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 = $$\frac{e}{2{{\uppi }}{l}_{B}^{2}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfrac> </mml:math> , 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.