Quantized Landau-level crossing checkerboards for cryogenic magnetometry

Abstract When charge transport occurs under conditions such as topological protection or ballistic motion, the conductance of low-dimensional systems often exhibits quantized values in units of e 2 / h, underpinning advances in quantum metrology and computing. Here we report a quantized quantity: the ratio of displacement field to magnetic field, D / B, in large-twist-angle bilayer graphene. In high magnetic fields, Landau-level crossings between the top and bottom layers produce equal-sized checkerboard patterns across the D / B – ν space. These arise from electric-field-driven interlayer charge transfer of one elementary charge per flux quantum, yielding quantized critical displacement intervals, δ D = e2{{ }l₁^2} e 2 π l B 2, where l B is the magnetic length. This mechanism offers a route to magnetic sensing, as the displacement-to-magnetic-field ratio is defined solely by fundamental constants. We propose a prototype magnetometer based on this principle, potentially enabling planar mapping of magnetic fields with micrometre resolution via large-twist-angle bilayer graphene sensor arrays. Our results demonstrate that interlayer charge transfer in the quantum Hall regime gives rise to novel phenomena with potential applications in cryogenic magnetometry.