Majorana Multipole Response of Topological Superconductors

Abstract

In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensedmatter 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.

Tuning the Parity Mixing of Singlet-Septet Pairing in a Half-Heusler Superconductor

“…It has been proposed that the existence or absence of gap nodes in the singlet-septet state critically affects novel phenomena, such as topological Majorana surface states [24,25] with intriguing multiple responses [26]. Thus our findings provide a novel perspective on research for topological superconducting states.…”

“…In the previous studies [12], however, it has not been clarified whether the nodes in the super-conducting gap are symmetry-protected or not. We note that such a nodal singlet-septet state and time-reversal symmetry breaking E or T 2 states can have different exotic topological properties [23][24][25][26]. Moreover, recent theoretical studies have suggested other types of possible topological superconducting states with s-wave singlet and d-wave quintet components [21,22].…”

Inducing chiral superconductivity on honeycomb lattice systems

“…Localized Majorana states exist at the boundaries of topological superconductors, and can be created by placing chains or islands of magnetic atoms on an s-wave superconductor [31,32]. Realization of superconductivity by proximity using hybrid systems, combining magnetism and strong spin orbit coupling, creates novel quasi-particle excitations that open new possibilities for the realization of topological superconductor phases in experiments [33][34][35][36]. The ability to control and tune different phases can be experimentally achieved, allowing their characterization through measurements such as magneto-resistance and related transport probes.…”

Josephson effect of superconductors with J=32 electrons

“…Such high angular-momentum pairing states would feature superconducting phenomena of a J = 3 2 superconductor. At present, however, only little has been known about the physics of superconductors with J = 3 2 electrons [20,21]. In this paper, we discuss a low-energy transport property unique to J = 3 2electron superconductors.…”