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The super-Planckian features of radiative heat transfer in the near-field areknown to depend strongly on both material and geometric design properties.However, the relative importance and interplay of these two facets, and thedegree to which they can be used to ultimately control energy flow, remains anopen question. Recently derived bounds suggest that enhancements as large as$|\chi|^4 \lambda^{2} / \left(\left(4\pi\right)^{2} \Im\left[\chi\right]^{2}d^{2}\right)$ are possible between extended structures (compared to blackbody);but neither geometries reaching this bound, nor designs revealing the predictedmaterial ($\chi$) scaling, have been previously reported. Here, exploitinginverse techniques, in combination with fast computational approaches enabledby the low-rank properties of elliptic operators for disjoint bodies, weinvestigate this relation between material and geometry on an enlarged spacestructures. Crucially, we find that the material proportionality given abovedoes indeed emerge in realistic structures. In reaching this result, we alsoshow that (in two dimensions) lossy metals such as tungsten, typicallyconsidered to be poor candidate materials for strongly enhancing heat transferin the near infrared, can be structured to selectively realize flux rates thatcome within $50\%$ of those exhibited by an ideal pair of resonant losslessmetals for separations as small as $2\%$ of a tunable design wavelength.

Material Scaling and Frequency-Selective Enhancement of Near-Field Radiative Heat Transfer for Lossy Metals in Two Dimensions via Inverse Design