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Topology has emerged as a field for describing and controlling order and matter, and thereby the physical properties of materials. There are several largely disparate fields focused on examining and manipulating topology. One of these arenas is in the realm of real space, manipulating systems in terms of their spatial properties, to control the corresponding structural, mechanical, and self- assembling responses. Much of the work in soft matter topology falls within this domain. A second arena is in the domain of momentum or k-space wherein topology controls the features of the electronic band structure of materials, and topologically non-trivial features result in the development of materials with truly unique properties. This work focuses squarely on the realm of condensed matter physics. Here, we review concepts of real- and k-space topology and propose areas for convergence between these two disparate fields. 

Abstract The rational design of molecular electronics remains a grand challenge of materials science. DNA nanotechnology has offered unmatched control over molecular geometry, but direct electronic functionalization is a challenge. Here a generalized method is presented for tuning the local band structure of DNA using transmetalation in metal‐mediated base pairs (mmDNA). A method is developed for time‐resolved X‐ray diffraction using self‐assembling DNA crystals to establish the exchange of Ag⁺ and Hg²⁺ in T:T base pairs driven by pH exchange. Transmetalation is tracked over six reaction phases as crystal pH is changed from pH 8.0 to 11.0, and vice versa. A detailed computational analysis of the electronic configuration and transmission in the ensuing crystal structures is then performed. This findings reveal a high conductance contrast in the lowest unoccupied molecular orbitals (LUMO) as a result of metalation. The ability to exchange single transition metal ions as a result of environmental stimuli heralds a means of modulating the conductance of DNA‐based molecular electronics. In this way, both theoretical and experimental basis are established by which mmDNA can be leveraged to build rewritable memory devices and nanoelectronics.