Anisotropy of the upper critical field and its thickness dependence in superconducting FeSe electric-double-layer transistors

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Anisotropy of the upper critical field and its thickness dependence in superconducting FeSe electric-double-layer transistors

Junichi Shiogai, Shojiro Kimura, Satoshi Awaji, Tsutomu Nojima, and Atsushi Tsukazaki

Phys. Rev. B 97, 174520 – Published 29 May 2018

Abstract

Anisotropy of superconductivity is one of the fundamental physical parameters for understanding layered iron-based superconductors (IBSs). Here we investigated the anisotropic response of resistive transition as a function of thickness $(d)$ in iron selenide (FeSe) based electric-double-layer transistors (EDLTs) on $SrTi O_{3}$ , which exhibit superconducting transition temperatures $T_{c}$ as high as 40 K below $d = 10 nm$ . According to the analyses of the in-plane $(H_{c 2}^{/ /})$ and out-of-plane $(H_{c 2}^{⊥})$ upper critical fields $(H_{c 2})$ and the magnetic field angle dependence of the resistance $(R_{s} - θ)$ in ultrathin condition, we found that the anisotropy factor $ɛ_{0} = H_{c 2}^{/ /} / H_{c 2}^{⊥}$ is 7.4 in the thin limit of $d \sim 1 nm$ , which is larger than that of bulk IBSs. In addition, we observed the shorter out-of-plane coherence length $ξ_{c}$ of 0.19 nm compared to the $c$ -axis lattice constant, which implies the confinement of the order parameter in the one unit cell FeSe. These findings suggest that high- $T_{c}$ superconductivity in the ultrathin FeSe-EDLT exhibits an anisotropic three-dimensional (3D) or quasi-two-dimensional (2D) nature rather than the pure 2D one, leading to the robust superconductivity. Moreover, we carried out the systematic evaluation of the anisotropic $H_{c 2}$ against thickness reduction in the FeSe channel. The in-plane $H_{c 2}$ as a function of normalized temperature $T / T_{c}$ is almost independent of $d$ until the thin limit condition. On the other hand, the out-of-plane $H_{c 2}$ near $T / T_{c} \sim 1$ decreases with increasing $d$ , resulting in the increase of $ɛ_{0}$ at around $T_{c}$ to 32.0 at the thick condition of $d = 9.3 nm$ , which is also confirmed by $R_{s} - θ$ measurements. The counterintuitive behavior can be attributed to the degree of coupling strength between two electron-rich layers possessing a high superconducting order parameter induced by electrostatic gating at the top interface and charge transfer from $SrTi O_{3}$ substrates at the bottom interface. Besides a large $H_{c 2}^{⊥}$ for $d = 9.3 nm$ exceeding 20 T even at $T = 0.8 T_{c}$ , we observe the decoupling crossover of the two superconducting layers at low temperature, which is a unique feature for the high- $T_{c}$ FeSe-EDLT on $SrTi O_{3}$ .

Received 11 December 2017
Revised 5 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.174520

Physics Subject Headings (PhySH)

Critical field Electric field effects Superconducting phase transition Vortices in superconductors

Chalcogenides

Etching

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Junichi Shiogai^*, Shojiro Kimura, Satoshi Awaji, Tsutomu Nojima, and Atsushi Tsukazaki

Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

^*junichi.shiogai@imr.tohoku.ac.jp

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Vol. 97, Iss. 17 — 1 May 2018

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Images

Figure 1
(a) Schematics of measurement configuration in FeSe-EDLT device (not to scale, left top) and cross section of electron accumulation (right bottom) from top ionic gating within $d_{EDL}$ and bottom charge transfer within $d_{CT}$ . (b) Sheet resistance $R_{s}$ as a function of temperature $T$ at zero magnetic field under $V_{G} = 5 V$ . For clarity, $R_{s}$ is normalized to the value at $T = 100 K$ . The thickness $d$ was tuned by a series of electrochemical events. Inset: Thickness dependence of onset $T_{c} (T_{c}^{on}$ : the intersection of extrapolation lines from normal state and superconducting transition).
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Figure 2
(a), (b) Sheet resistance $R_{s}$ as a function of temperature $T$ at $V_{G} = 5 V$ for the film thickness $d \sim 1 nm$ under the (a) out-of-plane $(μ_{0} H_{⊥})$ and (b) in-plane $(μ_{0} H_{/ /})$ magnetic field, respectively. The field increases in steps of 0.2 T from zero (black solid line) to 1 T and in steps of 1 T from 2 to 9 T (purple solid line). Dashed lines are extrapolation of half resistance curves, $0.5 R_{s} (T)$ , in the normal state which define midpoint superconducting transition temperatures $T_{c} (H)$ . Insets: Enlarged views of $R_{s} (T)$ in the transition region near $T_{c}$ . (c) In-plane (open symbols) and out-of-plane (filled symbols) upper critical field $μ_{0} H_{c 2}$ of FeSe-EDLT (sample A) for $d \sim 1.0 nm$ . Out-of-plane $μ_{0} H_{c 2} - T_{c}$ plots follow a linear relation around $T_{c} (0)$ (black dashed lines). (d) $R_{s}$ as a function of the angle of applied magnetic field at $T = T_{c} (0) = 39.0 K$ under $μ_{0} H = 3$ (orange), 6 (green), and 9 T (blue) in sample A for $d \sim 1.0 nm$ . Inset shows the same trace of $R_{s} (θ)$ as a function of reduced magnetic field $μ_{0} H_{red}$ (see text).
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Figure 3
(a), (b) Sheet resistance $R_{s}$ as a function of temperature $T$ at $V_{G} = 5 V$ for the film thickness $d \sim 9.3 nm$ under the (a) out-of-plane $μ_{0} H_{⊥}$ and (b) in-plane $μ_{0} H_{/ /}$ magnetic field, respectively. Insets: Enlarged views of $R_{s} (T)$ in the transition region near $T_{c}$ . (c), (d) The same traces of (a), (b) for $d \sim 6.3 nm$ . (e) In-plane (open symbols) and out-of-plane (filled symbols) upper critical field $H_{c 2}$ of FeSe-EDLT (sample A) for $d \sim 9.3$ (blue squares), 6.3 (green circles), and 1.0 nm [red triangles, the same data from Fig. 2]. Out-of-plane $H_{c 2} - T_{c}$ plots follow a linear relation around $T_{c} (0)$ (black dashed lines). (f), (g) $R_{s}$ as a function of the angle of applied magnetic field at $T = T_{c} (0)$ under $μ_{0} H = 3$ (orange), 6 (green), and 9 T (blue) in sample A for (f) $d = 9.3 [T_{c} (0) = 29.3 K]$ and (g) $d = 6.3 nm [T_{c} (0) = 38.9 K]$ . Inset shows the same trace of $R_{s} (θ)$ as a function of reduced magnetic field $μ_{0} H_{red}$ (see text). (h) The slope of the $μ_{0} H_{c 2}^{⊥} - T_{c}$ plot in (e) defined as $- T_{c} (0) Δ μ_{0} H_{c 2}^{⊥} / Δ T$ . Inset: $μ_{0} H_{c 2}^{⊥} - T_{c}$ plots of FeSe-EDLT (sample B) for $d \sim 10 nm$ (blue filled squares) and 1.0 nm (red filled triangles) measured up to 24 T.
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Figure 4
(a), (b) Thickness dependence of (a) $ɛ_{0} (T_{c})$ and (b) $ξ_{ab} (0)$ (filled squares) and $ξ_{c} (0)$ (open squares) in FeSe-EDLT (sample A). (c), (d) Schematic of distribution of superconducting order parameter $Δ_{SC} (z)$ for (c) coupled state and (d) decoupled state of FeSe-EDLT for the thick condition (not to scale).
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