| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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Effect of Anisotropic Impurity Scattering in D-Wave Superconductors |
| Ze-Long Wang1, Rui-Ying Mao1, Da Wang1,2*, and Qiang-Hua Wang1,2* |
1National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing 210093, China
2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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| Cite this article: |
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Ze-Long Wang, Rui-Ying Mao, Da Wang et al 2023 Chin. Phys. Lett. 40 057402 |
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Abstract In $d_{x^2-y^2}$-wave superconductors, the effect of s-wave point disorder has been extensively studied in literature. We study the anisotropic disorder in the form of $V_{kk'}^{\rm imp}=V_{\rm i}f_{k}f_{k'}$ with $f_k=\cos(2\theta)$ ($\theta$ the azimuthal angle of $k$), as proposed to be caused by apical oxygen vacancies in overdoped La-based cuprate films, under the Born approximation. The disorder self-energy and d-wave pairing affect each other and must be solved simultaneously self-consistently. We find that the self-energy is reduced at low frequencies and thus weakens the pair-breaking effect. This frequency dependence vanishes in the dirty limit for which the disorder is well described by a scattering rate $\varGamma_k=\varGamma_{\rm i}f_k^2$. One consequence of the disorder effect is that the gap-to-$T_{\rm c}$ ratio $2\varDelta(0)/T_{\rm c}$ is greatly enhanced by the d-wave disorder, much larger than the s-wave disorder and the clean BCS value $4.28$. Lastly, we generalize the d-wave scattering rate to a general form $\varGamma_\theta=\varGamma_\alpha|\theta-\theta_0|^\alpha$ around each nodal direction $\theta_0$. We find the density of states $\rho(\omega)-\rho(0)\propto|\omega|$ ($\omega^2$) for all $\alpha\ge1$ ($\alpha < 1$) in the limit of $\omega\to0$. As a result, the superfluid density $\rho_{\rm s}$ exhibits two and only two possible scaling behaviors: $\rho_{\rm s}(0)-\rho_{\rm s}(T)\propto T$ ($T^2$) for $\alpha\ge1$ ($\alpha < 1$) in the low temperature limit.
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Received: 07 March 2023
Published: 04 May 2023
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| PACS: |
74.62.En
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(Effects of disorder)
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74.72.-h
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(Cuprate superconductors)
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74.20.-z
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(Theories and models of superconducting state)
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