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

Aiying Zhao; Qiang Gu; Richard A. Klemm

doi:10.1088/1361-648X/ac75a4

paper

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

arXiv:2204.01246 · doi:10.1088/1361-648X/ac75a4

Abstract

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 $B_{c 2} (θ, ϕ, T)$ 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 $b_{c 2}$ 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, $B_{c 2} (π /2, ϕ, T)$ 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.

12 pages, 8 figures

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Angular dependence of the upper critical induction of clean s- and dx2−y2​-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies

Abstract

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Cited by in corpus (1)

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