We theoretically investigate the electronic properties of twisted bilayer systems formed by two coupled anisotropic two-dimensional electron gases (2DEGs) with different effective masses along orthogonal directions, subjected to in-plane and out-of-plane magnetic fields, as well as a perpendicular electric bias. Within a two-band effective mass approximation, we derive and solve the $2\times 2$ Schrödinger Hamiltonian analytically, obtaining exact expressions for the energy spectra and layer-resolved wave functions. We demonstrate that the interlayer coupling energy breaks the energy degeneracy, creating bonding and antibonding subbands whose splitting competes with the bias voltage to control the degree of layer decoupling. The in-plane magnetic field induces momentum-space shifts, leading to the anticrossing of energy dispersion curves when coupling is present. In contrast, the combination of perpendicular electric and in-plane magnetic fields generates a two-valley structure with distinct Fermi surfaces. Remarkably, we identify a Rashba-like term acting on the pseudospin space that emerges exclusively from the twist between anisotropic layers, providing spin-orbit-like coupling without intrinsic spin-orbit interaction. For the Landau level spectrum, we derive analytical expressions revealing a twist-angle-dependent deviation from the conventional linear magnetic field dependence, arising from an effective complex interlayer coupling that introduces a unique twist-angle/magnetic-field coupling. This coupling enables tunable control of inter-Landau-level optical transition energies, with field- and level-dependent blueshifts and redshifts.

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• Electronic structure
• Landau levels
• 2-dimensional systems
• Twisted heterostructures
• Two-dimensional electron gas
• Effective mass theory