<p>RT 1 addresses electron transport across mixed-dimensional heterostructures, in which the heterogeneities in dimensions (<em>e.g.</em>, 0D, 2D, 3D) and materials properties are used to precisely manipulate electron transport, allowing only electrons with a specific energy and momentum to participate in electron tunneling. This energy/momentum filtering can lower the effective electron temperature to extreme values (<em>e.g.</em>,&lt;1K), allowing the study of ultra-cold electrons across hetero-dimensional components at room temperature. Novel electronic, spintronic, and optoelectronic phenomena and their applications that have so far been limited to the low-temperature regime can now be explored and manipulated at room temperature. Under this thrust, new generations of compound semiconductors, alloys, and epitaxial heterostructures will also be investigated. How chemical composition and material architecture (<em>e.g.</em>, epitaxy) influence resulting properties such as electron affinity, dielectric constant, and band alignments will be quantified. These results will have impact on both fundamental understanding and practical applications.</p>