Symmetry Breaking and Berry Curvature in 2D Janus γ-Ge ₂ XY (X, Y = S, Se, and Te)

Two-dimensional (2D) Janus materials have recently attracted considerable attention as promising building blocks for next-generation multifunctional nanoscale devices owing to the unconventional physical phenomena arising from their intrinsic structural asymmetry. In this study, we demonstrate that the sombrero-shaped electronic dispersion in monolayer Janus γ-Ge₂XY (X, Y = S, Se, Te) produces a pronounced Berry curvature. To elucidate the spin-resolved origin of this Berry-curvature response, we incorporate spin-orbit coupling (SOC) into the band-structure calculations, which reveals momentum-dependent Zeeman-type spin splitting along the Γ-centered inverted-sombrero rim as well as opposite spin polarizations at the K₁ and K₁' valleys. Subsequent Berry-curvature analyses show that γ-Ge₂SSe and γ-Ge₂SeTe possess comparable magnitudes of approximately 129 and 110 Ų, respectively, but with opposite signs at K₁ and K₁'. Remarkably, γ-Ge₂STe exhibits an even larger Berry curvature of about 180 Ų, underscoring its enhanced potential for valleytronic and spintronic applications.