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Anisotropic structure of the order parameter in FeSe(0.45)Te(0.55) revealed by angle-resolved specific heat.

Zeng B, Mu G, Luo HQ, Xiang T, Mazin II, Yang H, Shan L, Ren C, Dai PC, Wen HH - Nat Commun (2010)

Bottom Line: So far the experimental data and theoretical models have been highly controversial.Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes').Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.

View Article: PubMed Central - PubMed

Affiliation: National Laboratory for Superconductivity, Institute of Physics and National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China.

ABSTRACT
The central issues for understanding iron (Fe)-based superconductors are the symmetry and structure of the superconducting gap. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes'). A unique method for addressing this issue, and one of very few methods that are bulk and angle resolved, is measuring the electronic-specific heat in a rotating magnetic field. In this study, we present the first such measurement for an Fe-based high-T(c) superconductor. We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction. Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.

No MeSH data available.


Related in: MedlinePlus

Angle dependence of specific heat coefficient and proposed positions of gap minimum.Data measured at (a) 3.65, 3.7 and 3.75 K and (b) 2.6, 2.65 and 2.7 K in the in-plane magnetic field of 9 T, where α is the angle between the field and the Fe-Se-Fe bond direction. Fourfold oscillations are observed and the amplitude is ~0.12 mJ mol−1 K−2 (T=2.6 K). The fourfold oscillations were repeatable in two separate samples. The maximum of C/T is located at about zero degrees (H//Fe-Se-Fe), whereas the sign of the oscillations is reversed when the temperature is increased to 3.7 K. The red lines are theoretical simulations (see Supplementary Methods) using the d(x2−y2) order parameter Δk=Δ0 (cos kx−cos ky). The actual functional dependence is not important: any reasonable model that yields the gap nodes located at the same directions4647 would produce a very similar angular dependence. (c) The temperature dependence of the difference of C/T at 0° and 45°, a crossover is clearly seen at ~2.9 K. The random error bars (after the averaging of 300 data points) of specific heat are ±0.04 mJ mol−1 K−2. (d) Possible locations of nodes or gap minima suggested by our data are shown by the red and blue balls on the folded electron Fermi pockets, and by red segments on the hole Fermi surfaces. The ellipticity of the electron pockets is exaggerated in this drawing.
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f2: Angle dependence of specific heat coefficient and proposed positions of gap minimum.Data measured at (a) 3.65, 3.7 and 3.75 K and (b) 2.6, 2.65 and 2.7 K in the in-plane magnetic field of 9 T, where α is the angle between the field and the Fe-Se-Fe bond direction. Fourfold oscillations are observed and the amplitude is ~0.12 mJ mol−1 K−2 (T=2.6 K). The fourfold oscillations were repeatable in two separate samples. The maximum of C/T is located at about zero degrees (H//Fe-Se-Fe), whereas the sign of the oscillations is reversed when the temperature is increased to 3.7 K. The red lines are theoretical simulations (see Supplementary Methods) using the d(x2−y2) order parameter Δk=Δ0 (cos kx−cos ky). The actual functional dependence is not important: any reasonable model that yields the gap nodes located at the same directions4647 would produce a very similar angular dependence. (c) The temperature dependence of the difference of C/T at 0° and 45°, a crossover is clearly seen at ~2.9 K. The random error bars (after the averaging of 300 data points) of specific heat are ±0.04 mJ mol−1 K−2. (d) Possible locations of nodes or gap minima suggested by our data are shown by the red and blue balls on the folded electron Fermi pockets, and by red segments on the hole Fermi surfaces. The ellipticity of the electron pockets is exaggerated in this drawing.

Mentions: The FeSe0.45Te0.55 single crystals were grown using the self-flux method. Details regarding the growth of the samples are given in the Methods section. In Figure 1a, we plot the resistivity in a wide temperature range; a broad bump appears in the intermediate temperature regime, which seems to be an intrinsic feature of the FeSexTe1−x system and has been reported by others28. The resistive transition at 14.5 K is narrower than 0.5 K (10–90% ρn). The magnetization measured in zero-field-cooling process demonstrates a perfect Meissner effect, as shown in Figure 1b. The magnetic field dependence of the resistivity is shown in Figure 1c (H//ab) and Figure 1d (H//c). The broadening of the resistive transition is quite small, indicating a high upper critical field. In the Figure 1e, we show the temperature dependence of the upper critical fields with two field orientations. In H//c, the superconducting transition temperature decreases by ~1.79 K at 9 T, but only by 0.91 K in H//ab. The slope of the upper critical field is dHc2,ab(T)/dT/T=Tc=−10.4 T/K, and dHc2,c(T)/dT/T=Tc=−5.26 T/K, yielding an anisotropy ~2. The sharp magnetic and resistive transitions, together with the very small residual-specific heat coefficient γ0 (see Methods), demonstrate the good quality of the sample and allow us to proceed with the ARSH measurements, as shown in Figure 2a–c.


Anisotropic structure of the order parameter in FeSe(0.45)Te(0.55) revealed by angle-resolved specific heat.

Zeng B, Mu G, Luo HQ, Xiang T, Mazin II, Yang H, Shan L, Ren C, Dai PC, Wen HH - Nat Commun (2010)

Angle dependence of specific heat coefficient and proposed positions of gap minimum.Data measured at (a) 3.65, 3.7 and 3.75 K and (b) 2.6, 2.65 and 2.7 K in the in-plane magnetic field of 9 T, where α is the angle between the field and the Fe-Se-Fe bond direction. Fourfold oscillations are observed and the amplitude is ~0.12 mJ mol−1 K−2 (T=2.6 K). The fourfold oscillations were repeatable in two separate samples. The maximum of C/T is located at about zero degrees (H//Fe-Se-Fe), whereas the sign of the oscillations is reversed when the temperature is increased to 3.7 K. The red lines are theoretical simulations (see Supplementary Methods) using the d(x2−y2) order parameter Δk=Δ0 (cos kx−cos ky). The actual functional dependence is not important: any reasonable model that yields the gap nodes located at the same directions4647 would produce a very similar angular dependence. (c) The temperature dependence of the difference of C/T at 0° and 45°, a crossover is clearly seen at ~2.9 K. The random error bars (after the averaging of 300 data points) of specific heat are ±0.04 mJ mol−1 K−2. (d) Possible locations of nodes or gap minima suggested by our data are shown by the red and blue balls on the folded electron Fermi pockets, and by red segments on the hole Fermi surfaces. The ellipticity of the electron pockets is exaggerated in this drawing.
© Copyright Policy - open-access
Related In: Results  -  Collection

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f2: Angle dependence of specific heat coefficient and proposed positions of gap minimum.Data measured at (a) 3.65, 3.7 and 3.75 K and (b) 2.6, 2.65 and 2.7 K in the in-plane magnetic field of 9 T, where α is the angle between the field and the Fe-Se-Fe bond direction. Fourfold oscillations are observed and the amplitude is ~0.12 mJ mol−1 K−2 (T=2.6 K). The fourfold oscillations were repeatable in two separate samples. The maximum of C/T is located at about zero degrees (H//Fe-Se-Fe), whereas the sign of the oscillations is reversed when the temperature is increased to 3.7 K. The red lines are theoretical simulations (see Supplementary Methods) using the d(x2−y2) order parameter Δk=Δ0 (cos kx−cos ky). The actual functional dependence is not important: any reasonable model that yields the gap nodes located at the same directions4647 would produce a very similar angular dependence. (c) The temperature dependence of the difference of C/T at 0° and 45°, a crossover is clearly seen at ~2.9 K. The random error bars (after the averaging of 300 data points) of specific heat are ±0.04 mJ mol−1 K−2. (d) Possible locations of nodes or gap minima suggested by our data are shown by the red and blue balls on the folded electron Fermi pockets, and by red segments on the hole Fermi surfaces. The ellipticity of the electron pockets is exaggerated in this drawing.
Mentions: The FeSe0.45Te0.55 single crystals were grown using the self-flux method. Details regarding the growth of the samples are given in the Methods section. In Figure 1a, we plot the resistivity in a wide temperature range; a broad bump appears in the intermediate temperature regime, which seems to be an intrinsic feature of the FeSexTe1−x system and has been reported by others28. The resistive transition at 14.5 K is narrower than 0.5 K (10–90% ρn). The magnetization measured in zero-field-cooling process demonstrates a perfect Meissner effect, as shown in Figure 1b. The magnetic field dependence of the resistivity is shown in Figure 1c (H//ab) and Figure 1d (H//c). The broadening of the resistive transition is quite small, indicating a high upper critical field. In the Figure 1e, we show the temperature dependence of the upper critical fields with two field orientations. In H//c, the superconducting transition temperature decreases by ~1.79 K at 9 T, but only by 0.91 K in H//ab. The slope of the upper critical field is dHc2,ab(T)/dT/T=Tc=−10.4 T/K, and dHc2,c(T)/dT/T=Tc=−5.26 T/K, yielding an anisotropy ~2. The sharp magnetic and resistive transitions, together with the very small residual-specific heat coefficient γ0 (see Methods), demonstrate the good quality of the sample and allow us to proceed with the ARSH measurements, as shown in Figure 2a–c.

Bottom Line: So far the experimental data and theoretical models have been highly controversial.Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes').Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.

View Article: PubMed Central - PubMed

Affiliation: National Laboratory for Superconductivity, Institute of Physics and National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100190, China.

ABSTRACT
The central issues for understanding iron (Fe)-based superconductors are the symmetry and structure of the superconducting gap. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ('nodes'). A unique method for addressing this issue, and one of very few methods that are bulk and angle resolved, is measuring the electronic-specific heat in a rotating magnetic field. In this study, we present the first such measurement for an Fe-based high-T(c) superconductor. We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction. Our results are consistent with the expectations for an extended s-wave model, with a significant gap anisotropy on the electron pockets and the gap minima along the ΓM (Fe-Fe bond) direction.

No MeSH data available.


Related in: MedlinePlus