Searching for even-denominator states in wide quantum wells with self-attention neural networks

Recent experiments have shown that wide quantum wells host exotic even-denominator Hall states, in correspondence of a bilayer metallic charge distribution with significant interlayer tunneling at zero magnetic field. These even-denominator states are robust and promise a pathway to realizing fault-tolerant topological quantum computing. In this work, we use a self-attention neural network to study quantum wells in three-dimensions for a variety of electron densities and well thicknesses. At zero magnetic field, we find a monolayer to bilayer transition that is in quantitative agreement with experiments. We characterize these states by their one-body reduced density matrix, highlighting their different in-plane momentum distribution and out-of-plane occupation. Incorporating out-of-plane magnetic fields, we study the character of quantum Hall states during the transition from monolayer to bilayer. By comparing with experiment, we find our method is quantitatively accurate and holds the promise to become a new standard in the study of realistic semiconductor systems.