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Self-Consistent Two-Gap Description of MgB_{2} Superconductor

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## Abstract

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## 1. Introduction

## 2. Results and Discussion

## 3. Materials and Methods

## 4. Summary

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

TDR | Tunnel diode resonator |

ARPES | Angle-resolved photoemission spectroscopy |

FC | Field-cooled |

ZFC | Zero-field-cooled |

MPMS | Magnetic property measurement system |

## References

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**Figure 1.**(

**a**) Normalized magnetic moment, $M\left(T\right)/{M}_{ZFC}\left(5\phantom{\rule{4.pt}{0ex}}\mathrm{K}\right)$, measured after cooling in zero magnetic field to 5 K, applying ${H}_{DC}=10$ Oe and then measuring on warming (zero-field cooling (ZFC)) above ${T}_{c}$ and then on cooling (field-cooling (FC)). (

**b**) Magnetization loop, $M\left(H\right)$, in MgB${}_{2}$ crystal measured at 5 K.

**Figure 2.**Temperature variation of London penetration depth $\Delta \lambda \left(T\right)$ in MgB${}_{2}$. Inset: $\Delta \lambda \left(T\right)$ over the full temperature range. Main panel: low-temperature part of experimental $\Delta \lambda \left(T\right)$ (symbols). Solid curve is the best fitting to a single-gap s-wave BCS asymptotic behavior, $\Delta \lambda \left(T\right)=\lambda \left(0\right)\sqrt{\pi \Delta \left(0\right)/2{k}_{B}T}exp(-\Delta \left(0\right)/{k}_{B}T)$ with $\lambda \left(0\right)$ and $\Delta \left(0\right)$ as fitting parameters within “low-temperature” range up to 0.3${T}_{c}$.

**Figure 3.**(

**a**) Fitting of the experimental superfluid density, ${\rho}_{s}={\lambda}^{2}\left(0\right)/{\lambda}^{2}\left(T\right)$ (symbols), to the $\gamma $-model (lines). Partial superfluid densities, $\gamma {\rho}_{1}$ and $(1-\gamma ){\rho}_{2}$ are also shown. (

**b**) Temperature dependent superconducting energy gaps ${\Delta}_{1}\left(T\right)/{k}_{B}{T}_{c}$ and ${\Delta}_{2}\left(T\right)/{k}_{B}{T}_{c}$ calculated from the fitting procedure (lines). These results are compared with the experimental tunneling spectroscopy results [38] (purple open squares) and theoretical estimates [29] (red dashed lines), [30] (brown dotted lines).

**Figure 5.**(

**a**) Temperature dependent upper critical field ${H}_{c2}\left(T\right)$ in MgB${}_{2}$ with the applied magnetic fields ${H}_{dc}$ along ab-axis and c-axis. (

**b**) Temperature dependent ${H}_{c2}$ anisotropy $\gamma \left(T\right)={H}_{c2,ab}\left(T\right)/{H}_{c2,c}\left(T\right)$. Solid line represent a calculated result by using $\gamma $ model [32] and symbols are experimental results by Lyard et al. (squares) [41], Karpinski et al. (triangles) [42], and Zehetmayer et al. (circles) [43], respectively.

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## Share and Cite

**MDPI and ACS Style**

Kim, H.; Cho, K.; Tanatar, M.A.; Taufour, V.; Kim, S.K.; Bud’ko, S.L.; Canfield, P.C.; Kogan, V.G.; Prozorov, R.
Self-Consistent Two-Gap Description of MgB_{2} Superconductor. *Symmetry* **2019**, *11*, 1012.
https://doi.org/10.3390/sym11081012

**AMA Style**

Kim H, Cho K, Tanatar MA, Taufour V, Kim SK, Bud’ko SL, Canfield PC, Kogan VG, Prozorov R.
Self-Consistent Two-Gap Description of MgB_{2} Superconductor. *Symmetry*. 2019; 11(8):1012.
https://doi.org/10.3390/sym11081012

**Chicago/Turabian Style**

Kim, Hyunsoo, Kyuil Cho, Makariy A. Tanatar, Valentin Taufour, Stella K. Kim, Sergey L. Bud’ko, Paul C. Canfield, Vladimir G. Kogan, and Ruslan Prozorov.
2019. "Self-Consistent Two-Gap Description of MgB_{2} Superconductor" *Symmetry* 11, no. 8: 1012.
https://doi.org/10.3390/sym11081012