论文标题
清洁$ s $ - 和$ d_ {x^2-y^2} $的上部关键诱导的角度依赖性 - 带有自稳态的椭圆形有效质量和Zeeman Anisotropies的波浪超导体
Angular dependence of the upper critical induction of clean $s$- and $d_{x^2-y^2}$-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies
论文作者
论文摘要
我们采用SCHR {Ö}浸入式diRAC方法，该方法始终始终如一地将椭圆形有效的质量各向异性概括为旋转和轨道有效的质量各向异性自我，这一点很重要，当Pauli限制对单线超导性的临界场特征的影响时，这一点很重要。通过使用KLEMM-CLEM转换将运动方程映射到各向同性形式中，我们在任意方向和温度方向$ b_ {c2}（θ，ϕ，t）$计算上的临界磁性磁感应$ b_ {c2} $ $ s $ s $ s $ - wave和anisotropic $ d_ d_ d _ {x 2^2^2^2^^2^^2^^2^^2^^2^^2 Y^^2 Y^^2 Y-wave。至于各向异性$ S $ - 波超导体，降低的上部关键场$ b_ {c2} $在最低有效质量的方向上最大，并且与通用方向因子$α（θ，ϕ）$成比例。 However, for $d_{x^2-y^2}$-wave pairing, ${\bm B}_{c2}(π/2,ϕ,T)$ exhibits either a four-fold pattern with $C_4$ symmetry just below the transition temperature $T_c$ that rotates by $π/4$ as $T$ is lowered, or a two-fold pattern with $C_2$ symmetry, depending upon the平面有效质量各向异性。这提供了一种新的方法，可以在干净的非常规超导体中区分这些配对对称性。
We employ the Schr{ö}dinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm-Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic induction $B_{c2}(θ, ϕ, T)$ at arbitrary directions and temperatures $T$ for isotropic $s$-wave and for anisotropic $d_{x^2-y^2}$-wave superconducting order parameters. As for anisotropic $s$-wave superconductors, the reduced upper critical field $b_{c2}$ is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factor $α(θ,ϕ)$. However, for $d_{x^2-y^2}$-wave pairing, ${\bm B}_{c2}(π/2,ϕ,T)$ exhibits either a four-fold pattern with $C_4$ symmetry just below the transition temperature $T_c$ that rotates by $π/4$ as $T$ is lowered, or a two-fold pattern with $C_2$ symmetry, depending upon the planar effective mass anisotropy. This provides a new method to distinguish these pairing symmetries in clean unconventional superconductors.
