Modulation of bilayer quantum Hall states by tilted-field-induced subband-Landau-level coupling

We study effects of tilted magnetic fields on energy levels in a double-quantum-well (DQW) system, focusing on the coupling of subbands and Landau levels (LLs). The subband-LL coupling induces anticrossings between LLs, manifested directly in the magnetoresistance. The anticrossing gap becomes larger than the spin splitting at the tilting angle $\theta \sim 20^\circ $ and larger than the cyclotron energy at $\theta \sim 50^\circ $, demonstrating that the subband-LL coupling exerts a strong influence on quantum Hall states even in at a relatively small $\theta $ and plays a dominant role for larger $\theta $. We also find that when the DQW potential is asymmetric, LL coupling occurs even within a subband. Calculations including higher-order coupling reproduce the experimental results quantitatively well.