Quantum criticality tuned by magnetic field in optimally electron-doped cuprate thin films

Xu Zhang, Heshan Yu, Qihong Chen, Runqiu Yang, Ge He, Ziquan Lin, Qian Li, Jie Yuan, Beiyi Zhu, Liang Li, Yi-feng Yang, Tao Xiang, Rong-Gen Cai, Anna Kusmartseva, F. V. Kusmartsev, Jun-Feng Wang, and Kui Jin

Phys. Rev. B 103, 014517 – Published 22 January 2021

Abstract

Antiferromagnetic (AF) spin fluctuations are commonly believed to play a key role in electron pairing of cuprate superconductors. In electron-doped cuprates, a paradox still exists about the interplay among different electronic states in quantum perturbations, especially between superconducting and magnetic states. Here, we report a systematic transport study of cation-optimized ${La}_{2 - x} {Ce}_{x} {CuO}_{4 \pm δ}$ $(x = 0.10)$ thin films in high magnetic fields. We find an AF quantum phase transition near 60 T, where the Hall number jumps from $n_{H} = - x$ to $n_{H} = 1 - x$ , resembling the change in $n_{H}$ at the AF boundary $(x_{AF} = 0.14)$ tuned by Ce doping. In the AF region a spin-dependent state manifesting anomalous positive magnetoresistance is observed, which is closely related to superconductivity. Once the AF state is suppressed by magnetic field, a polarized ferromagnetic state is predicted, reminiscent of the recently reported ferromagnetic state at the quantum end point of the superconducting dome by Ce doping. The magnetic field that drives phase transitions in a manner similar to but distinct from doping thereby provides a unique perspective to understand the quantum criticality of electron-doped cuprates.

Received 24 September 2020
Revised 5 December 2020
Accepted 5 January 2021

DOI:https://doi.org/10.1103/PhysRevB.103.014517

Physics Subject Headings (PhySH)

Antiferromagnetism Hall effect Magnetoresistance Quantum phase transitions Superconductivity

Cuprates Thin films

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xu Zhang ^1,2,*, Heshan Yu^1,2,3,*, Qihong Chen^1,2, Runqiu Yang^4,5, Ge He ^1,2, Ziquan Lin⁶, Qian Li¹, Jie Yuan ^1,2,7, Beiyi Zhu^1,2, Liang Li⁶, Yi-feng Yang^1,2, Tao Xiang^1,2, Rong-Gen Cai^8,2, Anna Kusmartseva⁹, F. V. Kusmartsev^9,10, Jun-Feng Wang⁶, and Kui Jin ^1,2,7,†

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
³Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, USA
⁴Quantum Universe Center, Korea Institute for Advanced Study, Seoul 130-722, Korea
⁵Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Yaguan Road 135, Jinnan District, Tianjin 300350, China
⁶Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
⁷Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
⁸CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
⁹Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom
¹⁰College of Art and Science, Khalifa University, P.O. Box 127788, Abu Dhabi, United Arab Emirates

^*These authors contributed equally to this work.
^†kuijin@iphy.ac.cn

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Vol. 103, Iss. 1 — 1 January 2021

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Figure 1
Phase diagram of LCCO obtained from magnetoelectrical transport measurements. The side panel illustrates the Ce doping dependence of the superconducting dome. With increasing doping, LCCO exhibits a maximum $T_{c}$ at $x = 0.10$ . The main panel shows the field-temperature ( $B − T$ ) diagram of $x = 0.10$ samples (S1, S2, and S3). The coordinate axes are normalized by two characteristic quantities $B_{c}$ and $T_{k}^{0}$ , respectively. Here, $B_{c}$ is obtained by extrapolating the boundary of the canted AF state to the zero-temperature limit (for the three samples, $B_{c} \sim$ 62, 55, and 52 T). $T_{k}^{0}$ corresponds to the temperature of the Fermi surface reconstruction in the zero-field limit (for the three samples, $T_{k}^{0} \sim$ 32, 27, and 26 K), manifesting as a kink in the Hall coefficient (see Fig. 2). The normalized boundaries of the three samples can be fitted by the holographic model (black solid line), which also predicts an energy gap (dotted line) above $B_{c}$ . Three regions can be identified in the $B − T$ diagram, i.e., $n$ -MR (blue), $p$ -MR (white), and superconducting (orange) regions. The dashed line is mean-field fitting, which deviates from the experimental data near $B_{c}$ .
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Figure 2
Hall kink and resistivity upturn in LCCO. (a) Temperature dependence of $R_{H}$ and $ρ_{x x}$ at 15 T for sample S1. $T_{k}$ ( $T_{u}$ ) is extracted from the maximum (minimum) of the $R_{H}$ ( $ρ_{x x}$ ) curves. (b) Temperature dependence of the Hall coefficient (top panel) and resistivity (bottom panel) at different fields up to 55 T for sample S1. (c) The magnetic field dependence of $T_{k}$ . Inset: The magnetic field dependence of $T_{u}$ .
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Figure 3
Longitudinal resistivity and Hall resistivity of sample S1 from 1.8 to 100 K. (a) and (b) The field-dependent longitudinal resistivity displays nonmonotonous behavior below 30 K. $B_{max}$ marks the characteristic magnetic fields where the resistivity reaches the maximum. Above 30 K, magnetoresistance shows linearity at high magnetic fields. (c) and (d) With decreasing temperature, there is a switching from linear to nonlinear behavior. The minimum in the $ρ_{x y}$ curves corresponding to $B_{max}$ also disappears above 30 K.
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Figure 4
The Hall number and AF transition. (a) The Hall number $n_{H}$ as a function of magnetic field. $n_{H}$ deviates from $- 0.1$ at $B_{max}^{0}$ . Inset: Temperature dependence of the Hall coefficient at 15 and 55 T for sample S2. (b) The Hall number $n_{H}$ as a function of Ce doping (squares from Ref. [16] and diamonds from Ref. [17]). The upper dashed line marks $n_{H} = 1 - x$ ; the lower dashed line marks $n_{H} = - x$ .
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Figure 5
The characteristic quantities of $p$ -MR related to $T_{c}$ . (a) $δ ρ = {\frac{d ρ (B)}{d B} \frac{1}{ρ (B)}|}_{B = 12 T}$ as a function of temperature for different LCCO samples (white dots for $x = 0.16$ from Ref. [25]). (b) The slope of $ρ_{x x} (B)$ for LCCO with different dopings (square at 1.8 K and circles at 400 mK from Ref. [25]). (c) The correlation between $δ ρ$ and $T_{c 0}$ for different LCCO samples (solid circles at 1.8 K, triangle at 8 K, and square at 2 K from Ref. [23]; diamond at 4.5 K from Ref. [26]). (d) The correlation between $B_{max}^{0}$ and $T_{c 0}$ . Inset: The temperature dependence of $B_{max}$ for sample S1. $B_{max}^{0}$ is obtained from the epitaxial curve to zero temperature.
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Figure 6
The schematic description of the topological order. (a) The topological order is best visualized by considering a Cu-O-O triangular plaquette on the Cu-O plane. On the plaquette the ${Cu}^{2 +}$ ion has a prelocalized spin and two neighboring oxygens. Clockwise and counterclockwise $π$ -orbital currents or moments are shown in pink and blue, respectively. (b) The sequence tunneling of a doped electron. Such a state is unstable, and this instability can lead to the formation of a spontaneous local orbital current. (c) A schematic depiction of the dissociation of the vortex-antivortex pairs (or clockwise and counterclockwise orbital currents) by magnetic field. The magnetic field is applied perpendicular to the plane of the quadruple moments. The field polarizes orbital currents of a particular chirality and thereby causes an unbinding of the vortex-antivortex pairs when the limit is approached. This leads to a Beresinkii-Kosterlitz-Thouless-like phase transition.
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