Engineering Helical Superconductors with Multiple Majorana Kramers Pairs via Higher-Order Rashba Spin-Orbit Coupling

Abstract

The momentum dependence of Rashba spin-orbit coupling (RSOC) is a key ingredient for engineering topological superconductors (TSCs), yet research has overwhelmingly focused on its linear-in-momentum form. This focus has restricted time-reversal invariant TSCs to helical $p$-wave states, which are characterized by a $\mathbb{Z}_2$ topological invariant that permits at most a single Majorana Kramers pair at a given boundary. Their existence has also been tied to the stringent criterion of an odd number of Fermi surfaces (FSs). In this work, we establish higher-order RSOC as a powerful design principle to go beyond the $\mathbb{Z}_2$ classification and the odd-FS criterion. We demonstrate that a bilayer system with a pure cubic RSOC and an intrinsic odd-parity pairing on a single FS yields a rare 2D helical $f$-wave TSC. This state is characterized by a large mirror Chern number (MCN) of ${\cal N}_{\text{M}}=3$ and hosts three Kramers pairs of Majorana edge modes. Remarkably, the interplay of linear and cubic RSOCs in this bilayer can generate a helical hybrid $p+f$-wave TSC with an even larger MCN of ${\cal N}_{\text{M}}=4$ from a normal state with two FSs, thereby circumventing the conventional odd-FS criterion. Our work establishes higher-order RSOC as a "topology multiplier" for realizing TSCs with multiple Majorana Kramers channels, fundamentally reshapes the criteria for helical TSCs, and holds immediate relevance for tunable platforms like oxide heterostructures.