Chiral topological superconductivity arising from the interplay of geometric phase and electron correlation

Abstract

In modern theory of solids, many-electron correlations can give rise to superconductivity, while the Berry or geometric phase is responsible for non-trivial topology. So far, these two physical ingredients have been taken into account only in a simple additive manner. Here, we carry out a systematic study of the interplay between geometric phase and electron correlation as well as their combined effects on topological and superconducting properties. Based on first-principles studies of Pb3Bi/Ge(111) as a prototypical system, we develop a generic two-dimensional effective formalism that respects hexagonal symmetry with Rashba spin–orbit coupling, displays a van Hove singularity and includes geometric phase-decorated electron correlations. Our functional renormalization group analysis shows that superconductivity dominates the competing orders in the weak interaction regime, with two consequences. First, the renormalized geometric phase flows to three stable fixed points, favouring chiral (px ± ipy)-wave and f-wave superconducting states. Second, the corresponding superconductivity can be substantially enhanced. We construct the phase diagram of the topological quantum states, and identify hole-doped Pb3Bi/Ge(111) as an appealing platform for realizing chiral topological superconductivity in two-dimensional systems that are highly desirable for detecting and braiding Majorana fermions. Renormalization group calculations incorporate band structure and interaction effects on an equal footing. Applying this methodology to Ge-doped Pb3Bi shows that this material is a chiral topological superconductor and hosts Majorana fermions.