Demonstration of Self-Balance Mechanism with Bloch Oscillations in Momentum Bandgap Engineering.

We investigate Bloch oscillations in a lattice system featuring a momentum gap (k gap), where in-gap modes exhibit exponential growth or decay. We demonstrate that the interplay of k-gap amplification, attenuation, and interband interference gives rise to a critical regime, where the wave packet alternates between the growing and decaying channels, forming a period-doubled oscillation with globally stable intensity under critical driving-a phenomenon we term self-balanced Bloch oscillations. This self-balance arises from phase-accumulation-dependent selection of the k-gap channels during band traversal, as confirmed by numerical simulations and spectral analysis. This mechanism, broadly applicable to k-gap-engineered systems, not only enables intrinsic stabilization beyond mere amplification but also offers a powerful route for controlling wave propagation in time-varying media and non-Hermitian physics.