High-Eccentricity Tidal Migration Driven by Secular Chaos in Wide-Binary Systems

High-eccentricity tidal migration driven by a distant stellar companion offers a natural pathway for producing some hot Jupiters; yet, most theoretical work has relied on an idealized three-body configuration whose simplicity makes the problem especially tractable. In reality, many cold-Jupiter systems may host additional planets or substellar objects, whose interactions can dramatically alter the pathways to secularly excite extreme eccentricities. We investigate how secular chaos can drive high-eccentricity tidal migration in hierarchical ``3+1'' systems--stellar binaries hosting a planet and an additional intermediate companion orbiting the primary star. We show that the onset of secular chaos is regulated by the ratio of the von-Zeipel-Lidov-Kozai (ZLK) timescales of the inner and outer orbits R. When R about 0.5-2, most systems can undergo migration even when their mutual inclinations remain modest--below the 39.2 critical angle for ZLK oscillations--with diffusion timescales spanning a broad range, up to thousands of inner orbit ZLK timescales. For larger mutual inclinations, secular migration operates over a much broader region of parameter space with R about 0.05-100, but most evolutionary pathways become non-secular and potentially unstable--behavior recently identified as an alternative pathway to tidal migration. Our model predicts hot Jupiters in nearly polar orbits relative to both the host star's stellar equator (stellar obliquities about 60-120) and the orbits of the outer two companions. Future Gaia releases and long-term radial velocity campaigns are likely to uncover additional ``3+1'' systems, providing valuable opportunities to test this migration pathway.