is consistent with the previous studies; for example, the resistivity of monolayer or few layer MBE-grown FeSe 11,14 is comparable to that of 10 nm thick (~15 layers) FeSe 17,18 owing to the interface or surface electron doping. Actually, ρ 2D 200 K~1 kΩ at V G = 5 V in the thin limit (Fig. 2c) is close to that in doped FeSe monolayers 11,14,15 . On the other hand, the small α and high ρ 2D 200 K at V G = 0 V indicate that the charge transfer layer does not produce the enhanced values of α. Consequently, the thermoelectric power factor α 2 /ρ at 200 K achieved a dramatic development in Fig. 2d owing to the enhancement of α and the concomitant reduction of electrical resistivity ρ = ρ 2D × d, which rarely occurs in the framework of conventional material design and fabrication. Along with the reduction of d from 18 nm to 1 nm, α 2 /ρ kept increasing and finally reached~1500 μW cm −1 K −2 .
Temperature-thickness mapping of thermoelectric response. Figures 3a, b display the temperature T-thickness d mappings of the absolute value of α (i.e., |α|) and α 2 /ρ, respectively, for another FeSe thin film, Sample B. The values of |α| and α 2 /ρ showed dramatic developments in the nanometer-thick region, which agrees well with the results for Sample A (see Figs. 2b, c). Moreover, the enhancement for both |α| and α 2 /ρ covers a wide temperature range from 50 K (just above T c ) to 280 K. Figure 3c summarizes α 2 /ρ for representative thermoelectric materials that possess high α 2 /ρ values (see Supplementary Table 1). The values of α 2 /ρ for the FeSe ultrathin film increased from~260 μW cm −1 K −2 at 280 K up tõ 13,000 μW cm −1 K −2 at 50 K, being the largest among existing bulk materials reported so far. Assuming the thermal conductivity for bulk Fe-based superconductors 25,26 , κ~5 W m −1 K −1 , the dimensionless figure of merit ZT of the FeSe ultrathin film reaches as large as~1.5 at 280 K.   temperature dependence, α for Sample B showed a peak at around~200 K, which follows neither the T-linear behavior expected in conventional metals nor the phonon drag thermopower (see Supplementary Figure 1 and Supplementary Note 1). Actually, the temperature dependence of α in the FeSe thin film is qualitatively similar to that in bulk Fe-based high-T c superconductors such as Ba(Fe 0.9 Co 0.1 ) 2 As 2 27 , LaFeAs(O 0.9 F 0.1 ) 28 , and La(Fe 0.9 Co 0.1 )AsO 29 , as shown in Fig. 4b. This trend can be seen even more clearly in Fig. 4c, where the data in Fig. 4a, b are normalized by the peak value α peak of each sample. These similarities further prove that α observed in Fig. 4a is attributed to FeSe itself rather than other artifacts such as substrates and ionic liquids. The characteristic temperature dependence of α/α peak in Fig. 4c is considered unique to Fe-based superconductors and has been discussed in the context of quantum criticality [30][31][32] or the two carrier model 27,33 . For example, it was reported that |α|/T in Ba(Fe 0.9 Co 0.1 ) 2 As 2 27 shows a divergence above T c and a strong enhancement when in proximity to the quantum critical point.  (Fig. 3a) for the initial (d~19.1 nm) and final (d~1 nm) thicknesses, respectively. On the other hand, our calculation based on the Fermi liquid picture predicts T-linear behavior and does not explain the nonmonotonous temperature dependence of α in ultrathin FeSe. The experimentally observed broad peak in α located at~200 K (Fig. 4a) is suggestive of a crucial role of electronic correlations in the Seebeck response of ultrathin FeSe; in fact, the recent ARPES studies pointed out a strong electronic correlation 9 in the high-T c phase of FeSe. A quantitative theoretical analysis of this effect remains to be performed.

Discussion
Nanostructures or low-dimensional structures have been a powerful guideline for the exploration of high-performance thermoelectric materials 8,[37][38][39][40] . The present results show that further enhancement of thermoelectric properties should be possible, if peculiar band structures of nano-structured systems including 2D layered materials are combined with additional ingredients such as strong electronic correlations. The unprecedented coexistence of giant thermoelectric power factor and high-T c superconductivity in ultrathin FeSe exemplifies that there may exist unknown multifunctional materials waiting to be disclosed in extreme conditions, illuminating a next research direction of functional thermoelectric materials.

Methods
Device fabrication. We fabricated ion-gated devices based on FeSe-thin films on SrTiO 3 substrates 15 with channel size of 1.2 × 2 mm 2 . The details of the thin-film preparation were reported in our previous study 15 . The device structure used in this study is schematically shown in Fig. 1c. The FeSe thin films were patterned by using a laser cutter to perform four-terminal resistance measurements. The gold wires were attached at both edges of the patterned film, working as a drain terminal D and a source terminal S. An ionic liquid, which worked as a gate dielectric, was placed on the FeSe surface. We used N,N-diethyl-N-(2-methoxyethyl)-N-methylammonium bis-(trifluoromethylsulfonyl)-imide (DEME-TFSI) as the ionic liquid. A Pt plate was placed on top of them, working as a gate electrode.
Thermoelectric measurements under gate biases. As shown in Fig. 1c, a heater and a heat sink were attached to either side of the ion-gated device to produce a thermal gradient. The type E thermocouples were attached to monitor the temperature difference ΔT and the thermoelectric voltage ΔV. The thermocouples were also used for the four-terminal resistance measurements. The temperature difference ΔT (0-1 K) and the voltage ΔV between the thermocouples were measured, and the values of α were evaluated from the slope of the ΔV−ΔT plots (See Fig. 2a). This device configuration allows us to measure α and ρ simultaneously. The thermoelectric measurements with solid [41][42][43][44][45][46][47] and ionic gate dielectrics [48][49][50][51][52][53][54][55][56][57] are widely accepted as a method to evaluate the thermoelectric properties of semiconductors with changing the carrier densities. Calculations. We performed first-principles band structure calculations using the Perdew-Burke-Ernzerhof parameterization of the generalized gradient approximation 58 and the full-potential (linearized) augmented plane-wave method, with the inclusion of spin-orbit coupling as implemented in the wien2k code 59 . Muffintin radii (R MT ) of 2.38 and 2.11 Bohr were used for Fe and Se, respectively. The maximum modulus for the reciprocal vectors K max was chosen such that R MT K max = 7.0 and a 10 × 10 × 10 k-mesh in the first Brillouin zone was used. The tightbinding Hamiltonian for the 3d orbitals of the Fe atom was constructed with Wannier90 60 and wien2wannier 61 .

Data availability
The authors declare that all data supporting the findings of this study are available within the paper and its Supplementary Information or from the authors upon reasonable request.