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This paper reports the discovery that resistively-coupled coplanar waveguides in van der Waals heterostructures are dominated by Hall conductivity rather than longitudinal conductivity, unlike traditional capacitively-coupled systems. We observed clear integer quantum Hall effect plateaus that were frequency-independent from below 1 GHz to over 7 GHz, with sensitivity strongly dependent on device geometry. We developed a T-network circuit model that successfully explains the nearly threefold enhancement in measurement sensitivity observed in samples with long contact regions compared to theoretical predictions. This work establishes important design principles for microwave measurements of two-dimensional electron systems in van der Waals materials and opens pathways for contactless characterization of materials where Ohmic contacts are challenging to achieve. 

Abstract Element isotopes are characterized by distinct atomic masses and nuclear spins, which can significantly influence material properties. Notably, however, isotopes in natural materials are homogenously distributed in space. Here, we propose a method to configure material properties by repositioning isotopes in engineered van der Waals (vdW) isotopic heterostructures. We showcase the properties of hexagonal boron nitride (hBN) isotopic heterostructures in engineering confined photon-lattice waves—hyperbolic phonon polaritons. By varying the composition, stacking order, and thicknesses of h 10 BN and h 11 BN building blocks, hyperbolic phonon polaritons can be engineered into a variety of energy-momentum dispersions. These confined and tailored polaritons are promising for various nanophotonic and thermal functionalities. Due to the universality and importance of isotopes, our vdW isotope heterostructuring method can be applied to engineer the properties of a broad range of materials.