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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2306.00259 |
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| author | Kogan, V. G. Prozorov, R. |
| author_facet | Kogan, V. G. Prozorov, R. |
| contents | We study the slopes of the upper critical field $\partial_{T}H_{c2}|_{T_{c}}\equiv\partial H_{_{c2}}/\partial T$ at $T_{c}$ in anisotropic superconductors with transport (non-magnetic) scattering employing the Ginzburg-Landau theory, developed for this situation by S. Pokrovsky and V. Pokrovsky, Phys. Rev. B 54, 13275 (1996). We found unexpected behavior of the slopes for a $d-$wave superconductor and in a more general case of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes $\partial_{T}H_{c2}|_{T_{c}}$ to decrease with increasing non-magnetic scattering parameter $P$, unlike the nodeless case where the slope increases. In a pure $d-$wave case, the slope $\partial H_{c2}|_{T_{c}}$ changes from decreasing to increasing when scattering parameter approaches $P\approx0.91\,P_{\rm crit}$, where $P_{\rm crit}\approx0.2807$ at which $T_{c}\to0$ that implies the the existence of a gapless state in $d-$wave superconductors with transport scattering in the interval, $0.91\,P_{\rm {crit}}<P<P_{\rm crit}$. Furthermore, we have considered the mixed $s+d$ order parameter that has 4 nodes on a cylindrical Fermi surface when a $d-$part is dominant, or no nodes at all when an $s-$phase is the major one. We find that presence of nodes causes the slope $\partial_{T}H_{c2}|_{T_{c}},$ to decrease initially with increasing $P$, whereas in the nodeless state, $\partial_{T}H_{c2}|_{T_{c}}$ monotonically increases. Therefore, fairly straightforward experiments make it possible to decide whether or not the order parameter of a superconductor has nodes by measuring the disorder-dependence of the slope of $H_{c2}$ at $T_{c}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_00259 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors Kogan, V. G. Prozorov, R. Superconductivity We study the slopes of the upper critical field $\partial_{T}H_{c2}|_{T_{c}}\equiv\partial H_{_{c2}}/\partial T$ at $T_{c}$ in anisotropic superconductors with transport (non-magnetic) scattering employing the Ginzburg-Landau theory, developed for this situation by S. Pokrovsky and V. Pokrovsky, Phys. Rev. B 54, 13275 (1996). We found unexpected behavior of the slopes for a $d-$wave superconductor and in a more general case of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes $\partial_{T}H_{c2}|_{T_{c}}$ to decrease with increasing non-magnetic scattering parameter $P$, unlike the nodeless case where the slope increases. In a pure $d-$wave case, the slope $\partial H_{c2}|_{T_{c}}$ changes from decreasing to increasing when scattering parameter approaches $P\approx0.91\,P_{\rm crit}$, where $P_{\rm crit}\approx0.2807$ at which $T_{c}\to0$ that implies the the existence of a gapless state in $d-$wave superconductors with transport scattering in the interval, $0.91\,P_{\rm {crit}}<P<P_{\rm crit}$. Furthermore, we have considered the mixed $s+d$ order parameter that has 4 nodes on a cylindrical Fermi surface when a $d-$part is dominant, or no nodes at all when an $s-$phase is the major one. We find that presence of nodes causes the slope $\partial_{T}H_{c2}|_{T_{c}},$ to decrease initially with increasing $P$, whereas in the nodeless state, $\partial_{T}H_{c2}|_{T_{c}}$ monotonically increases. Therefore, fairly straightforward experiments make it possible to decide whether or not the order parameter of a superconductor has nodes by measuring the disorder-dependence of the slope of $H_{c2}$ at $T_{c}$. |
| title | Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2306.00259 |