Bandgap transition and second-harmonic generation in ABC and ACB stacked γ-trilayers of Janus-Ga₂SeTe

Stacking engineering has been investigated in even-layer and bulk Janus-Ga₂SeTe, but whether odd-layer systems host unconventional physics remains unclear. In this work, we study the influence of stacking order on the physical properties of γ-phase trilayers of Janus-Ga₂SeTe using first-principles calculations. Despite identical space groups and similar bandgaps (∼1 eV), the γ[ABC] and γ[ACB] trilayers show indirect and direct bandgaps, respectively. Stacking-modulated built-in electric fields of 0.471 V nm^-1 (ABC) and 0.434 V nm^-1 (ACB) modulate orbital hybridization, charge delocalization, and spin textures, highlighting that the stacking sequence becomes capable of altering band topology in such an odd-layer system. By contrast, such bandgap-type switching is absent in their bilayers and bulk phases, revealing an odd-even layer effect. A pronounced change in out-of-plane nonlinear response is found, where the static d₃₃ coefficient retains 93.6% of the monolayer value in γ[ABC] but drops to only 15.9% in γ[ACB]. As a result, by comparing with the even bilayer, the alternatively stacked odd trilayers enable control over band type, spin-orbit coupling competition, and nonlinear polarization. Our work establishes odd-even layer parity as a new design paradigm for Janus multilayer optoelectronics.