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Suppression of the s-Wave Order Parameter Near the Surface of the Infinite-Layer Electron-Doped Cuprate Superconductor Sr_{0.9}La_{0.1}CuO_{2}

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## Abstract

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## Preface

**2002**, 82, 279–288). As a result of our studies, complex order parameters were detected in $\lambda \left(T\right)$ measurements for hole-doped HTSs such as La${}_{1.83}$Sr${}_{0.17}$CuO${}_{4}$, YBa${}_{2}$Cu${}_{3}$O${}_{7-\delta}$, and YBa${}_{2}$Cu${}_{4}$O${}_{8}$. Here, we present evidence that the mixed order parameter symmetry is realized in Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$, i.e., in a superconductor belonging to the family of electron-doped cuprate HTSs.

## 1. Introduction

## 2. Experimental Details

## 3. Results and Discussion

- (i)
- When a small magnetic field is applied along the c-axis, the screening currents flow in the $ab$-plane, decaying at a distance ${\lambda}_{ab}$ from the grain surface, so that ${\lambda}_{\Vert}^{*}={\lambda}_{ab}$.
- (ii)
- With the magnetic field applied perpendicular to the c-axis, the screening currents flow within the $ab$-plane and along the c-axis, thus implying that both components (${\lambda}_{ab}$ and ${\lambda}_{c}$) enter the measured AC magnetization. For ${\lambda}_{c}\gg {\lambda}_{ab}$ (which is generally the case for highly anisotropic HTSs), the effective penetration depth ${\lambda}_{\perp}^{*}$ is mainly determined by the out-of-plane component, and for grains of arbitrary size, the relation ${\lambda}_{\perp}^{*}\simeq 0.7{\lambda}_{c}$ holds [37].

- (i)
- The absolute value of the s-wave gap is larger than the maximum value of the anisotropic d-wave gap (Table 1 and Panels (a) and (b) of Figure 3) with $2{\Delta}_{0}^{s}/{k}_{B}{T}_{c}=6.02\left(6\right)$ and $2{\Delta}_{0}^{{d}_{An}}/{k}_{B}{T}_{c}=3.89\left(3\right)$, respectively (${T}_{c}\simeq 42$ K). This implies that in electron-doped Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$, the s-wave component of the order parameter is the dominant one. This agrees with the results of small-angle neutron scattering experiments revealing that at fields higher than 1.5 T, the superfluid density of Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$ is determined entirely by the s-wave component of the order parameter [44].
- (ii)
- (iii)
- The temperature dependence of the anisotropic d-wave contribution to the superfluid density (solid red line in Figure 3c) is very close to the quadratic (${T}^{2}$) dependence (dash-dotted line in Figure 3c), which is often observed in various electron-doped HTSs (see [30] and the references therein). Generally, the ${T}^{2}$ behavior is attributed to a “dirty” d-wave scenario and is explained by impurity scattering of the carriers. However, it is difficult to explain how an order parameter that changes sign persists in the dirty limit, since any scattering centers would act as pair breakers [46]. Therefore, we believe that the anisotropic d-wave approach is more appropriate for electron-doped HTSs.
- (iv)
- For ${\lambda}_{ab}^{-2}\left(T\right)$, the s-wave contribution to the superfluid density is almost negligible (${\omega}_{ab}=0.04$), whereas for ${\lambda}_{c}^{-2}\left(T\right)$, it is substantial (${\omega}_{c}=0.54$) (see Table 1). Bearing in mind that our experiments were performed in the Meissner state, the different behavior of ${\lambda}_{ab}^{-2}\left(T\right)$ and ${\lambda}_{c}^{-2}\left(T\right)$ can be explained within the scenario proposed by Müller [21,22]. Since ${\lambda}_{ab}\left(0\right)$ is rather small (see Table 1), one can assume that its temperature dependence is mainly determined by surface properties and therefore follows the one expected for a d-wave superconductor. In contrast, ${\lambda}_{c}\left(0\right)$ is almost a factor 10 larger than ${\lambda}_{ab}\left(0\right)$, and thus, ${\lambda}_{c}^{-2}\left(T\right)$ contains contributions from both the surface and the bulk (mixed $s+d$-wave order parameter).

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References and Note

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**Figure 1.**(

**a**) An example of the scanning electron microscope photograph of the powdered Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$ sample. (

**b**) The grain size distribution $N\left(R\right)$ determined from scanning electron microscope photographs. The thin vertical lines represent the statistical errors ($\pm \sqrt{N\left(R\right)}$).

**Figure 2.**Temperature dependencies of ${\lambda}_{ab}^{-2}$ (

**a**) and ${\lambda}_{c}^{-2}$ (

**b**) for Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$ extracted from the measured ${M}_{AC}\left(T\right)$ by using Equation (1). Solid lines represent fits with the two-gap $s+d$-wave model. ${\lambda}_{ab}^{-2}\left(T\right)$ and ${\lambda}_{c}^{-2}\left(T\right)$ were analyzed simultaneously by means of Equation (2) with ${\omega}_{ab}$, ${\omega}_{c}$, ${\lambda}_{ab}\left(0\right)$, and ${\lambda}_{c}\left(0\right)$ as the individual fitting parameters and common s-wave and anisotropic d-wave gap functions as described by Equations (4)–(6). See the text for details.

**Figure 3.**(

**a**) The angular dependence of the s-wave gap at $T=0$ (${\Delta}_{0}^{s}\xb7{g}^{s}\left(\phi \right)$; see Equation (5) and Table 1). (

**b**) The angular dependence of the anisotropic d-wave gap (${\Delta}_{0}^{d}\xb7{g}^{d}\left(\phi \right)$; Equation (6) and Table 1). (

**c**) Contributions of the s-wave (blue line) and the anisotropic d-wave (red line) gaps to the superfluid density (${\rho}_{s}\propto {\lambda}^{-2}$) obtained by means of Equation (3). The dashed-dotted line represents the ${T}^{2}$ behavior, which is generally observed in various electron-doped HTSs (see [30] and the references therein).

**Figure 4.**The normalized superfluid density ${\lambda}_{ab}^{-2}\left(T\right)/{\lambda}_{ab}^{-2}\left(0\right)$ (open circles and squares) and ${\lambda}_{c}^{-2}\left(T\right)/{\lambda}_{c}^{-2}\left(0\right)$ (closed circles) obtained in the present study (closed and open circles) and by the transverse-field $\mu $SR experiments (open squares) in [34]. The solid lines correspond to fits by means of Equation (2) with the parameters summarized in Table 1.

**Table 1.**Summary of the analysis of ${\lambda}_{ab}^{-2}\left(T\right)$ and ${\lambda}_{c}^{-2}\left(T\right)$ for Sr${}_{0.9}$La${}_{0.1}$CuO${}_{2}$ by means of Equation (2). The absolute errors of ${\lambda}_{ab,c}\left(0\right)$ account for the uncertainties in the grain size distribution $N\left(R\right)\pm \sqrt{N\left(R\right)}$ and that of the demagnetization factor $1/3\pm 10$%; see the text for details. TF-$\mu $SR, denotes the transverse-field muon-spin rotation/relaxation (TF-$\mu $SR) experiments.

Method | Quantity | ${\mathbf{\Delta}}_{0}^{\mathit{s}}$ | ${\mathbf{\Delta}}_{0}^{{\mathit{d}}_{\mathbf{An}}}$ | a | ${\mathit{\omega}}_{\mathbf{ab},\mathit{c}}$ | ${\mathit{\lambda}}_{\mathbf{ab},\mathit{c}}\left(0\right)$ |
---|---|---|---|---|---|---|

(meV) | (meV) | (nm) | ||||

ACsusc. | ${\lambda}_{ab}^{-2}\left(T\right)$ | 10.9(1) | 7.03(6) | 0.90(2) | 0.04(2) | 157(15) |

${\lambda}_{c}^{-2}\left(T\right)$ | 0.54(2) | 1140(100) | ||||

TF-$\mu $SR [34] | ${\lambda}_{ab}^{-2}\left(T\right)$ | 10.9 ${}^{a}$ | 7.03 ${}^{a}$ | 0.90 ${}^{a}$ | 0.72(4) | 93(2) |

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**MDPI and ACS Style**

Khasanov, R.; Shengelaya, A.; Brütsch, R.; Keller, H.
Suppression of the *s*-Wave Order Parameter Near the Surface of the Infinite-Layer Electron-Doped Cuprate Superconductor Sr_{0.9}La_{0.1}CuO_{2}. *Condens. Matter* **2020**, *5*, 50.
https://doi.org/10.3390/condmat5030050

**AMA Style**

Khasanov R, Shengelaya A, Brütsch R, Keller H.
Suppression of the *s*-Wave Order Parameter Near the Surface of the Infinite-Layer Electron-Doped Cuprate Superconductor Sr_{0.9}La_{0.1}CuO_{2}. *Condensed Matter*. 2020; 5(3):50.
https://doi.org/10.3390/condmat5030050

**Chicago/Turabian Style**

Khasanov, Rustem, Alexander Shengelaya, Roland Brütsch, and Hugo Keller.
2020. "Suppression of the *s*-Wave Order Parameter Near the Surface of the Infinite-Layer Electron-Doped Cuprate Superconductor Sr_{0.9}La_{0.1}CuO_{2}" *Condensed Matter* 5, no. 3: 50.
https://doi.org/10.3390/condmat5030050