Vortex-induced quantum metallicity in the mono-unit-layer superconductor $\mathrm{NbS}{\mathrm{e}}_{2}$

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Vortex-induced quantum metallicity in the mono-unit-layer superconductor $NbS e_{2}$

Satoru Ichinokura, Yuki Nakata, Katsuaki Sugawara, Yukihiro Endo, Akari Takayama, Takashi Takahashi, and Shuji Hasegawa

Phys. Rev. B 99, 220501(R) – Published 5 June 2019

Abstract

We performed in situ magnetoresistance measurements in the ultrahigh-vacuum environment to reveal the quantum phase transitions of single unit-layer $NbS e_{2}$ epitaxially grown on bilayer graphene. It was found that the superconductor-normal state transition caused by the surface-normal magnetic field was intermediated by a quasimetallic state. This behavior is consistent with the “Bose metal” picture where a finite dissipation is caused by the breaking of phase coherence due to strong gauge-field fluctuation. On one hand, around the mean-field critical temperature, the onset of transition from the normal state to the low-temperature states was governed by the amplitude-fluctuation effect, prominently under the magnetic field. We applied scaling theories to determine the phase boundaries. The result of scaling analyses revealed a complex but essential phase diagram of the single unit-layer $NbS e_{2}$ as a two-dimensional superconductor.

Received 17 August 2018

DOI:https://doi.org/10.1103/PhysRevB.99.220501

Physics Subject Headings (PhySH)

Superconducting fluctuations Superconducting order parameter Superconducting phase transition

2-dimensional systems Low-temperature superconductors Transition metal dichalcogenides Ultrathin films

Molecular beam epitaxy Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Satoru Ichinokura^1,*, Yuki Nakata², Katsuaki Sugawara^2,3, Yukihiro Endo¹, Akari Takayama¹, Takashi Takahashi^2,3,4, and Shuji Hasegawa¹

¹Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Toyko 113-0033, Japan
²Department of Physics, Tohoku University, Sendai 980-8578, Japan
³Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan
⁴WPI Research Center, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan

^*Current address: Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan; ichinokura@phys.titech.ac.jp

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Vol. 99, Iss. 22 — 1 June 2019

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Figure 1
(a) Schematic of a sectional view of the crystal structure of 1UL 2H- $NbS e_{2}$ /bilayer graphene (BLG) on SiC substrate. Atoms colored by green, purple, black (gray), and blue represent Se, Nb, C, and Si, respectively. (b) RHEED pattern of the present sample. Streaks indicated by yellow arrows are diffraction spots from $NbS e_{2}$ , while those indicated by green arrows are from the underlying graphene. (c) Schematic of electrical transport measurements. Four-point probe directly touches on 1UL $NbS e_{2}$ in UHV.
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Figure 2
Electrical transport properties of the 1UL $2 H − NbS e_{2}$ /bilayer graphene. (a) Temperature dependence of sheet resistivity under zero magnetic field. The abrupt change from zero to 680 Ω indicates the emergence of superconductivity at 1.51 K. Inset shows a closed-up resistivity curve from 1.3 to 2.0 K in semilogarithmic scale. The red solid line indicates the fitting result by Halperin-Nelson equation [2]. (b) Temperature dependence of sheet resistivity under a fixed magnetic field. It increases in step $Δ B = 0.05 T$ from 0.0 to 0.9 T, and $Δ B = 0.2 T$ from 1.0 to 1.6 T. Inset shows a closeup of $R_{sheet} − T$ curves $0.65 \leq B \leq 1.2 T$ . (c) Comparison of the temperature-dependent upper critical field defined in two different ways. Black open triangles represent the midpoint of resistivity curves, which shows an upturn towards low temperature, apart from the linear region guided by the gray dashed line. Red filled squares represent interpolated $(T_{c}, B_{c 2})$ from UD scaling of fluctuation conductivity. (d) Result of UD scaling. The $R_{sheet} (T)$ at $0.05 \leq B \leq 0.9 T$ is replotted with variable change. Here, $T_{c}$ is appropriately chosen to reproduce the universal function in Eq. (1). The red solid line in (c) indicates numerical fitting with GL theory [4].
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Figure 3
(a) Arrhenius plot of resistivity, which is converted from data in Fig. 2 with the same color code. The black solid lines indicate the fitting by $R \propto exp (- U (B) / k_{B} T)$ , where $U (B)$ is an activation energy. (b) The activation energy extrapolated from the fitting in (a), plotted as a function of the magnetic field B. The red solid line is the least-squares fitting by $U (B) = U_{0} ln (B^{*} / B)$ .
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Figure 4
(a), (b) Application of scaling theories at transitions from (a) SC−BM, and (b) BM−INS phases [29, 30, 38, 39]. In (a), sheet resistivity $R_{sheet}$ at fixed temperatures was measured as a function of the magnetic field. $R_{sheet} (B)$ at 0.85 K showing a power-law dependence described by Eq. (2). The fitting result in Eq. (2) is shown as a black solid line. (b) Another variable transformation of $R_{sheet} (T, B)$ function reproducing the universal curve in Eq. (3) at $1.0 \leq B \leq 1.6 T$ . (c) Schematically drawn phase diagram of superconductivity-related states in 1UL $NbS e_{2}$ . Black open circles are the same points as red squares in Fig. 2, which represent the mean-field transition point. Gray dashed line is the result of the GL fitting. Purple open squares are inflection points between the TAFF-like behavior and saturation of resistivity. Orange filled diamonds show the critical field of QPTs at absolute zero temperature extrapolated from the scaling behavior of Eqs. (1, 2, 3). The true SC region (indicated by the red bar) lies near the $B = 0$ axis. Phase boundaries are drawn to smoothly connect the experimental data points.
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Physical Review B

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Vortex-induced quantum metallicity in the mono-unit-layer superconductor $NbS e_{2}$

Satoru Ichinokura, Yuki Nakata, Katsuaki Sugawara, Yukihiro Endo, Akari Takayama, Takashi Takahashi, and Shuji Hasegawa

Phys. Rev. B 99, 220501(R) – Published 5 June 2019

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Physical Review B

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Vortex-induced quantum metallicity in the mono-unit-layer superconductor NbSe2

Satoru Ichinokura, Yuki Nakata, Katsuaki Sugawara, Yukihiro Endo, Akari Takayama, Takashi Takahashi, and Shuji Hasegawa

Phys. Rev. B 99, 220501(R) – Published 5 June 2019

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Vortex-induced quantum metallicity in the mono-unit-layer superconductor $NbS e_{2}$