Carrier-Envelope Phase Control of Orbital Angular Momentum in Solid-State High-Harmonic Generation

High-order harmonic generation (HHG) driven by optical vortices is a powerful route to produce structured light in different spectral regions. The nonlinear process transfers orbital angular momentum (OAM) from the driving field to the emitted harmonics according to the scaling law $l_q = q\times l$, a consequence of the rotational invariance and angular momentum conservation. Here, we show that, in the regime of few-cycle pulses, the topological charge (TC) of the harmonic radiation detected within a finite spectral window is no longer fixed by this scaling law alone, but is governed by the interplay between broken crystal inversion symmetry and carrier-envelope phase (CEP)-sensitive sub-cycle electron dynamics. By driving HHG in a ZnO crystal with few-cycle ($\approx 1.5$ cycles) vortex beams centered at 3.2~$\mu$m, we observed that the measured TC becomes strongly CEP-dependent, switching between adjacent integer values, but only when the inversion symmetry is broken and the harmonic emission is CEP-sensitive. The TC switching vanishes when either condition is removed. Numerical analysis reveals that the TC switching originates from a CEP-controlled redistribution of spectral weight among spectrally overlapping harmonic orders, which changes the dominant OAM channel within the detection window. These results identify the CEP as a degree of freedom for tailoring the topological structure of high-harmonic radiation, pointing toward waveform-controlled structured attosecond light sources.