Zhao A, Gu Q, Klemm RA. Angular dependence of the upper critical induction of clean
s- and
dx2-y2-wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies.
JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022;
34:355601. [PMID:
35654027 DOI:
10.1088/1361-648x/ac75a4]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2022] [Accepted: 06/01/2022] [Indexed: 06/15/2023]
Abstract
We employ the Schrödinger-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 inductionBc2(θ,ϕ,T)at arbitrary directions and temperaturesTfor isotropics-wave and for anisotropicdx2-y2-wave superconducting order parameters. As for anisotropics-wave superconductors,Bc2is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factorα(θ,ϕ). However, fordx2-y2-wave pairing and vanishing planar effective mass anisotropy,Bc2(π/2,ϕ,T)exhibits a four-fold azimuthal pattern withC4symmetry the maxima of which are along the crystal axes just below the transition temperatureTc, but these maxima are rotated byπ/4about thezaxis asTis lowered to 0. However fordx2-y2-wave pairing with weak planar effective mass anisotropy,Bc2(π/2,ϕ,T)exhibits a two-fold pattern withC2symmetry for allT ⩽ Tc, which also rotates byπ/4about thezaxis asTis lowered to 0. These low planar effective mass anisotropy cases provide a new method to distinguishs-wave anddx2-y2-wave pairing symmetries in clean unconventional superconductors.
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