Identification of nematic superconductivity from the upper critical field

Jörn W. F. Venderbos; Vladyslav Kozii; Liang Fu

doi:10.1103/PhysRevB.94.094522

paper

Identification of nematic superconductivity from the upper critical field

arXiv:1603.03406 · doi:10.1103/PhysRevB.94.094522

Abstract

Recent nuclear magnetic resonance and specific heat measurements have provided concurring evidence of spontaneously broken rotational symmetry in the superconducting state of the doped topological insulator Cu $_{x}$ Bi $_{2}$ Se $_{3}$ . This suggests that the pairing symmetry corresponds to a two-dimensional representation of the $D_{3 d}$ crystal point group, and that Cu $_{x}$ Bi $_{2}$ Se $_{3}$ is a nematic superconductor. In this work, we present a comprehensive study of the upper critical field $H_{c 2}$ of nematic superconductors within Ginzburg-Landau (GL) theory. Contrary to typical GL theories which have an emergent U(1) rotational symmetry obscuring the discrete symmetry of the crystal, the theory of two-component superconductors in trigonal crystals reflects the true $D_{3 d}$ crystal symmetry. This has direct implications for the upper critical field. First, $H_{c 2}$ of trigonal superconductors exhibits a sixfold anisotropy in the basal plane. Second, when the degeneracy of the two components is lifted by, e.g., uniaxial strain, $H_{c 2}$ exhibits a twofold anisotropy with characteristic angle and temperature dependence. Our thorough study shows that measurement of the upper critical field is a direct method of detecting nematic superconductivity, which is directly applicable to recently-discovered trigonal superconductors Cu $_{x}$ Bi $_{2}$ Se $_{3}$ , Sr $_{x}$ Bi $_{2}$ Se $_{3}$ , Nb $_{x}$ Bi $_{2}$ Se $_{3}$ , and Tl $_{x}$ Bi $_{2}$ Se $_{3}$ .

6 pages, 2 figs; 20 pages supplemental material; published version

Identification of nematic superconductivity from the upper critical field

Abstract

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