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

Flat bands are associated with a range of desirable physical phenomena and potential applications, including enhanced superconducting tendencies due to the high density of states, strongly correlated phases such as quantum Hall states. Systems in which flat bands can be switched or tuned are therefore of particular interest. In this study, we analyze the electronic structure of two-dimensional electron gases (2DEGs) subjected to a linearly increasing magnetic-field dipole together with a transverse electric field, using the operator formalism of the quantum harmonic oscillator. When the electric field magnitude is tuned to a sequence of discrete values, different levels of energy bands are flattened. Moreover, at a specific electric field strength, the ground-state wave function admits an exact closed-form solution that can be understood through the magnetic drifts cancellation in the classical electrodynamics. We also demonstrate two distinct transmission properties, the quantized Hall conductance and the enhanced density of states, of the electrically switchable flat band. These findings establish a new route toward magnetoelectric band engineering and electrically guided transport in low-dimensional systems.