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SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 64 , Issue 3 : 237413(2021) https://doi.org/10.1007/s11433-020-1615-y

Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa$_2$Cu$_4$O$_8$

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  • ReceivedApr 8, 2020
  • AcceptedAug 26, 2020
  • PublishedJan 21, 2021
PACS numbers

Abstract


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11974405, 11674377, and 11634015), the Ministry of Science and Technology of China (Grant Nos. 2016YFA0300502, and 2017YFA0302904), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33010100).


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The supporting information is available online at phys.scichina.com and link.springer.com The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.


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  • Figure 1

    (Color online) (a) Typical $^{17}$O-NMR spectrum of YBa$_2$Cu$_4$O$_8$ at $T$ = 90 K and $B_0$ = 16.05 T applied parallel to the $c$-axis. O(2) and O(3) are the sites in CuO$_2$ planes lying in bonds oriented along the crystalline $a$ and $b$ axes, as shown in the insert. HF1 (HF2) represents the first (second) high-frequency satellites, and LF1 (LF2) represents the first (second) low-frequency satellites. The five small peaks close to the O(2,3) central peak correspond to the O(1) site of CuO chains, as labeled using yellow arrows. The central line from the apical oxygen site is also observed, as labeled by O(4). (b) and (c) are the magnified view of LF2 and HF2 with fits by three Lorentzian functions. The small gray peak is from the misaligned part of the powder sample.

  • Figure 2

    (Color online) (a) $T$-dependent Knight shift of the O(2) and O(3) sites. The dashed line indicates the value of $K_{\rm~orb}$ = 0.008 $%$ [33]. Solid lines are the guide to the eye. The error bars are the standard deviation in fitting the NMR spectra, as shown in Figure 1(b) and (c), and are smaller than the symbol size. (b) Superposition of ${\Delta}K~=~K~_{\rm~c}^{\text{O(2)}}-~K~_{\rm~c}^{\text{O(3)}}$ and 1/$T_1$$T$ of the planar Cu site as a function of temperature. The red circles are from the previous report measured at 11 T [29]. The 1/$T_1$$T$ result is from a previous study that used NQR [30]. The solid line is a fit of 1/$T_1$$T$ above $T$ = 150 K obtained using the Curie-Weiss law as (1/$T_{1}$$T$) = a+ b/(T+$\theta$).

  • Figure 3

    (Color online) Comparison of the oxygen site differentiation in the Knight shift defined as $\left(~K~_{\rm~c}^{{\rm~O}(2)}-K~_{\rm~c}^{{\rm~O}(3)}\right)/\left(~K~_{\rm~c}^{\text{O(2)}}+K~_{\rm~c}^{\text{O(3)}}\right)$ with that in the quadrupole frequency $\nu~_{\rm~c}$ defined as $\left(~\nu~_{\rm~c}^{\text{O(2)}}-\nu~_{\rm~c}^{\text{O(3)}}\right)/{\left(~\nu~_{\rm~c}^{\text{O(2)}}+\nu~_{\rm~c}^{\text{O(3)}}\right)}$. The inset shows the $T$-dependence of $\nu~_{\rm~c}^{\text{O(2)}}$ and $\nu~_{\rm~c}^{\text{O(3)}}$. Solid lines are the guide to the eye.

  • Figure 4

    (Color online) The results obtained in this work are plotted in the global phase diagram. The red circle is the onset temperature $T_{\rm~nem}$ of nematicity in YBa$_2$Cu$_4$O$_8$ determined based on the emergence of $\Delta~K$. The red square is the onset temperature $T_{\rm~CDW}$ of short-range CDW in YBa$_2$Cu$_4$O$_8$ determined from the $T$-dependence of the $^{17}$O-NMR linewidth. The blue circle is the nematic transition temperature $T_{\rm~nem}$ reported using torque magnetometry in YBa$_2$Cu$_3$O$_y$ [10]. The open red and solid green squares are $T_{\rm~CDW}$ reported by NMR [41]and through the resonant X-ray scattering measurements in YBa$_2$Cu$_3$O$_y$ [42,43], respectively. AF and SC denote the antiferromagnetic ordered and superconducting phase, respectively.

  • Figure 5

    (Color online) Evidence of the short-range charge density wave order. The temperature dependence of the full width at half maximum (FWHM) of HF2 and LF2 for O(2) (a) and O(3) (b), which was measured in a magnetic field of 16.05 T. Solid lines are the guide to the eye.

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