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We present a theoretical study of the structure and functionality of ferroelastic domain walls in tungsten trioxide, WO_{3}. WO_{3} has a rich structural phase diagram, with the stability and properties of the various structural phases strongly affected both by temperature and by electron doping. The existence of superconductivity is of particular interest, with the underlying mechanism as of now not well understood. In addition, reports of enhanced superconductivity at structural domain walls are particularly intriguing. Focusing specifically on the orthorhombic β phase, we calculate the structure and properties of the domain walls both with and without electron doping. We use two theoretical approaches: Landau-Ginzburg theory, with free energies constructed from symmetry considerations and parameters extracted from our first-principles density functional calculations, and direct calculation using large-scale, GPU-enabled density functional theory. We find that the structure of the β-phase domain walls resembles that of the bulk tetragonal α_{1} phase, and that the electronic charge tends to accumulate at the walls. Motivated by this finding, we perform ab initio computations of electron-phonon coupling in the bulk α_{1} structure and extract the superconducting critical temperatures, T_{c}, within Bardeen-Cooper-Schrieffer theory. Our results provide insight into the experimentally observed unusual trend of decreasing T_{c} with increasing electronic charge carrier concentration.

We study the effects of temperature on the topological nature of ZrTe_{5}, which sits near the phase boundary between strong and weak topological insulating orders. Using first-principles calculations, we show that the band gap and the topological indices of ZrTe_{5} are extremely sensitive to thermal expansion and that the electron-phonon interaction accounts for more than a third of the total temperature-dependent effects in ZrTe_{5}. We find that the temperature dependence of the band gap has an opposite sign in the strong and weak topological insulator phases. Based on this insight, we propose a robust and unambiguous method to determine the topological nature of any given sample of ZrTe_{5}: If the band gap decreases with temperature it is a strong topological insulator, and if it increases with temperature it is a weak topological insulator. An analogous strategy is expected to be generally applicable to other materials and to become particularly important in the vicinity of topological phase boundaries where other methods provide ambiguous results.