Electrically Controllable Flat Band in Two-Dimensional Electron Gases under Nonuniform Magnetic Fields

Flat bands underlie a diverse range of quantum phenomena, from strongly correlated phases to superconductivity. We theoretically establish that a two-dimensional electron gas under a linear magnetic-field gradient and a transverse electric field exhibits electrically tunable flat bands. At specific field values, these bands become strictly dispersionless. By providing exact classical and quantum solutions, we demonstrate that these states are high-order Landau levels associated with drift-compensated cyclotron orbits of carriers arising from the synergy between the magnetic-field gradient and the electric field. These electrically controllable Landau levels exhibit quantized Hall conductance and a strongly enhanced density of states. Our results provide a new route for flat-band creation, magnetoelectric band engineering, and quantized Hall currents controlled via source-drain voltage.