Quantum superconductor-insulator transition in titanium monoxide thin films with a wide range of oxygen contents

Y. J. Fan, C. Ma, T. Y. Wang, C. Zhang, Q. L. Chen, X. Liu, Z. Q. Wang, Q. Li, Y. W. Yin, and X. G. Li

Phys. Rev. B 98, 064501 – Published 7 August 2018

Abstract

The superconductor-insulator transition (SIT), one of the most fascinating quantum phase transitions, is closely related to the competition between superconductivity and carrier localization in disordered thin films. Here, superconducting $Ti O_{x}$ films with different oxygen contents were grown on $A l_{2} O_{3}$ substrates by a pulsed laser deposition technique. The increasing oxygen content leads to an increase of disorder, a reduction of carrier density, an enhancement of carrier localization, and therefore a decrease of superconducting transition temperature. A fascinating SIT emerges in cubic $Ti O_{x}$ films with increasing oxygen content and its critical sheet resistance is close to the quantum resistance $h / {(2 e)}^{2} \sim 6.45 k Ω$ . The scaling analyses of magnetic field–tuned SITs show that the critical exponent products zν increase from 1.02 to 1.31 with increasing disorder. Based on the results, the SIT can be described by the “dirty boson” model, and a schematic phase diagram for $Ti O_{x}$ films was constructed.

Received 1 April 2018
Revised 21 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064501

Physics Subject Headings (PhySH)

Superconducting phase transition Superconductor-insulator transition

Low-temperature superconductors Thin films

First-principles calculations Hall bar Resistivity measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. J. Fan¹, C. Ma¹, T. Y. Wang^1,2, C. Zhang¹, Q. L. Chen¹, X. Liu¹, Z. Q. Wang², Q. Li², Y. W. Yin^1,*, and X. G. Li^1,3,†

¹Hefei National Laboratory for Physical Sciences at the Microscale, Department of Physics, and CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, University of Science and Technology of China, Hefei 230026, China
²Department of Physics, Pennsylvania State University, University Park, Pennsylvania 19019, USA
³Key Laboratory of Materials Physics, Institute of Solid State Physics, Hefei 230026, China and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China

^*Corresponding author: yyw@ustc.edu.cn
^†Corresponding author: lixg@ustc.edu.cn

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Issue

Vol. 98, Iss. 6 — 1 August 2018

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Images

Figure 1
Temperature-dependent resistivities for $Ti O_{x}$ films (P-6, P-6.5, P-7, P-7.5, P-8, P-8.5, and P-9). Right inset: The enlarged view of sheet resistances for $Ti O_{x}$ films at low temperatures, and the critical quantum resistance $R_{Q} = 6.45 k Ω$ . Left inset: The gray open circle and arrow correspond to the enlarged sheet resistance of P-8.5 below 2 K.
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Figure 2
Scaling behaviors of magnetic field–tuned SIT in $Ti O_{x}$ films: (a) P-7.5, (b) P-8, and (c) P-8.5. Left panels: Magnetoresistance isotherms for samples P-7.5, P-8, and P-8.5 near the SIT. Right panels: The scaling analysis corresponding to the left panels. Insets: The fitting results of a power law to the inverse temperature-dependent $d R / d H$ at $H_{c}$ .
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Figure 3
(a,b) Temperature-dependent resistivities of P-7 in magnetic fields for $H ⊥ (111)$ and $H ∥ (111)$ from 0 to 9 T (0, 0.5, 1, 3, 5, 7, and 9 T), respectively. (c) Temperature-dependent $H_{c 2} (T)$ of P-7 for $H ⊥ (111)$ (closed circles) and $H ∥ (111)$ (closed stars). Solid lines are the fitting curves with the WHH model. (d) $P_{O 2}$ -dependent $H_{c 2} (0)$ (red symbol lines) and α (blue symbol lines) for $H ⊥ (111)$ (closed circles) and $H ∥ (111)$ (closed stars).
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Figure 4
(a) Oxygen content $x$ -dependent total and partial DOS $N (E_{F})$ at the Fermi level of $Ti O_{x}$ . Experimental values of the carrier density of $Ti O_{x}$ films as a function of oxygen content $x$ . (b) Lattice parameters $a$ from the theoretical calculation, experimental data, and reference values of $Ti O_{x}$ as a function of oxygen content $x$ . Open symbols are experimental data, and solid symbols are calculated values.
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Figure 5
(a) The fitting results of $ρ − T$ curves with the VRH model for $Ti O_{x}$ films (P-6, P-7, P-8, and P-9) in the temperature range from 300 to 100 K. The points are the experimental values, and the black lines represent the fitting results. (b) Oxygen content $x$ -dependent on the characteristic temperature $T_{0}$ and localization length $ξ_{l}$ in $Ti O_{x}$ .
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Figure 6
Schematic phase diagram of $Ti O_{x}$ films for oxygen content ( $x$ ), magnetic field ( $H$ ) and temperature ( $T$ ). The points are the experimental values. The WHH theory and an empirical equation $H_{irr} (T) = H_{irr} (0) [1 - {(T / T_{c, zero})}^{2}]$ [where $H_{irr} (0)$ is the irreversibility field at absolute zero temperature] are used to fit the temperature-dependent $H_{c 2}$ and $H_{irr}$ , respectively. Other solid lines are quadratic fitting curves. The different regimes of the diagram are described in the text.
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