Majorana multipole response of topological superconductors

Abstract

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for surface helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify nonconventional pairing symmetry via the magnetic response of surface MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but those on superconductors with spin-3/2 electrons may display a magnetic-octupole response in leading order, which uniquely characterizes high-spin superconductors. Detection of such an octupole response provides direct evidence of high-spin superconductivity, such as in half-Heusler superconductors.

17 pages, 5 figures

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• Theory of Magnetic-Texture-Induced Anomalous Hall Effect on the Surface of Topological Insulators
• Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors
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• Inducing chiral superconductivity on honeycomb lattice systems
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Spin Susceptibility of a J=3/2 Superconductor
• Josephson effect of superconductors with $J=3/2$ electrons
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• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Euler band topology in superfluids and superconductors
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Singular flat bands in three dimensions: Landau level spreading, quantum geometry, and Weyl reconstruction